Beam_Model_Neural_Network_Energy.ipynb

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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/StructuresComp/DER_Book_Codes/blob/master/Beam_Model_Neural_Network_Energy.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "from autograd import grad, hessian\n",
        "\n",
        "from logging import ERROR"
      ],
      "metadata": {
        "id": "_Ao2F5iFtt1j"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Helper function"
      ],
      "metadata": {
        "id": "0VKh3YVTuDTc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def crossMat(a):\n",
        "    \"\"\"\n",
        "    Returns the cross product matrix of vector 'a'.\n",
        "\n",
        "    Parameters:\n",
        "    a : np.ndarray\n",
        "        A 3-element array representing a vector.\n",
        "\n",
        "    Returns:\n",
        "    A : np.ndarray\n",
        "        The cross product matrix corresponding to vector 'a'.\n",
        "    \"\"\"\n",
        "    A = np.array([[0, -a[2], a[1]],\n",
        "                  [a[2], 0, -a[0]],\n",
        "                  [-a[1], a[0], 0]])\n",
        "\n",
        "    return A"
      ],
      "metadata": {
        "id": "-kojfrzXuF9B"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of Strains (axial stretch) on one edge in 2D"
      ],
      "metadata": {
        "id": "Fl-pMdKMrFdU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_strain_stretch_edge2D(node0, node1, l_k):\n",
        "  '''\n",
        "    Compute the axial stretch of a edge connecting node0 and node1.\n",
        "    The code does not change even if we move from 2D to 3D.\n",
        "\n",
        "    Parameters:\n",
        "        node0 (array-like): Coordinates of the first node (start of the edge),\n",
        "                            typically a 2-element array [x0, y0] for the 2D case.\n",
        "        node1 (array-like): Coordinates of the second node (end of the edge),\n",
        "                            typically a 2-element array [x1, y1].\n",
        "        l_k (float): Reference (undeformed) length of the edge.\n",
        "\n",
        "    Returns:\n",
        "        epsX (float): Axial stretch of the edge, defined as:\n",
        "                      epsX = (current_length / reference_length) - 1,\n",
        "                      where current_length is the Euclidean distance between node0 and node1.\n",
        "\n",
        "    Description:\n",
        "        The function calculates the axial stretch of a 2D edge by:\n",
        "        1. Computing the edge vector as the difference between node1 and node0.\n",
        "        2. Calculating the current length of the edge as the Euclidean norm of the edge vector.\n",
        "        3. Using the ratio of the current length to the reference length to compute the stretch.\n",
        "  '''\n",
        "  edge = node1 - node0\n",
        "  edgeLen = np.linalg.norm(edge)\n",
        "  epsX = edgeLen / l_k - 1\n",
        "  return epsX"
      ],
      "metadata": {
        "id": "1v72C5FhrWp9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_get_strain_stretch_edge2D():\n",
        "  '''\n",
        "  This function shows the usage of get_strain_stretch_edge2D() function.\n",
        "  '''\n",
        "  node0 = np.array([0.0, 0.0])\n",
        "  node1 = np.array([1.0, 1.0])\n",
        "  l_k = 1.5\n",
        "  stretch = get_strain_stretch_edge2D(node0, node1, l_k)\n",
        "  print(\"Axial stretch:\", stretch)\n",
        "\n",
        "# test_get_strain_stretch_edge2D()"
      ],
      "metadata": {
        "id": "389Y82geyiDO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_strain_stretch_edge2D(node0, node1, l_k):\n",
        "  '''\n",
        "  Compute the gradient and hessian of the axial stretch of a 2D edge with\n",
        "  respect to the dof vector (4 dofs: x,y coordinates of the two nodes)\n",
        "\n",
        "  Inputs:\n",
        "  node0: 2x1 vector - position of the first node\n",
        "  node1: 2x1 vector - position of the last node\n",
        "  l_k: reference length (undeformed) of the edge\n",
        "\n",
        "  Outputs:\n",
        "  dF: 4x1  vector - gradient of axial stretch between node0 and node 1.\n",
        "  dJ: 4x4 vector - hessian of axial stretch between node0 and node 1.\n",
        "  '''\n",
        "\n",
        "  edge = node1 - node0\n",
        "  edgeLen = np.linalg.norm(edge)\n",
        "  tangent = edge / edgeLen\n",
        "  epsX = get_strain_stretch_edge2D(node0, node1, l_k)\n",
        "\n",
        "  dF_unit = tangent / l_k # gradient of stretch with respect to the edge vector\n",
        "  dF = np.zeros((4))\n",
        "  dF[0:2] = - dF_unit\n",
        "  dF[2:4] = dF_unit\n",
        "\n",
        "  # M (see below) is the Hessian of square(stretch) with respect to the edge vector\n",
        "  Id3 = np.eye(2)\n",
        "  M = 2.0 / l_k * ((1 / l_k - 1 / edgeLen) * Id3 + 1 / edgeLen * ( np.outer( edge, edge ) ) / edgeLen ** 2)\n",
        "\n",
        "  # M is the Hessian of stretch with respect to the edge vector\n",
        "  if epsX == 0: # Edge case\n",
        "    M2 = np.zeros_like(M)\n",
        "  else:\n",
        "    M2 = 1.0/(2.0*epsX) * (M - 2.0*np.outer(dF_unit,dF_unit))\n",
        "\n",
        "  dJ = np.zeros((4,4))\n",
        "  dJ[0:2,0:2] = M2\n",
        "  dJ[2:4,2:4] = M2\n",
        "  dJ[0:2,2:4] = - M2\n",
        "  dJ[2:4,0:2] = - M2\n",
        "\n",
        "  return dF,dJ"
      ],
      "metadata": {
        "id": "VI-yxnlkrbsi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_stretch_edge2D():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_strain_stretch_edge2D() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Undeformed configuration (2 nodes, 1 edge)\n",
        "  x0 = np.random.rand(4)\n",
        "  l_k = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "\n",
        "  # Deformed configuration (2 nodes, 1 edge)\n",
        "  x = np.random.rand(4)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "\n",
        "  # Stretching force and Jacobian\n",
        "  grad, hess = grad_and_hess_strain_stretch_edge2D(node0, node1, l_k)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-6\n",
        "  strain_ground = get_strain_stretch_edge2D(node0, node1, l_k)\n",
        "  grad_fdm = np.zeros(4)\n",
        "  hess_fdm = np.zeros((4,4))\n",
        "  for c in range(4):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    strain_plus = get_strain_stretch_edge2D(node0_plus, node1_plus, l_k)\n",
        "    grad_fdm[c] = (strain_plus - strain_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_strain_stretch_edge2D(node0_plus, node1_plus, l_k)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "# test_stretch_edge2D()"
      ],
      "metadata": {
        "id": "r--jijCMrxUS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of Strains (axial stretch) on one node in 2D\n",
        "**Node-based formulation allows us to easily have coupled terms like stretch times curvature. Otherwise, curvature and twist are node-based, whereas, conventionally strain is edge-based. It is straightforward to formulate edge-based stretch.**"
      ],
      "metadata": {
        "id": "FQDF_ZelsIMb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_strain_stretch2D(node0, node1, node2=None, l_0=1.0, l_1=1.0):\n",
        "  '''\n",
        "    Compute the axial stretch of an node (node1) based on the stretches on the two edges\n",
        "    connected to that node. The first edge connects node0 and node1, whereas\n",
        "    the second edge connects node1 and node2. The code does not change even if\n",
        "    we move from 2D to 3D.\n",
        "\n",
        "    Parameters:\n",
        "        node0 (array-like): Coordinates of the first node (start of the first edge),\n",
        "                            typically a 2-element array [x0, y0] for the 2D case.\n",
        "        node1 (array-like): Coordinates of the second node (end of the first edge\n",
        "                            and start of the second edge),\n",
        "                            typically a 2-element array [x1, y1].\n",
        "        node2 (array-like): Coordinates of the third node (end of the second edge),\n",
        "                            typically a 2-element array [x2, y2].\n",
        "        l_0 (float): Reference (undeformed) length of the first edge.\n",
        "        l_1 (float): Reference (undeformed) length of the second edge.\n",
        "\n",
        "    Returns:\n",
        "        epsilon_1 (float): Axial stretch at node1, defined as the average of the\n",
        "                            stretches on the two edges connected to node1. If\n",
        "                            only two nodes are specified, the stretch is defined\n",
        "                            as half of the stretch on the first edge.\n",
        "  '''\n",
        "  # Convert inputs to numpy arrays for vectorized operations\n",
        "  node0 = np.array(node0, dtype=float)\n",
        "  node1 = np.array(node1, dtype=float)\n",
        "\n",
        "  if node2 is not None:\n",
        "    # If all the nodes are specified (i.e., node1 is an internal node),\n",
        "    # computation is as usual (average of the strains of the two edges).\n",
        "    node2 = np.array(node2, dtype=float)\n",
        "\n",
        "    stretch_firstEdge  = get_strain_stretch_edge2D(node0, node1, l_0)\n",
        "    stretch_secondEdge = get_strain_stretch_edge2D(node1, node2, l_1)\n",
        "\n",
        "    epsilon_1 = 0.5 * stretch_firstEdge + 0.5 * stretch_secondEdge\n",
        "  else:\n",
        "    # Simplified case if only two nodes are specified.\n",
        "    epsilon_1 = 0.5 * get_strain_stretch_edge2D(node0, node1, l_0)\n",
        "\n",
        "  return epsilon_1"
      ],
      "metadata": {
        "id": "_rsQWw6WsOMd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_strain_stretch2D(node0, node1, node2=None, l_0=1.0, l_1=1.0):\n",
        "  '''\n",
        "  Compute the gradient and hessian of the axial stretch at node1 with\n",
        "  respect to the dof vector (6 dofs: x,y coordinates of three nodes).\n",
        "\n",
        "  Inputs:\n",
        "  node0: 2x1 vector - position of the first node\n",
        "  node1: 2x1 vector - position of the middle node\n",
        "  node2: 2x1 vector - position of the last node\n",
        "  l_0: reference length (undeformed) of the first edge\n",
        "  l_1: reference length (undeformed) of the second edge\n",
        "\n",
        "  Outputs:\n",
        "  dF: 6x1  vector - gradient of axial stretch between node0 and node 1.\n",
        "  dJ: 6x6 vector - hessian of axial stretch between node0 and node 1.\n",
        "\n",
        "  Description:\n",
        "  The gradient and hessian at node1 is the average of the gradients and hessians\n",
        "  of the two edges (one between node0 and node1 and the other one between node1\n",
        "  and node2).\n",
        "  '''\n",
        "  # Ensure inputs are numpy arrays\n",
        "  node0 = np.array(node0, dtype=float)\n",
        "  node1 = np.array(node1, dtype=float)\n",
        "\n",
        "  if node2 is not None:\n",
        "    node2 = np.array(node2, dtype=float)\n",
        "\n",
        "    G_varepsilon = np.zeros(6)\n",
        "    H_varepsilon = np.zeros((6, 6))\n",
        "\n",
        "    G1, H1 = grad_and_hess_strain_stretch_edge2D(node0, node1, l_0)\n",
        "    G2, H2 = grad_and_hess_strain_stretch_edge2D(node1, node2, l_1)\n",
        "    G_varepsilon[0:4] = 0.5 * G1\n",
        "    G_varepsilon[2:6] += 0.5 * G2\n",
        "    H_varepsilon[0:4,0:4] = 0.5 * H1\n",
        "    H_varepsilon[2:6,2:6] += 0.5 * H2\n",
        "  else:\n",
        "    G1, H1 = grad_and_hess_strain_stretch_edge2D(node0, node1, l_0)\n",
        "    G_varepsilon = 0.5 * G1\n",
        "    H_varepsilon = 0.5 * H1\n",
        "\n",
        "  return G_varepsilon, H_varepsilon"
      ],
      "metadata": {
        "id": "ADaJFS96sUf9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_stretch_node2D():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_strain_stretch2D() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Undeformed configuration (2 nodes, 1 edge)\n",
        "  x0 = np.random.rand(6)\n",
        "  l_0 = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "  l_1 = np.linalg.norm(x0[2:4] - x0[4:6])\n",
        "\n",
        "  # Deformed configuration (2 nodes, 1 edge)\n",
        "  x = np.random.rand(6)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "  node2 = x[4:6]\n",
        "\n",
        "  # Stretching force and Jacobian\n",
        "  grad, hess = grad_and_hess_strain_stretch2D(node0, node1, node2, l_0, l_1)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-6\n",
        "  strain_ground = get_strain_stretch2D(node0, node1, node2, l_0, l_1)\n",
        "  grad_fdm = np.zeros(6)\n",
        "  hess_fdm = np.zeros((6,6))\n",
        "  for c in range(6):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    node2_plus = x_plus[4:6]\n",
        "    strain_plus = get_strain_stretch2D(node0_plus, node1_plus, node2_plus, \\\n",
        "                                          l_0, l_1)\n",
        "    grad_fdm[c] = (strain_plus - strain_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_strain_stretch2D(node0_plus, node1_plus, \\\n",
        "                                                  node2_plus, l_0, l_1)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "# test_stretch_node2D()"
      ],
      "metadata": {
        "id": "s_TF-qAFsYaE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of Strains (curvature in 2D)"
      ],
      "metadata": {
        "id": "kMs4s3mBfIPT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_strain_curvature2D(node0, node1, node2):\n",
        "  '''\n",
        "  Compute the curvature (scalar) in 2D at node1 that is connected to node0 and\n",
        "  node2.\n",
        "\n",
        "  Inputs:\n",
        "  node0: 2x1 vector - position of the first node\n",
        "  node1: 2x1 vector - position of the middle node\n",
        "  node2: 2x1 vector - position of the last node\n",
        "\n",
        "  Outputs:\n",
        "  kappa1: scalar - curvature at node1 (a scalar)\n",
        "\n",
        "  Description:\n",
        "  The function converts 2D nodes into 3D; computers the curvature binormal\n",
        "  (a vector) and extracts the scalar curvature (z-component of curvature\n",
        "  binormal)\n",
        "  '''\n",
        "\n",
        "  # Nodes in 3D\n",
        "  node0 = np.array([node0[0], node0[1], 0.0])\n",
        "  node1 = np.array([node1[0], node1[1], 0.0])\n",
        "  node2 = np.array([node2[0], node2[1], 0.0])\n",
        "\n",
        "  # Edge vectors\n",
        "  ee = node1 - node0\n",
        "  ef = node2 - node1\n",
        "\n",
        "  # Norms of edge vectors\n",
        "  norm_e = np.linalg.norm(ee)\n",
        "  norm_f = np.linalg.norm(ef)\n",
        "\n",
        "  # Unit tangents\n",
        "  te = ee / norm_e\n",
        "  tf = ef / norm_f\n",
        "\n",
        "  # Curvature binormal\n",
        "  kb = 2.0 * np.cross(te, tf) / (1.0 + np.dot(te, tf))\n",
        "\n",
        "  # Curvature\n",
        "  kappa1 = kb[2]\n",
        "\n",
        "  return kappa1"
      ],
      "metadata": {
        "id": "ZHaQexaSh6lF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_strain_curvature2D(node0, node1, node2):\n",
        "  '''\n",
        "  Compute the gradient and hessian of the curvature at node1 with\n",
        "  respect to the dof vector (6 dofs: x,y coordinates of three nodes).\n",
        "\n",
        "  Inputs:\n",
        "  node0: 2x1 vector - position of the first node\n",
        "  node1: 2x1 vector - position of the middle node\n",
        "  node2: 2x1 vector - position of the last node\n",
        "\n",
        "  Outputs:\n",
        "  dF: 6x1 vector - gradient of curvature at node 1\n",
        "  dJ: 6x6 vector - hessian of curvature at node 1.\n",
        "\n",
        "  Description:\n",
        "  The gradient and hessian at node1 is the average of the gradients and hessians\n",
        "  of the two edges (one between node0 and node1 and the other one between node1\n",
        "  and node2).\n",
        "  '''\n",
        "\n",
        "  # Nodes in 3D\n",
        "  node0 = np.array([node0[0], node0[1], 0.0])\n",
        "  node1 = np.array([node1[0], node1[1], 0.0])\n",
        "  node2 = np.array([node2[0], node2[1], 0.0])\n",
        "\n",
        "  # Unit vectors along z-axis\n",
        "  m2e = np.array([0, 0, 1])\n",
        "  m2f = np.array([0, 0, 1])\n",
        "\n",
        "  # Initialize gradient of curvature\n",
        "  gradKappa = np.zeros(6)\n",
        "\n",
        "  # Edge vectors\n",
        "  ee = node1 - node0\n",
        "  ef = node2 - node1\n",
        "\n",
        "  # Norms of edge vectors\n",
        "  norm_e = np.linalg.norm(ee)\n",
        "  norm_f = np.linalg.norm(ef)\n",
        "\n",
        "  # Unit tangents\n",
        "  te = ee / norm_e\n",
        "  tf = ef / norm_f\n",
        "\n",
        "  # Curvature binormal\n",
        "  kb = 2.0 * np.cross(te, tf) / (1.0 + np.dot(te, tf))\n",
        "\n",
        "  chi = 1.0 + np.dot(te, tf)\n",
        "  tilde_t = (te + tf) / chi\n",
        "  tilde_d2 = (m2e + m2f) / chi\n",
        "\n",
        "  # Curvature\n",
        "  kappa1 = get_strain_curvature2D(node0, node1, node2)\n",
        "\n",
        "  # Gradient of kappa1 with respect to edge vectors\n",
        "  Dkappa1De = 1.0 / norm_e * (-kappa1 * tilde_t + np.cross(tf, tilde_d2))\n",
        "  Dkappa1Df = 1.0 / norm_f * (-kappa1 * tilde_t - np.cross(te, tilde_d2))\n",
        "\n",
        "  # Populate the gradient of kappa\n",
        "  gradKappa[0:2] = -Dkappa1De[0:2]\n",
        "  gradKappa[2:4] = Dkappa1De[0:2] - Dkappa1Df[0:2]\n",
        "  gradKappa[4:6] = Dkappa1Df[0:2]\n",
        "\n",
        "  # Compute the Hessian (second derivative of kappa)\n",
        "  DDkappa1 = np.zeros((6, 6))\n",
        "\n",
        "  norm2_e = norm_e**2\n",
        "  norm2_f = norm_f**2\n",
        "\n",
        "  Id3 = np.eye(3)\n",
        "\n",
        "  # Helper matrices for second derivatives\n",
        "  tt_o_tt = np.outer(tilde_t, tilde_t)\n",
        "  tmp = np.cross(tf, tilde_d2)\n",
        "  tf_c_d2t_o_tt = np.outer(tmp, tilde_t)\n",
        "  kb_o_d2e = np.outer(kb, m2e)\n",
        "\n",
        "  D2kappa1De2 = (2 * kappa1 * tt_o_tt - tf_c_d2t_o_tt - tf_c_d2t_o_tt.T) / norm2_e - \\\n",
        "    kappa1 / (chi * norm2_e) * (Id3 - np.outer(te, te)) + \\\n",
        "    (kb_o_d2e + kb_o_d2e.T) / (4 * norm2_e)\n",
        "\n",
        "  tmp = np.cross(te, tilde_d2)\n",
        "  te_c_d2t_o_tt = np.outer(tmp, tilde_t)\n",
        "  tt_o_te_c_d2t = te_c_d2t_o_tt.T\n",
        "  kb_o_d2f = np.outer(kb, m2f)\n",
        "\n",
        "  D2kappa1Df2 = (2 * kappa1 * tt_o_tt + te_c_d2t_o_tt + te_c_d2t_o_tt.T) / norm2_f - \\\n",
        "                  kappa1 / (chi * norm2_f) * (Id3 - np.outer(tf, tf)) + \\\n",
        "                  (kb_o_d2f + kb_o_d2f.T) / (4 * norm2_f)\n",
        "  D2kappa1DeDf = -kappa1 / (chi * norm_e * norm_f) * (Id3 + np.outer(te, tf)) \\\n",
        "                  + 1.0 / (norm_e * norm_f) * (2 * kappa1 * tt_o_tt - tf_c_d2t_o_tt + \\\n",
        "                  tt_o_te_c_d2t - crossMat(tilde_d2))\n",
        "  D2kappa1DfDe = D2kappa1DeDf.T\n",
        "\n",
        "  # Populate the Hessian of kappa\n",
        "  DDkappa1[0:2, 0:2] = D2kappa1De2[0:2, 0:2]\n",
        "  DDkappa1[0:2, 2:4] = -D2kappa1De2[0:2, 0:2] + D2kappa1DeDf[0:2, 0:2]\n",
        "  DDkappa1[0:2, 4:6] = -D2kappa1DeDf[0:2, 0:2]\n",
        "  DDkappa1[2:4, 0:2] = -D2kappa1De2[0:2, 0:2] + D2kappa1DfDe[0:2, 0:2]\n",
        "  DDkappa1[2:4, 2:4] = D2kappa1De2[0:2, 0:2] - D2kappa1DeDf[0:2, 0:2] - \\\n",
        "                         D2kappa1DfDe[0:2, 0:2] + D2kappa1Df2[0:2, 0:2]\n",
        "  DDkappa1[2:4, 4:6] = D2kappa1DeDf[0:2, 0:2] - D2kappa1Df2[0:2, 0:2]\n",
        "  DDkappa1[4:6, 0:2] = -D2kappa1DfDe[0:2, 0:2]\n",
        "  DDkappa1[4:6, 2:4] = D2kappa1DfDe[0:2, 0:2] - D2kappa1Df2[0:2, 0:2]\n",
        "  DDkappa1[4:6, 4:6] = D2kappa1Df2[0:2, 0:2]\n",
        "\n",
        "\n",
        "  return gradKappa, DDkappa1"
      ],
      "metadata": {
        "id": "qZgexMO8fK_f"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_curvature2D():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_strain_curvature2D() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Deformed configuration (3 nodes)\n",
        "  x = np.random.rand(6)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "  node2 = x[4:6]\n",
        "\n",
        "  # Stretching force and Jacobian\n",
        "  grad, hess = grad_and_hess_strain_curvature2D(node0, node1, node2)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-6\n",
        "  strain_ground = get_strain_curvature2D(node0, node1, node2)\n",
        "  grad_fdm = np.zeros(6)\n",
        "  hess_fdm = np.zeros((6,6))\n",
        "  for c in range(6):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    node2_plus = x_plus[4:6]\n",
        "    strain_plus = get_strain_curvature2D(node0_plus, node1_plus, node2_plus)\n",
        "    grad_fdm[c] = (strain_plus - strain_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_strain_curvature2D(node0_plus, node1_plus, node2_plus)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "# test_curvature2D()"
      ],
      "metadata": {
        "id": "DK3jOrhOgSS4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of Elastic Energy - Stretching Energy in Conventional (Linear Elastic) Formulation"
      ],
      "metadata": {
        "id": "YpMvLiLVlVKj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_energy_stretch_linear_elastic(node0, node1, node2 = None, l_eff = None, EA = None):\n",
        "  strain_stretch = get_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "  E_s = 0.5 * EA * strain_stretch**2.0 * l_eff\n",
        "  return E_s"
      ],
      "metadata": {
        "id": "52-nftG_lWUX"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**TODO: In the code below, I assume that l_1 and l_2 are both l_eff.\n",
        "This only works if the mesh is uniform. The code should be updated so that it takes two lengths as inputs. The first length is mandatory. The second one is optional.**"
      ],
      "metadata": {
        "id": "sHdfevDEY_5R"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_energy_stretch_linear_elastic(node0, node1, node2 = None, l_eff = None, EA = None):\n",
        "\n",
        "  strain_stretch = get_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "  G_strain, H_strain = grad_and_hess_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "\n",
        "  gradE_strain = EA * strain_stretch * l_eff\n",
        "  hessE_strain = EA * l_eff\n",
        "\n",
        "  G = gradE_strain * G_strain\n",
        "  H = gradE_strain * H_strain + hessE_strain * np.outer(G_strain, G_strain)\n",
        "\n",
        "  return G, H"
      ],
      "metadata": {
        "id": "eu9RbtrAlnGY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_energy_stretch_linear_elastic():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_strain_stretch2D() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Stretching stiffness\n",
        "  EA = np.random.rand()\n",
        "\n",
        "  # Undeformed configuration (2 nodes, 1 edge)\n",
        "  x0 = np.random.rand(6)\n",
        "  l_0 = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "  l_1 = np.linalg.norm(x0[2:4] - x0[4:6])\n",
        "  l_eff = 0.5 * (l_0 + l_1)\n",
        "\n",
        "  # Deformed configuration (2 nodes, 1 edge)\n",
        "  x = np.random.rand(9)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "  node2 = x[4:6]\n",
        "\n",
        "  # Stretching force and Jacobian\n",
        "  grad, hess = grad_and_hess_energy_stretch_linear_elastic(node0, node1, node2, l_eff, EA)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-6\n",
        "  energy_ground = get_energy_stretch_linear_elastic(node0, node1, node2, l_eff, EA)\n",
        "  grad_fdm = np.zeros(6)\n",
        "  hess_fdm = np.zeros((6,6))\n",
        "  for c in range(6):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    node2_plus = x_plus[4:6]\n",
        "    energy_plus = get_energy_stretch_linear_elastic(node0_plus, node1_plus, node2_plus, \\\n",
        "                                          l_eff, EA)\n",
        "    grad_fdm[c] = (energy_plus - energy_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_energy_stretch_linear_elastic(node0_plus, node1_plus, \\\n",
        "                                                  node2_plus, l_eff, EA)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "test_energy_stretch_linear_elastic()"
      ],
      "metadata": {
        "id": "6HgyQ4wnlr5Q",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 927
        },
        "outputId": "dded2cf6-62e4-4863-90b5-2233cf93dc04"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of Elastic Energy - Bending Energy in Conventional (Linear Elastic) Formulation"
      ],
      "metadata": {
        "id": "knHDkl9rwui8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_energy_bending_linear_elastic(node0, node1, node2 = None, l_eff = None, EI = None):\n",
        "  if node2 is None:\n",
        "    return 0\n",
        "  strain_curvature = get_strain_curvature2D(node0, node1, node2)\n",
        "  E_b = 0.5 * EI / l_eff * strain_curvature**2.0\n",
        "  return E_b"
      ],
      "metadata": {
        "id": "LcfUOFTAw3T1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_energy_bending_linear_elastic(node0, node1, node2 = None, l_eff = None, EI = None):\n",
        "\n",
        "  if node2 is None:\n",
        "    return np.zeros(4), np.zeros((4,4))\n",
        "\n",
        "  strain_curvature = get_strain_curvature2D(node0, node1, node2)\n",
        "  G_strain, H_strain = grad_and_hess_strain_curvature2D(node0, node1, node2)\n",
        "\n",
        "  gradE_strain = EI * strain_curvature / l_eff\n",
        "  hessE_strain = EI / l_eff\n",
        "\n",
        "  G = gradE_strain * G_strain\n",
        "  H = gradE_strain * H_strain + hessE_strain * np.outer(G_strain, G_strain)\n",
        "\n",
        "  return G, H"
      ],
      "metadata": {
        "id": "YmnWMV0IvZqv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_energy_bending_linear_elastic():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_strain_stretch2D() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Bending stiffness\n",
        "  EI = np.random.rand()\n",
        "\n",
        "  # Undeformed configuration (2 nodes, 1 edge)\n",
        "  x0 = np.random.rand(6)\n",
        "  l_0 = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "  l_1 = np.linalg.norm(x0[2:4] - x0[4:6])\n",
        "  l_eff = 0.5 * (l_0 + l_1)\n",
        "\n",
        "  # Deformed configuration (2 nodes, 1 edge)\n",
        "  x = np.random.rand(9)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "  node2 = x[4:6]\n",
        "\n",
        "  # Bending force and Jacobian\n",
        "  grad, hess = grad_and_hess_energy_bending_linear_elastic(node0, node1, node2, l_eff, EI)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-6\n",
        "  energy_ground = get_energy_bending_linear_elastic(node0, node1, node2, l_eff, EI)\n",
        "  grad_fdm = np.zeros(6)\n",
        "  hess_fdm = np.zeros((6,6))\n",
        "  for c in range(6):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    node2_plus = x_plus[4:6]\n",
        "    energy_plus = get_energy_bending_linear_elastic(node0_plus, node1_plus, node2_plus, \\\n",
        "                                          l_eff, EI)\n",
        "    grad_fdm[c] = (energy_plus - energy_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_energy_bending_linear_elastic(node0_plus, node1_plus, \\\n",
        "                                                  node2_plus, l_eff, EI)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "test_energy_bending_linear_elastic()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 927
        },
        "id": "V7QROly0w4bH",
        "outputId": "6b0306fe-d536-482e-9ff4-091ff9334887"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Neural Network Model\n",
        "\n",
        "**NN approximation of y = x^2**"
      ],
      "metadata": {
        "id": "2xY2aUxSZ-CZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class ElasticEnergy(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(ElasticEnergy, self).__init__()\n",
        "        self.layers = nn.Sequential(\n",
        "            nn.Linear(1, 16, dtype=torch.float64),  # Initialize with float64\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(16, 16, dtype=torch.float64),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(16, 1, dtype=torch.float64),\n",
        "        )\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.layers(x)\n",
        "\n",
        "    def compute_energy_grad_hess(self, x):\n",
        "        \"\"\"\n",
        "        Compute energy, gradient, and Hessian with respect to the input.\n",
        "\n",
        "        Parameters:\n",
        "            x (float): Input value.\n",
        "\n",
        "        Returns:\n",
        "            tuple: (energy, gradient, Hessian), where:\n",
        "                - energy (float): Energy at the input.\n",
        "                - gradient (float): dE/dx at the input.\n",
        "                - Hessian (float): d²E/dx² at the input.\n",
        "        \"\"\"\n",
        "        # Create a tensor for the input\n",
        "        x_tensor = torch.tensor([[x]], requires_grad=True, dtype=torch.float64)\n",
        "\n",
        "        # Forward pass to compute energy\n",
        "        energy = self.forward(x_tensor)\n",
        "\n",
        "        # Compute gradient (dE/dx)\n",
        "        if x_tensor.grad is not None:\n",
        "            x_tensor.grad.zero_()  # Clear existing gradients\n",
        "        energy.backward(retain_graph=True)\n",
        "        gradient = x_tensor.grad.item()\n",
        "\n",
        "        # Compute Hessian (d²E/dx²)\n",
        "        grad_tensor = torch.autograd.grad(energy, x_tensor, create_graph=True)[0]\n",
        "        hessian = torch.autograd.grad(grad_tensor, x_tensor, retain_graph=True)[0].item()\n",
        "\n",
        "        return energy.item(), gradient, hessian"
      ],
      "metadata": {
        "id": "9wUdiMw_tL0u"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Train the energy**"
      ],
      "metadata": {
        "id": "6RvlG1FCiHBh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate training data\n",
        "x_train = np.linspace(-5, 5, 100).reshape(-1, 1)  # Inputs (positions)\n",
        "E_train = x_train**2                    # Outputs (energies)\n",
        "\n",
        "# Convert to PyTorch tensors\n",
        "x_train_tensor = torch.tensor(x_train, dtype=torch.float64)\n",
        "E_train_tensor = torch.tensor(E_train, dtype=torch.float64)\n",
        "\n",
        "# Instantiate the model\n",
        "energy_model = ElasticEnergy()\n",
        "\n",
        "# Define loss function and optimizer\n",
        "criterion = nn.MSELoss()\n",
        "optimizer = optim.Adam(energy_model.parameters(), lr=0.01)\n",
        "\n",
        "# Training loop\n",
        "epochs = 10000\n",
        "for epoch in range(epochs):\n",
        "    # Forward pass\n",
        "    predictions = energy_model(x_train_tensor)\n",
        "    loss = criterion(predictions, E_train_tensor)\n",
        "\n",
        "    # Backward pass\n",
        "    optimizer.zero_grad()\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    # Print progress\n",
        "    if (epoch + 1) % 1000 == 0:\n",
        "        print(f'Epoch [{epoch + 1}/{epochs}], Loss: {loss.item():.4f}')\n",
        "\n",
        "# Generate predictions\n",
        "x_test = np.linspace(-5, 5, 100).reshape(-1, 1)\n",
        "x_test_tensor = torch.tensor(x_test, dtype=torch.float64)\n",
        "E_pred = energy_model(x_test_tensor).detach().numpy()\n",
        "\n",
        "# Plot the true and predicted energies\n",
        "plt.figure()\n",
        "plt.plot(x_test, x_test**2, label='True Energy')\n",
        "plt.plot(x_test, E_pred, label='Predicted Energy', linestyle='--')\n",
        "plt.xlabel('x (Position)')\n",
        "plt.ylabel('E (Energy)')\n",
        "plt.legend()\n",
        "plt.title('Energy Approximation by Neural Network')\n",
        "plt.show()\n",
        "\n",
        "# torch.save(energy_model, \"energy_model_complete.pth\")"
      ],
      "metadata": {
        "id": "eDCfoyrj0gUN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 646
        },
        "outputId": "998cb821-e5bc-48fe-d2f5-9e50f30221f4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch [1000/10000], Loss: 0.0094\n",
            "Epoch [2000/10000], Loss: 0.0015\n",
            "Epoch [3000/10000], Loss: 0.0007\n",
            "Epoch [4000/10000], Loss: 0.0005\n",
            "Epoch [5000/10000], Loss: 0.0004\n",
            "Epoch [6000/10000], Loss: 0.0004\n",
            "Epoch [7000/10000], Loss: 0.0004\n",
            "Epoch [8000/10000], Loss: 0.0002\n",
            "Epoch [9000/10000], Loss: 0.0001\n",
            "Epoch [10000/10000], Loss: 0.0033\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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5vVC+p8mI3iP3jx7duXOHS5cuWX55Ps3jXs+nvc5RUVHUqVMHDw8PhgwZQlhYGE5OTuzfv59PPvkky7p6Py1nRnje99ejfP3119StW5dJkyaleY2e5bPzqIa+gFVD6wc96j125swZGjRoQNGiRfnll18ICQnB0dGRFStWMHLkyAx5DT///HNmzpzJDz/8QJs2baxuu7/9zp07061bt0fev3Tp0k/dR82aNUlJSWHHjh1s2bLFUrDUqlWLLVu2cPLkSSIjI60KmWf1pM9okyZNWLVqFSNGjKBu3bo5oieelqSQEZmuQIECwL3TIA0bNnyubYSGhgL3fqE+eFQoNTWViIiINH/cSpYsSbly5Zg1axZ58uThwoULjB079qn72bRpE5cuXWLIkCGWX2L33blzh7feeoslS5ZYnUK4cuVKmi7i//33H0Cao0WnT5+2uq6qKuHh4en64xwaGsrhw4cxm81WR2Xun7K5/xwBrFq1iilTpvDxxx8za9YsunXrxq5du6xODWW0jRs3cuvWLRYtWkTt2rUty8+dO5dm3cd96T7s/mM6depUmttOnjyJr69vhnbNT+9r+bzvr0epU6cOdevW5YcffuCrr76yuu1ZPjv3jzxFRUVZFUQPH0l4kn/++YekpCT+/vtvqyNbGzZsSPc2niYsLIzOnTszadIky2nL+/z8/HB3d8dkMj318T7pPVS5cmUcHR3ZsmULW7Zs4aOPPgLuHQGbPHky69evt1y/LzQ0lHXr1hEbG2t1VOZRn6+nqVq1Kr179+all17i1VdfZfHixZn62cvp5NSSyHT+/v6WX5yPO5z8NBUrVsTHx4fJkyeTmppqWT5r1qzHnjLo0qULa9asYdSoUfj4+NCsWbOn7uf+aaWPPvqIV155xerSq1cvChUqlOb0UmpqqqXrKtw7Pz5p0iT8/PyoUKGC1bp//PEHsbGxlusLFizg6tWr6crWvHlzrl27xrx586z2PXbsWNzc3KhTpw5w74vszTffpHLlynz//fdMmTKF/fv38/333z91Hy/i/pGQB498JCcn8+uvv6ZZ19XVNV2nKYKCgihbtiwzZsyw6k579OhR1qxZQ/PmzV88+AOe5bV8nvfX49xvK/Pbb79ZLX+Wz05YWBiApW0I3OtO/GD3/Kd51GsYHR3NtGnT0r2N9Pjiiy9ISUlhxIgRafb/8ssvs3DhQo4ePZrmfg8+3vvF5oPvi/ucnJyoVKkSc+bM4cKFC1ZHZO7evcuYMWMICwsjKCjIcp/mzZtjMpkYN26c1bZGjhyJoijP/Po2bNiQuXPnsmrVKrp06aLZ4JM5gZSI4rFWrlz5yAaa1atXt/xSTK/x48dTs2ZNSpUqRa9evShQoADXr19nx44dXLp0iUOHDj3x/o6OjnzzzTf069eP+vXr0759eyIiIpg+fTphYWGP/HX2+uuv8/HHH7N48WLeeeedpw4Al5SUxMKFC2nUqNFjDwW3atWK0aNHc+PGDfz9/YF77Sp++OEHIiIiKFy4MPPmzePgwYP89ttvafbp7e1NzZo16dGjB9evX2fUqFEULFiQXr16PTEbwFtvvcWkSZPo3r07+/btI1++fCxYsIBt27YxatQoy6/I999/n1u3brFu3Tr0ej1NmzblzTff5Ntvv6V169aUKVPmqft6HtWrVydXrlx069aN9957D0VRmDlz5iNP6VSoUIF58+YxcOBAKlWqhJubGy1btnzkdn/88UeaNWtGtWrV6NmzJ3fv3mXs2LF4enryzTffZOhjeJbX8lnfX09Sp04d6tSpY9Vg+770fnYaN25M3rx56dmzJx999BF6vZ7ff/8dPz8/Lly4kK4cjRs3xtHRkZYtW/L2228TFxfH5MmT8ff3f2Qh9bzuH5V5VJE1fPhwNmzYQJUqVejVqxfFixfn9u3b7N+/n3Xr1lnGLgoLC8PLy4uJEyfi7u6Oq6srVapUsbRdqVWrFsOHD8fT05NSpUoB9wrDIkWKcOrUKbp3726135YtW1KvXj0+//xzIiIiKFOmDGvWrGHp0qX079/fUig+izZt2jBt2jS6du2Kh4eHVZEsMpAWXaWEbXtS92se6O748JgJDwLUr7/+2mrZmTNn1K5du6qBgYGqg4ODmjt3bvWll15SFyxYkGbfD3Y/fdCYMWPU0NBQ1Wg0qpUrV1a3bdumVqhQQW3atOkj12/evLkKqNu3b3/q4164cGGaMUMetnHjRqvu0nXq1FFLlCih7t27V61WrZrq5OSkhoaGphlz43430zlz5qiDBg1S/f39VWdnZ7VFixZpxh25v81HuX79utqjRw/V19dXdXR0VEuVKmXV/fR+1/cHuxCrqqrGxMSooaGhapkyZSzdiB/X/frh1/NRXWRV9dGv1bZt29SqVauqzs7OanBwsPrxxx9buivfH6dEVVU1Li5Off3111UvLy8VsOR4VPdrVVXVdevWqTVq1FCdnZ1VDw8PtWXLlurx48et1rnf/TgyMvKROR/sfvwo6X0tH/Qs76/7eKD79YPuP8+Pev+n57Ojqqq6b98+tUqVKqqjo6OaN29e9Zdffnls9+v7XaIf9vfff6ulS5dWnZyc1Hz58qk//PCD+vvvv6fZxvN0v37Q6dOnVb1e/8j31vXr19U+ffqoISEhqoODgxoYGKg2aNBA/e2336zWW7p0qVq8eHHVYDCked8sX75cBdRmzZpZ3ef+2EKP+pzHxsaqAwYMUIODg1UHBwe1UKFC6o8//qiazWar9R73Gj7uM3R/DKwHx1MSGUdR1QxsASdEFjObzfj5+dGuXTsmT56c5va2bdty5MgRwsPDM2X/devW5ebNm488DP6gjRs3Uq9ePebPn88rr7ySKVlE1svs95cQ4umkjYywG4mJiWlOU/zxxx/cvn37kV0cr169yvLly+nSpUsWJRQ5iby/hLAN0kZG2I2dO3cyYMAAXn31VXx8fNi/fz9Tp06lZMmSVuN3nDt3jm3btjFlyhQcHBysBjgT4kXJ+0sI2yKFjLAb+fLlIyQkhDFjxnD79m28vb3p2rUrw4cPtxo8btOmTfTo0YO8efMyY8YMAgMDNUwtsht5fwlhW6SNjBBCCCHslrSREUIIIYTdkkJGCCGEEHYr27eRMZvNXLlyBXd393QPiy6EEEIIbamqSmxsLMHBwWkmy31Qti9krly5kmbWXiGEEELYh4sXL5InT57H3p7tC5n7w7ZfvHgRDw8PjdMIIYQQIj1iYmIICQmxmsTzUbJ9IXP/dJKHh4cUMkIIIYSdeVqzEGnsK4QQQgi7JYWMEEIIIeyWFDJCCCGEsFvZvo2MELbIbDaTnJysdQwhLBwcHNDr9VrHEOKZSSEjRBZLTk7m3LlzmM1mraMIYcXLy4vAwEAZc0vYFSlkhMhCqqpy9epV9Ho9ISEhTxzkSYisoqoqCQkJ3LhxA4CgoCCNEwmRflLICJGFUlNTSUhIIDg4GBcXF63jCGHh7OwMwI0bN/D395fTTMJuyM9BIbKQyWQCwNHRUeMkQqR1v7hOSUnROIkQ6SeFjBAakDYIwhbJ+1LYIylkhBBCCGG3NC1khg0bRqVKlXB3d8ff3582bdpw6tQpq3Xq1q2LoihWl969e2uUWAghhBC2RNNCZtOmTfTp04edO3eydu1aUlJSaNy4MfHx8Vbr9erVi6tXr1ouI0aM0CixEDnPwz8kHr588803WZblUT9s5MeNEDmbpr2WVq1aZXV9+vTp+Pv7s2/fPmrXrm1Z7uLiQmBgYFbHeyJVVTl6OYa83i54ujhoHUeITHP16lXL/+fNm8dXX31ldeTUzc3N8n9VVTGZTBgMmfenpVevXgwZMsRqWWb3AEtOTpYG2kI8woVbCQDk9dGuF6ZNtZGJjo4GwNvb22r5rFmz8PX1pWTJkgwaNIiEhITHbiMpKYmYmBirS2bo/ec+Wo7byrIjVzJl+0LYisDAQMvF09MTRVEs10+ePIm7uzsrV66kQoUKGI1Gtm7dSvfu3WnTpo3Vdvr370/dunUt181mM8OGDSN//vw4OztTpkwZFixY8NQ893/YPHi5P7N9REQEiqKwaNEi6tWrh4uLC2XKlGHHjh1W29i6dSu1atXC2dmZkJAQ3nvvPasjwfny5WPo0KF07doVDw8P3nrrLQAmT55MSEgILi4utG3bll9++QUvLy/LvnU6HXv37rXa16hRowgNDZUBEEW2NGFTOLV/3MDY9ac1y2AzhYzZbKZ///7UqFGDkiVLWpa//vrr/Pnnn2zYsIFBgwYxc+ZMOnfu/NjtDBs2DE9PT8slJCQkU/KWy5sLgGWHrj5lTSEeT1VVEpJTNbmoqpphj+PTTz9l+PDhnDhxgtKlS6frPsOGDeOPP/5g4sSJHDt2jAEDBtC5c2c2bdr0wnk+//xzPvzwQw4ePEjhwoXp2LEjqampAJw5c4amTZvy8ssvc/jwYebNm8fWrVvp27ev1TZ++uknypQpw4EDB/jyyy/Ztm0bvXv35v333+fgwYM0atSI7777zrJ+vnz5aNiwIdOmTbPazrRp0+jevbsMfiiynRSTmdxHxtNCt5OKuZ01y2EzA+L16dOHo0ePsnXrVqvl938JAZQqVYqgoCAaNGjAmTNnCAsLS7OdQYMGMXDgQMv1mJiYTClmWpQKYvLKXdyOuMSN2LL4uztl+D5E9nc3xUTxr1Zrsu/jQ5rg4pgxfwKGDBlCo0aN0r1+UlIS33//PevWraNatWoAFChQgK1btzJp0iTq1Knz2Pv++uuvTJkyxWrZpEmT6NSpk+X6hx9+SIsWLQAYPHgwJUqUIDw8nKJFizJs2DA6depE//79AShUqBBjxoyhTp06TJgwASene5/l+vXr88EHH1i2+fnnn9OsWTM+/PBDAAoXLsz27dtZtmyZZZ0333yT3r1788svv2A0Gtm/fz9Hjhxh6dKl6X5uhLAXu4+eorf5LwyOZlJzPf4AQ2aziZ8Iffv2ZdmyZWzYsIE8efI8cd0qVaoAEB4e/sjbjUYjHh4eVpfMEHJlFbud+jDYMI2VR65lyj6EsBcVK1Z8pvXDw8NJSEigUaNGuLm5WS5//PEHZ86ceeJ9O3XqxMGDB60urVq1slrnwaNC94fbvz/8/qFDh5g+fbrVfps0aYLZbObcuXOPfUynTp2icuXKVssevt6mTRv0ej2LFy8G7rX7q1evHvny5UvHsyKEfbm28y8MipnLzkUwBBTRLIemR2RUVaVfv34sXryYjRs3kj9//qfe5+DBg4ANzAUSUhk9ZqrqTjDjwEG6Vc+nbR5hl5wd9Bwf0kSzfWcUV1dXq+s6nS7NqasHR4uNi4sDYPny5eTOndtqPaPR+MR9eXp6UrBgwSeu4+Dw/w3w7w/ydr+NSlxcHG+//TbvvfdemvvlzZvX8v+HH1N6ODo60rVrV6ZNm0a7du2YPXs2o0ePfubtCGHrklJN5Lu6AoDU4i9rmkXTQqZPnz7Mnj2bpUuX4u7uzrVr945seHp64uzszJkzZ5g9ezbNmzfHx8eHw4cPM2DAAGrXrp3u8/CZxjMPSXmqY7y0nXxXVnI1uglBntqdIxT2SVGUDDu9Y0v8/Pw4evSo1bKDBw9aCozixYtjNBq5cOHCE08jZYby5ctz/PjxpxZDDytSpAh79uyxWvbwdbh3eqlkyZL8+uuvpKam0q5duxfKK4Qt2nryGjEmH4rqnQmp1enpd8hEmp5amjBhAtHR0dStW5egoCDLZd68ecC9Xzfr1q2jcePGFC1alA8++ICXX36Zf/75R8vYFsbyHQFoq9/C8kPSe0mI++rXr8/evXv5448/OH36NF9//bVVYePu7s6HH37IgAEDmDFjBmfOnGH//v2MHTuWGTNmPHHbCQkJXLt2zepy586ddGf75JNP2L59O3379uXgwYOcPn2apUuXpmns+7B+/fqxYsUKfvnlF06fPs2kSZNYuXJlmmH9ixUrRtWqVfnkk0/o2LGjZTJGIbKTf47eYEBKH0aWW4nO68lNQjKbpoWMqqqPvHTv3h2AkJAQNm3axK1bt0hMTOT06dOMGDEi09q9PLNirTDpHCmsu8yxA9u0TiOEzWjSpAlffvklH3/8MZUqVSI2NpauXbtarTN06FC+/PJLhg0bRrFixWjatCnLly9/6inmyZMnW/3wCQoKomPHjunOVrp0aTZt2sR///1HrVq1KFeuHF999RXBwcFPvF+NGjWYOHEiv/zyC2XKlGHVqlUMGDDA0jj4QT179iQ5OZk33ngj3bmEsBeJKSbWHr8OQLOy+bQNAyhqRvbBtEExMTF4enoSHR2dKQVQ4uzOOP33D7+ltqDZwCmEeGs3KJCwfYmJiZw7d478+fM/8gtQ2JdevXpx8uRJtmzZYrV86NChzJ8/n8OHD2uU7PnI+1Okx4Y9Bxm+aAdxnkXY+km9TJtsNL3f3zbRa8meOf3v9FJz/S6WH5bTS0JkZz/99BOHDh0iPDzcchqsW7dultvj4uI4evQo48aNo1+/fhomFSLzJO6YzGrjp4z2mGUTM6ZLIfOiCjZiV4mvaJH0PcuOyOB4QmRnu3fvplGjRpQqVYqJEycyZswY3nzzTcvtffv2pUKFCtStW1dOK4lsKSEphZK31gDgV6KutmH+J/t1l8hqBkcKNe9H3IF1HL0cQ8TNePL5Pnu3TSGE7fvrr7+eePv06dOZPn161oQRQgP7tq+llnKDBJzIW802euTJEZkM4O3qSPUwHwCWHbqscRohhBAic6QcvFfMn/Oti+JoGz/apZDJIO/6HmSh49fE7nvyLzYhhBDCHsUm3KV01L8AuFVMf0/BzCaFTAYp53SdCrrTVI5dx+nrsVrHEUIIITLUoc3/4KtEE4UHeSs21zqOhRQyGcSpwr3qtI7uEGv3HtM4jRBCCJGxko7+DcD5wEYoBkeN0/w/KWQyim8horxKYFDMJB5anGaeGSGEEMJe3Y5Ppu/t9nRP/ohcdftoHceKFDIZyLl8ewCqJ27iyOVojdMIIYQQGWPl0avcNeuJDKxD3qIVtI5jRQqZDGQsfW8G0MrKSTbsPqhtGCHsVPfu3WnTpo3let26denfv3+W59i4cSOKohAVFZXl+xbC1vx98N6Ary3LPHkqDy1IIZORvEK441MenaKiHluC2Synl0T20L17dxRFQVEUHB0dKViwIEOGDCE1NTXT971o0SKGDh2arnWzuvjIly+f5Xl58DJ8+PAs2b8QWeH6zVsMvtyLTwxzaFkil9Zx0pAB8TKYW+XObFipsO9uALsjblO1gI/WkYTIEE2bNmXatGkkJSWxYsUK+vTpg4ODA4MGDUqzbnJyMo6OGdMY0NvbO0O2k1mGDBlCr169rJa5u7tn6j5TUlJwcHDI1H0Icd+xjX9RX3cRL4cUAn1sr5CRIzIZzKFKT1aUGMkWc2n+OSRzL4nsw2g0EhgYSGhoKO+88w4NGzbk77/v9WK4fzrou+++Izg4mCJFigBw8eJF2rdvj5eXF97e3rRu3ZqIiAjLNk0mEwMHDsTLywsfHx8+/vjjNA3lHz61lJSUxCeffEJISAhGo5GCBQsydepUIiIiqFevHgC5cuVCURS6d+8OgNlsZtiwYeTPnx9nZ2fKlCnDggULrPazYsUKChcujLOzM/Xq1bPK+STu7u4EBgZaXVxd7w0Udv8I0fr166lYsSIuLi5Ur16dU6dOWW1j6dKllC9fHicnJwoUKMDgwYOtjnYpisKECRNo1aoVrq6ufPfddwB8++23+Pv74+7uzptvvsmnn35K2bJlAdi8eTMODg5cu3bNal/9+/enVq1a6XpsQgC4/LcUgBuhL4ENzK30MClkMkGrsvfOIa44cpUUk1njNMIuJMc//pKS+Azr3k3fuhnA2dmZ5ORky/X169dz6tQp1q5dy7Jly0hJSaFJkya4u7uzZcsWtm3bhpubG02bNrXc7+eff2b69On8/vvvbN26ldu3b7N48eIn7rdr167MmTOHMWPGcOLECSZNmoSbmxshISEsXLgQgFOnTnH16lVGjx4NwLBhw/jjjz+YOHEix44dY8CAAXTu3JlNmzYB9wqudu3a0bJlSw4ePGgpCjLK559/zs8//8zevXsxGAxW8zBt2bKFrl278v7773P8+HEmTZrE9OnTLcXKfd988w1t27blyJEjvPHGG8yaNYvvvvuOH374gX379pE3b14mTJhgWb927doUKFCAmTNnWpalpKQwa9YsmQdKpNv5y1cpl7QHgJBanTVO8xhqNhcdHa0CanR0dJbtMyXVpL405E/1088GqP+evJ5l+xW27+7du+rx48fVu3fvWt/wtcfjL3++Yr3ut4GPX/f35tbr/pD/0es9o27duqmtW7dWVVVVzWazunbtWtVoNKoffvih5faAgAA1KSnJcp+ZM2eqRYoUUc1ms2VZUlKS6uzsrK5evVpVVVUNCgpSR4wYYbk9JSVFzZMnj2VfqqqqderUUd9//31VVVX11KlTKqCuXbv2kTk3bNigAuqdO3csyxITE1UXFxd1+/btVuv27NlT7dixo6qqqjpo0CC1ePHiVrd/8sknabb1sNDQUNXR0VF1dXW1umzevNkqz7p16yz3Wb58uQpY3gMNGjRQv//+e6vtzpw5Uw0KCrJcB9T+/ftbrVOlShW1T58+Vstq1KihlilTxnL9hx9+UIsVK2a5vnDhQtXNzU2Ni4t75ON57PtT5FhrZv2iql97qBeHllLVBz7LWSG939/SRiYTGFLjWWx+H4NDCsN31aZekTZaRxLihS1btgw3NzdSUlIwm828/vrrfPPNN5bbS5UqZdUu5tChQ4SHh6dpL5KYmMiZM2eIjo7m6tWrVKlSxXKbwWCgYsWKjx2H6eDBg+j1eurUqZPu3OHh4SQkJNCoUSOr5cnJyZQrVw6AEydOWOUAqFatWrq2/9FHH1lOYd2XO3duq+ulS5e2/D8oKAiAGzdukDdvXg4dOsS2bdusjsCYTCYSExNJSEjAxcUFgIoVK1pt89SpU7z77rtWyypXrsy///5rud69e3e++OILdu7cSdWqVZk+fTrt27e3nPoS4klUVcXzzL3Tx1EFWpLHBk8rgTT2zRxGd+Jy18Lr0r94nvmHxJSWODnotU4lbNlnT2hPpTz03vko/AnrPnS2uP+R58/0kHr16jFhwgQcHR0JDg7GYLD+8/Hwl2NcXBwVKlRg1qxZabbl5+f3XBmcnZ2f+T5xcXEALF++PE2BYTQanyvHg3x9fSlYsOAT13mwYa7yvy8Ds9lsyTd48GDatUs7k7CTk5Pl/89TfPj7+9OyZUumTZtG/vz5WblyJRs3bnzm7YicKTwigvKpB0GB0DpdtI7zWFLIZBKPSq/BpX9prG5jw4nrNCtte33vhQ15lllkM2vdp3B1dX3qF/aDypcvz7x58/D398fDw+OR6wQFBbFr1y5q164NQGpqKvv27aN8+fKPXL9UqVKYzWY2bdpEw4YN09x+/4iQyWSyLCtevDhGo5ELFy489khOsWLFLA2X79u5c+fTH2QGKF++PKdOnXqm5xagSJEi7Nmzh65du1qW7dmzJ816b775Jh07diRPnjyEhYVRo0aNF84scoa1hy/gYapHWfcYSuYuqnWcx5LGvplEV7Q5KYqRMN1V9u/erHUcIbJcp06d8PX1pXXr1mzZsoVz586xceNG3nvvPS5dugTA+++/z/Dhw1myZAknT57k3XfffeIYMPny5aNbt2688cYbLFmyxLLNv/66N+t8aGgoiqKwbNkyIiMjiYuLw93dnQ8//JABAwYwY8YMzpw5w/79+xk7diwzZswAoHfv3pw+fZqPPvqIU6dOMXv2bKZPn56uxxkbG8u1a9esLjExMel+nr766iv++OMPBg8ezLFjxzhx4gRz587liy++eOL9+vXrx9SpU5kxYwanT5/m22+/5fDhw5YjPvc1adIEDw8Pvv32W3r06JHuXCJnU1WV2SdNfJHak4hmf2gd54mkkMksRnfu5rv3i9H/wjKi76ZoHEiIrOXi4sLmzZvJmzcv7dq1o1ixYvTs2ZPExETLEZoPPviALl260K1bN6pVq4a7uztt27Z94nYnTJjAK6+8wrvvvkvRokXp1asX8fH3emLlzp2bwYMH8+mnnxIQEEDfvn0BGDp0KF9++SXDhg2jWLFiNG3alOXLl5M/f34A8ubNy8KFC1myZAllypRh4sSJfP/99+l6nF999RVBQUFWl48//jjdz1OTJk1YtmwZa9asoVKlSlStWpWRI0cSGhr6xPt16tSJQYMG8eGHH1K+fHnOnTtH9+7drU5HAeh0Orp3747JZLI6eiPEk+y/cIdLd+7i6qinQdEAreM8kaI+rlVdNhETE4OnpyfR0dGPPbydWdTjS1H+6spl1YdtLTbQvvKT/zCJ7C8xMZFz586RP3/+NF84QryoRo0aERgYaNXlGqBnz55ERkamOX32MHl/ivumzZzOsuO3yVemLj+/9uhTvZktvd/f0kYmEymFGpOsdyVXahw79+6RQkYIkWESEhKYOHEiTZo0Qa/XM2fOHNatW8fatWst60RHR3PkyBFmz5791CJGiPtSTGaqnhlND+NZTnk6AdoUMuklhUxmcnDmTrt51J15g8SLTnwcnUigp/zKEUK8OEVRWLFiBd999x2JiYkUKVKEhQsXWjWCbt26Nbt376Z3795pup8L8Th79+2mGmdJRUdYjVe0jvNUUshksoAStSgRup295++w7PAV3qxVQOtIQohswNnZmXXr1j1xHelqLZ5H1O45AJzzqEwhD3+N0zydNPbNAq3/N2XB8gPnNE4ihBBCPF58YgpFI1cD4FC2vcZp0kcKmSzQxv0Eqx0/oeON0YTfiNM6jrAB2byNvbBT8r4Uu3dsJL9ylSQcCa3+qtZx0kUKmSzg7uZOEd1Fmur3sHy/HJXJyfT6e6P0PjjZohC2IiEhAbAeiVjkLIkH5gFw3qcmilPW9vR9XtJGJivkrc5dpwA8Eq9zff9y1CYl0wxaJXIGg8GAi4sLkZGRODg4oNPJbwmhPVVVSUhI4MaNG3h5eVkKbpGz3IpLIiDqIOjAo/LrWsdJNylksoJOh6H0y7D7V6rd3cCBi29TPm8urVMJDSiKQlBQEOfOneP8+fNaxxHCipeXF4GBgVrHEBpZfuQqXyd/TXv/y/xQvqXWcdJNCpks4lDmFdj9Kw11+/ll72nK562sdSShEUdHRwoVKiSnl4RNcXBwkCMxOdySA5dR0VGoUmNwsJ+hQqSQySrB5Ulwy4tL3AXijywntXVFDHo5rZBT6XQ6GTlVCGEzLt6M5dCFWyiKnpZl7GuSY/kmzSqKgvF/XdnqpW5mS/hNjQMJIYQQ9xzYsIDdxnf52XcZAR729SNLCpkspC/9KodzNWaWqSGL91/WOo4QQgiBqqq4nFqEjxJLKR+t0zw7KWSykn9RzO0ms9FcljXHrxGXlKp1IiGEEDnc0bOXqZGyE4Dg2t21DfMcpJDJYmXyeFLA15XEFDOrjl7TOo4QQogc7vTmuTgrydxwyINrfvvriCKFTBZTFIWehe/ysWEuW/Yc0DqOEEKIHCzFZCbo/L2Z0eOLtAM7HONMChkNvHxjLO8a/ib40jKuRSdqHUcIIUQOtevwcSqrhwEIqdNd2zDPSQoZDTiVfw2AtrotLD1wSeM0Qgghcqpr22ejV1QuupbA4BemdZznIoWMFoq1wqRzpLDuMof2btU6jRBCiBwoNjGFqVcLMDH1JdSKb2od57lJIaMFZy/MhZoCUDZqDSeuxmgcSAghRE6z8ug1TqQGMT9XL0Lq9tA6znOTQkYjDuXunV5qrd/G0v0XNE4jhBAip1ly4N54Zm3L5bbriYylkNFKwUYkO3oRoERx8cAaTGZV60RCCCFyiKtRCTQ6/wt1dIdoXTpA6zgvRAoZrRgc0ZdsQxRuOCbcYMeZW1onEkIIkUPs3LSSHobVTDSOIcTDvqddlEJGQ/qGX/NzqX9YbK7FIum9JIQQIguoqorDsfkAXA1uBI4uGid6MVLIaMnFmzYV8wGw6ug14mXKAiGEEJns+MVIaiRtASCgRleN07w4KWQ0Vj5vLvJ7O5EnJYLVx2TKAiGEEJnr6Mb55FLiuGPwxbVofa3jvDApZDSmJMWwxNyPFY6DWLvniNZxhBBCZGMpJjMBZxcBEFOoHej0Gid6cVLIaM3JEyfPAAyKmdwX/+FK1F2tEwkhhMimth06RQ313jx/uevY79gxD5JCxgYYK3YC4GXdZhbvl0a/QgghMseO/QeJUAO54lIMQ2BxreNkCClkbEHJlzHpHCimu8ihvVtQVRlTRgghRMaKSkhm2jkvGiWPIPbVeVrHyTBSyNgC51yYCzcHoGrMag5ejNI2jxBCiGznn0NXSDaZKR7kSZH8oVrHyTBSyNgIh/Kdgf9NWbA3QtswQgghsp39uzbjRBLtyufWOkqGkkLGVoTVJ9nJDx8llsjDq0lKNWmdSAghRDZx5noUg+58yR7ju7wcdFvrOBlKChlboTegf+lHehuGsiKxBP+euKF1IiGEENnE/n8X4a9Egd6BXPlKax0nQ0khY0P0JduSv2JjVHQslN5LQgghMoDJrOJ1egEAt/K3AoOjxokylqaFzLBhw6hUqRLu7u74+/vTpk0bTp06ZbVOYmIiffr0wcfHBzc3N15++WWuX7+uUeLM9/L/zl1uPBXJzbgkjdMIIYSwd3tOnqO2aTcAQXXe0DhNxtO0kNm0aRN9+vRh586drF27lpSUFBo3bkx8fLxlnQEDBvDPP/8wf/58Nm3axJUrV2jXrp2GqTNXQed4xnvN5nf99yw9eEXrOEIIIezc+c2zMCopXHfKjzGkvNZxMpymc3evWrXK6vr06dPx9/dn37591K5dm+joaKZOncrs2bOpX//efBDTpk2jWLFi7Ny5k6pVq2oRO3PpHWmatAq9PpXZu7bwRo18KIqidSohhBB2KCYxhSJXl4ICqaVeg2z4fWJTbWSio6MB8Pb2BmDfvn2kpKTQsGFDyzpFixYlb9687Nix45HbSEpKIiYmxupiV1y8MRdqCkClOys4dsXO8gshhLAZG3bto6xyGhM6gmt31zpOprCZQsZsNtO/f39q1KhByZIlAbh27RqOjo54eXlZrRsQEMC1a4+eKXrYsGF4enpaLiEhIZkdPcM5VLw3rXpb/RYW7T6rcRohhBD2asYxE7WSRrKp2GAU90Ct42QKmylk+vTpw9GjR5k7d+4LbWfQoEFER0dbLhcvXsyghFkorAFJzgF4K3HEHP5bxpQRQgjxzMJvxLH/QhRXlEBKNn9L6ziZxiYKmb59+7Js2TI2bNhAnjx5LMsDAwNJTk4mKirKav3r168TGPjoytJoNOLh4WF1sTt6Aw7l700k2SJ1PeuOy5gyQgghns3CfRcAqFvYD393J43TZB5NCxlVVenbty+LFy/m33//JX/+/Fa3V6hQAQcHB9avX29ZdurUKS5cuEC1atWyOm6W0v1vyoLausOs27Vf4zRCCCHsicmsUnH3QCY7/EyPQvFPv4Md07TXUp8+fZg9ezZLly7F3d3d0u7F09MTZ2dnPD096dmzJwMHDsTb2xsPDw/69etHtWrVsmePpQf5hBFXqBUzT6hsOxvFtehEAj2zb0UthBAi4+w4fILa5t046E2kFPDTOk6m0vSIzIQJE4iOjqZu3boEBQVZLvPm/f/04iNHjuSll17i5Zdfpnbt2gQGBrJo0SINU2cdt04z+TfPu9xQvVh0QEb6FUIIkT43tv6Bg2LikksJHIJKaB0nU2l6REZV1aeu4+TkxPjx4xk/fnwWJLI9r1YIYU/EHRbsvcQ7dcJkTBkhhBBPFBWfRKnIf0AB3f/aW2ZnNtHYVzxe85L+NHY4TM07i9h/4Y7WcYQQQti4bZvXUEi5RBKOBNfsrHWcTCeFjI1zu3WU3/TD+cwwm793ndQ6jhBCCBunOzgLgIuBjcDJU+M0mU8KGVuXuzwJnoVwUlLQHVtEQnKq1omEEELYqBMXrlMjcRMA/rV7apwma0ghY+sUBecq3QBoo65n+eGrGgcSQghhqxbuv8yI1A4ccq2OR9F6WsfJElLI2AGlTEdMioEyurPs2rFJ6zhCCCFsUGKKifmHbvKnqRF3Ws0AXc74is8Zj9LeufqSXLA5ACWvL+VMZJzGgYQQQtiaNcevE303hWBPJ2oVyt5jxzxIChk74Vy1BwBt9VtZtPu0xmmEEELYmlsbfqWjfj2vl82FXpdzhurQdBwZ8Qzy1yXBJTdX43Ts3H+YlKZlcNBLHSqEEAIuRkbx0p0Z+DnEEOlbEyivdaQsI9+E9kKnw+Htf+ns8Av74n3ZcFImkhRCCHHPgXVz8VNiiNJ541e+pdZxspQUMnbEwTOQdhVCAPhr70WN0wghhLAFJrOK7+l7U/tEFnwZ9A4aJ8paUsjYmfYVQ3AhkZv/7eRGTKLWcYQQQmhs98HDVDUdACBvg7c0TpP1pJCxMwXN59jn3IfJhhEs2ntO6zhCCCE0dnPr7+gUlXNu5TEGFNY6TpaTQsbe+BUFR1f8lBiu7FqUrok3hRBCZE+3YhIof2sZAA6VumsbRiNSyNgbvQP6/81mWj9hNbvO3dY4kBBCCK2s2HOCk+YQYhQP8lRvr3UcTUghY4cc/1d119YdZvW23dqGEUIIoQlVVZl+MJaeKR+xosEacHDWOpImpJCxR94FiA2qjk5R8Tk9n6iEZK0TCSGEyGJ7z9/hTGQ8zg56WlQsqHUczUghY6fcqt+b1bSdsoEl+85rnEYIIURW27lxGcHcpGWZINydclaX6wdJIWOnlGItSXTwIpA77N/5rzT6FUKIHCQ6PomW575jq/F93go+q3UcTUkhY68MRkxtJ9HIPJq/b+Vh/4UorRMJIYTIIjv/XUI+5Rp3FSfCKjTSOo6mpJCxY67Fm1KudFkA5uy+oG0YIYQQWUJVVYyHZwJwMU9LFKObxom0JYWMnetY+d6UBWsPRxCTmKJxGiGEEJnt6H9nqJ68HYDcDd7ROI32pJCxc+W9Epjr9gv/KB/w9345KiOEENnd+Q1TcVRMXHAqinv+nDPL9eNIIWPnFBdfyvEfeXWRnNr+tzT6FUKIbCz2bjIlri4GwFS+m8ZpbIMUMvbOwQm1TEcAakYv4/ClaI0DCSGEyCzrt+/Cjzsk4Ey+Ol20jmMTpJDJBpyqvAFAA91+lm/fr3EaIYQQmWXKcaic9Cvry49DMbprHccmSCGTHfgXJca/IgbFjOuxucRKo18hhMh2jlyK5ujlGFL1LtRo0ErrODZDCplswv1/I/2+rKxn6YFLGqcRQgiR0ZZsOwioNC8ViLero9ZxbIYUMtmEUqItSQYP8ig3ObltqTT6FUKIbCTmbjJdjr/NSsdB9Cwq8+s9SAqZ7MLBGXPtT/ja1JMlN3Nz4GKU1omEEEJkkJ3rF5NPuUqoLpKSRYtpHcemSCGTjTjX7ktcqW7E4cKsnTKmjBBCZAeqqmI89AcAF/K8hOLkoXEi2yKFTDbTqWpeAJYdvkJUghx+FEIIe3fo5H9UT94BQO6G72qcxvZIIZPNlAty4gPvrUxUhrFo73mt4wghhHhBl/6dgoNi4rxzcdzzyUi+D5NCJptRFB29UuZQT3+IszsWSaNfIYSwY7fjEilzYwkASsUe2oaxUVLIZDcGI7rynQCoH7eCnWdvaxxICCHE89qxbhEhyg3iFFdCanXSOo5NkkImG3KsfG+k37q6Q6zcukvjNEIIIZ6H2azyy+kAuid/xLGSH6E4umodySZJIZMd+YQRF1wDnaISGD6PyNgkrRMJIYR4RjvO3uLMrUT2OlSi5Ev9tI5js6SQyabcarwFwCu6jSzYfVbjNEIIIZ7VrJ0RALQtlxtXo0HbMDZMCpnsqmgLEo0++CtRXNq5CJNZGv0KIYS9uHYnjnf+e5OPDHPpUj6X1nFsmhQy2ZXeAUOlHmyiAsfjXNlw8obWiYQQQqTT7tWzKaU7RxeHTRQO9tU6jk2TQiYbMzT4gu2Vx3NALcQfO2VMGSGEsAcpJjP+p/4E4HrBV8Fg1DiRbZNCJjtTFDpVCUVRYPN/kUTcjNc6kRBCiKfYumsXVdVDmFEIbdxX6zg2TwqZbC6vjwsvFzAzwDCfedtOah1HCCHEU8RtmwxAhFd1HP3ya5zG9kkhk92pKoNjvuR9w2LuHviLu8kmrRMJIYR4jNOXb1ArbhUAXnV6a5zGPkghk90pCs5V7g2Q97J5Ff8cvKxxICGEEI9zZNU0vJR4bhkC8C7TQus4dkEKmRxAV74zqTpHSuki2Ll1jcy/JIQQNiguKZWp5/2YkdqI6LJvg06vdSS7IIVMTuDijalYGwCq31nKwYtRmsYRQgiR1uL9lziWHMAfufqSv8VArePYDSlkcghjtbcBaKnbwcKthzVOI4QQ4kGqqjLzf8NkdKkaiqIoGieyH1LI5BS5K5DgUxKjkoLbiXncipP5l4QQwlbsOXGOt27/RHXHcNqVz611HLsihUxOoSi41HibBMUZvTmFuXsuap1ICCHE/5xf/xuv6Dfzi8sMPJwctI5jV6SQyUlKtWdds02MN7Xhz53nSTWZtU4khBA53uU78VS6uQgApUovkNNKz0QKmZzEwYkm5Qvi6+bI1ehE1hy/rnUiIYTI8bavmks+5TrxihsBNbpqHcfuSCGTwxgNel6vFEIF5RTLNu/SOo4QQuRoiSkmgk7NBCCy0Kvg6KpxIvsjhUwO1DtxMguNg6l0dTbHr8RoHUcIIXKsf7ftpCYHMKMQ0rif1nHskhQyOZBLiWYAvKLfzJwtxzVOI4QQOZOqqiTtmATARe8a6H3DNE5kn6SQyYkK1CfRIz/uyl0MR+dxJz5Z60RCCJHj7Im4w744by6pfvjUl1mun5cUMjmRToex+r3JyF5XVjN39wWNAwkhRM4zY3sEf5oa8Wvp+bgVb6J1HLulaSGzefNmWrZsSXBwMIqisGTJEqvbu3fvjqIoVpemTZtqEzabUcq+TorehUK6y5zc/o90xRZCiCx0Nfouq45dA6BrjTDQyXGF56XpMxcfH0+ZMmUYP378Y9dp2rQpV69etVzmzJmThQmzMScPlHKdAHgp8R/WnZCu2EIIkVXWrVtNC7ZRPZ87RQM9tI5j1wxa7rxZs2Y0a9bsiesYjUYCAwOzKFHOYqjyFuydTJhyma+2nqJpySCtIwkhRLaXmGIi6MgExjju5Jx7HFBb60h27ZkLmaSkJHbt2sX58+dJSEjAz8+PcuXKkT9//szIx8aNG/H39ydXrlzUr1+fb7/9Fh8fnyfmS0r6/3mEYmKke/Fj+RXmZodlNJ0ZTXJEPEcvR1Myt6fWqYQQIltbu30PzdVdoEBI/V5ax7F76S5ktm3bxujRo/nnn39ISUnB09MTZ2dnbt++TVJSEgUKFOCtt96id+/euLu7Z0i4pk2b0q5dO/Lnz8+ZM2f47LPPaNasGTt27ECv1z/yPsOGDWPw4MEZsv+cwLdYLZqWOsDfh64wbVsEP7cvo3UkIYTItlRVJXHbRPSKyqVcVcgTVFLrSHYvXW1kWrVqRYcOHciXLx9r1qwhNjaWW7ducenSJRISEjh9+jRffPEF69evp3DhwqxduzZDwr322mu0atWKUqVK0aZNG5YtW8aePXvYuHHjY+8zaNAgoqOjLZeLF2VyxKd5o2Z+HEnh6KG93IhN1DqOEEJkWztPXqBJ0moAvBu8r3Ga7CFdR2RatGjBwoULcXB49IycBQoUoECBAnTr1o3jx49z9erVDA354H58fX0JDw+nQYMGj1zHaDRiNBozZf/ZVVndGXa7vM/tVCf+3FGDgY2Lah1JCCGypTNrJ1NNSeCWMQSf4k9uIyrSJ11HZN5+++3HFjEPK168+GOLjBd16dIlbt26RVCQNErNUL5FcNWbKKC7xoWdi0lMMWmdSAghsp2zN2KodnMBAGqVt6XLdQZ55mexW7dubN68OUN2HhcXx8GDBzl48CAA586d4+DBg1y4cIG4uDg++ugjdu7cSUREBOvXr6d169YULFiQJk1k4KAMZXRDX7EbAK+k/MPfh65oHEgIIbKf+ZsPEYkXCTpXfGv00DpOtvHMhUx0dDQNGzakUKFCfP/991y+fPm5d753717KlStHuXLlABg4cCDlypXjq6++Qq/Xc/jwYVq1akXhwoXp2bMnFSpUYMuWLXLqKBPoqryNGR019cf4d9MGVFXVOpIQQmQb0QkpTD8Uz2vJX3Ks7XowumkdKdtQ1Of4xoqMjGTmzJnMmDGD48eP07BhQ3r27Enr1q3TfQoqq8TExODp6Ul0dDQeHjLo0JOkzOmCw6m/mZdal5AeU6ke5qt1JCGEyBZ+23yG71ecpGigOyvfr4WiKFpHsnnp/f5+rhN0fn5+DBw4kEOHDrFr1y4KFixIly5dCA4OZsCAAZw+ffq5gwvtONS4N2lZG/025m86oHEaIYTIHlJNZv7bsghvYnijRn4pYjLYC7U0unr1KmvXrmXt2rXo9XqaN2/OkSNHKF68OCNHjsyojCKrhFQm0b8sRiUF3Zl1nLsZr3UiIYSwe//uP8nQ5BHscOpH67x3tY6T7TxzIZOSksLChQt56aWXCA0NZf78+fTv358rV64wY8YM1q1bx19//cWQIUMyI6/ITIqCU8uf+DL4NxaaavP71nNaJxJCCLumqirXN0zEWUkmyrUARv9CWkfKdp55ioKgoCDMZjMdO3Zk9+7dlC1bNs069erVw8vLKwPiiSwXUolmDfIz8+wu5u+7yMBGhcnl6qh1KiGEsEv7zl6jSfxSUMClznsgp5Uy3DMfkRk5ciRXrlxh/PjxjyxiALy8vDh3Tn7N26tqBXwomdsD95Rb/LkjQus4Qghht46umoq/EkW0gx/uFTpoHSdbeuZCpkuXLjg5OWVGFmEjFEVhjMdsthnf47/tS2WAPCGEeA7nIuOodn0OACkV3wa9bfXqzS6e+dRSu3btHrlcURScnJwoWLAgr7/+OkWKFHnhcEI7of5e6M+Z6JCymL8Pvkb7SiFaRxJCCLuyeeVcuukucVdxwbfOW1rHybae+YiMh4cH//77L/v370dRFBRF4cCBA/z777+kpqYyb948ypQpw7Zt2zIjr8gi+mrvYFb09wbI27hWBsgTQohncCc+mUvhh0hSDdwp+ho4eWodKdt65kImMDCQ119/nbNnz7Jw4UIWLlzImTNn6Ny5M2FhYZw4cYJu3brxySefZEZekVW88mIq1hqAJjEL2PhfpMaBhBDCfvy58zyTk5vyRq5pBLUYpHWcbO2ZC5mpU6fSv39/dA9MdqXT6ejXrx+//fYbiqLQt29fjh49mqFBRdZzqPkeAC11O1i0YafGaYQQwj4kppiYseM8AO3rVkBx89c4Ufb2zIVMamoqJ0+eTLP85MmTmEz3GoU6OTnJyIXZQXA5kvLUwKCYKXVpLseuRGudSAghbN6anYcJiD9FkKcTzUsFaR0n23uuXks9e/Zk5MiRbN26la1btzJy5Eh69uxJ165dAdi0aRMlSpTI8LAi6xlr9wfuTVvw+2aZekIIIZ7EbFZJ3DKa5cbPmBiwGAf9Cw2gL9LhmXstjRw5koCAAEaMGMH169cBCAgIYMCAAZZ2MY0bN6Zp06YZm1Roo2BDLlcfSvN/A4g/fIOBTe+S28tZ61RCCGGTthw7S9Ok1aBAoUpNtI6TIzxTqZiamsqsWbN48803uXr1KlFRUURFRXH16lU+++wz9Ho9AHnz5iVPnjyZElhkMZ2O3I3fo0RYKKlmlalbZKBDIYR4nAtrxuOhJHDTKR8uJVpoHSdHeKZCxmAw0Lt3bxITE4F7XbGfNLW2yD561wkDYOWeY0QlJGucRgghbM/+s9doHLMQAIc6A0Anp5WywjM/y5UrV+bAgQOZkUXYsFre0Sx3/ZY/+ZKZ2+WojBBCPOzoikkEKFFEGfzwrPS61nFyjGduI/Puu+/ywQcfcOnSJSpUqICrq6vV7aVLl86wcMJ2KG7+FFYu4qCL5fz2+STWGYSTg17rWEIIYRPCr0VT88Yc0EFq5XfAIJPtZhVFfcYhW3WPOFSmKAqqqqIoiqULtq2IiYnB09OT6OhoOQ32gsxrv0G3bSQHzAU51mwhnavl0zqSEELYhBGzV9Ll1Lt46JNx/eQkGN21jmT30vv9/cxHZGRW65xLV+1dTDvGU45wpm36h45V+qLXyXhBQoic7UZMIlOOwWTTKJa+moviUsRkqWcuZEJDQzMjh7AHbv6Yy7yO/sB02sbPZ9XRV2hRWgZ7EkLkbL9viyDZZKZiqB/FK1TXOk6O81xNqmfOnEmNGjUIDg7m/Pl7wzCPGjWKpUuXZmg4YXscar2PGR319IdYtX6dTCYphMjRYhJTOL1zOXpMlt6dIms9cyEzYcIEBg4cSPPmzYmKirK0ifHy8mLUqFEZnU/YGu8CpBRtBUD5W/+wLfyWxoGEEEI7q9evY6oyhE0un1C/oLTD1MIzFzJjx45l8uTJfP7555YB8AAqVqzIkSNHMjScsE3Gep8wP98Qvk3tzK8bw7WOI4QQmkhMMeG5dywA5sAy6Bxl1HMtPHMhc+7cOcqVK5dmudFoJD4+PkNCCRsXUJzqbd5C0RnYfuYWBy7c0TqREEJkuVWbt9LQvB2AoJc+0zhNzvXMhUz+/Pk5ePBgmuWrVq2iWLFiGZFJ2IHcXs60KZcbR1L4/d/DWscRQogslWoyY9g+Gp2ictG3Ng7BMoaaVp6519LAgQPp06cPiYmJqKrK7t27mTNnDsOGDWPKlCmZkVHYqA/ynODDo5+yNLw6p66Vp0igdDkUQuQM63bupUnqRlDA/6XPtY6Toz1zIfPmm2/i7OzMF198QUJCAq+//jrBwcGMHj2a1157LTMyChsV5OMNyh0669fx3fp9fN+prtaRhBAi05nNKokbR+GgmLjkVYk8+apqHSlHe+ZCBqBTp0506tSJhIQE4uLi8Pf3z+hcwh4UasRdnxK43jpGwMk/uHCrMnl9XLROJYQQmWrt8Wt4J14APeRqOkjrODneC03N6eLiIkVMTqYoONf/CIBuulVM2yC91oQQ2Zuqqvy66SxdUwbxR6npuBapr3WkHO+ZC5nr16/TpUsXgoODMRgM6PV6q4vIYYq14q5HAbyUeJwOzeBGTKLWiYQQItNsP3OLQxejcHLQ0bxJc1BkmhatPfOppe7du3PhwgW+/PJLgoKCUORFzNl0epzqfQBL+/CGbhm/b3qTT1qW1zqVEEJkivWrFuGFB20qlcLXzah1HMFzFDJbt25ly5YtlC1bNhPiCHuklO5A4trv8Eu4wsU9y7ldvyTerjKFvRAiezkQfpG+kYP5wJhCfNHlWscR//PMp5ZCQkJkfh1hTe+Ase1Y3vMYxbLk8vy+VWZIF0JkP/8tG4W3EkeC0Q//gnLk2VY8cyEzatQoPv30UyIiIjIhjrBXSqGGNG/cDIDp2yOITkjROJEQQmScI2ev0ODOXwDoan8EOmkTaiue+dRShw4dSEhIICwsDBcXFxwcHKxuv337doaFE/alcfEAigS4E3X9PDO2nua9xsW1jiSEEBni+LLRlFJiuOkQjG+1TlrHEQ945kJGZrgWj6PTKYwNXE5o1BSGbn+L2NpDcHdyePodhRDChh2/cJ16t+aCAuaaA0Evf9dsyTMXMt26dcuMHCKbKJgnCN2pVN4wL2Lm9u68W7+I1pGEEOKFHPl7DB2UKG4bAvCvId+BtibdbWT++usvkpOTLdcvXbqE2Wy2XE9ISGDEiBEZm07YHV3lN0ly9KKA7hoXt/xJfFKq1pGEEOK5nboWy/Vrl0hW9aRU7w8G6ZFpa9JdyHTs2JGoqCjL9eLFi1s1+I2NjWXQIBmqOcczumGo0ReAN0wLmbVTejAJIezXuA3h/JLansH5/ySgdk+t44hHSHch83CXa+mCLR5HX+Vtkh08KKS7zJlNs7mbbNI6khBCPLPwG3EsO3wFgE6Na4JBBsCzRS8015IQj+Tkgb7auwB0T50vR2WEEHZp7bK5FCOCRsUDKB7soXUc8RhSyIhMoa/Wm2SDG6HKDdZs2ixHZYQQdiX86m1anh/GCuNnfBF2Vus44gmeqdfS6tWr8fT0BMBsNrN+/XqOHj0KYNV+Rgicc6FrP50Oi2M5csfInzvP06t2Aa1TCSFEuuxdMo7XlJtE6b0JrdxS6zjiCRQ1nY1ddLqnH7xRFAWTybZ+ecfExODp6Ul0dDQeHnJoMKv9teciHy88jI+rI1s+qYeL4zP3+BdCiCx1+sotXCZVJrdyk6vVviaoyUCtI+VI6f3+TvepJbPZ/NSLrRUxQntty+cmr7cLeROOMXO7tJURQti+fUvGklu5SZTeh6D672gdRzyFtJERmcpBr2O2x3gWG7/m7KbZMq6MEMKmnb5yk9rXZwCQWPV9cHDWOJF4mnQVMjt37kz3BhMSEjh27NhzBxLZT3Dhe7PE9jTNY+Z2aTQnhLBd+xaPIVi5zR29L4F139Y6jkiHdBUyXbp0oUmTJsyfP5/4+PhHrnP8+HE+++wzwsLC2LdvX4aGFPZNV+1dkg3uFNZd5tzmWcTJURkhhA06eS2GvVcSiVQ9Sar2Pjg4aR1JpEO6Cpnjx4/TokULvvjiC7y8vChRogSNGjWiZcuW1KxZE19fX8qXL8+5c+dYs2YNXbt2zezcwp44e6H/32i/b5rm88e2MxoHEkKItEatPc0CUx2+KziXwLq9tY4j0indvZbu27t3L1u3buX8+fPcvXsXX19fypUrR7169fD29s6snM9Nei3ZiMRokn8uiWNKDJ/wPp9/+iUeMjO2EMJGHLsSTYsxW1EUWN2/NoUD3LWOlOOl9/v7mfvCVqxYkYoVK75QOJEDOXliqNEPNn7HW+a/mLr5NQY0Lq51KiGEAGDbogm8pItDX7KtFDF2RnotiSyjq9qbZEcvDJhYtXUPt+KStI4khBAcCL9Iu8jxjHMcy+f5TmodRzwjKWRE1nHywND9H97z/Y1Tyb5M3CRtZYQQ2lJVlZNLf8JXieGmY278q7TXOpJ4RlLIiCylCy5N/yYlAPhjx3muxyRqnEgIkZPtPH6O5jF/AaCrNwj00nbP3kghI7Jc3cJ+VM3rRiv1XyasO6p1HCFEDqWqKueX/4inksANp/x4V3ld60jiOUghI7KcoihM0g3jR4ffcNw/jYu3E7SOJITIgTYdPMlL8YsAMDb6AnR6jROJ55HuQqZ58+ZER0dbrg8fPtxqxutbt25RvPiz9ULZvHkzLVu2JDg4GEVRWLJkidXtqqry1VdfERQUhLOzMw0bNuT06dPPtA9hmzwr3/vl87Z+Kb+uOaRxGiFETmM2q0SuGoGbksh1lyJ4lmundSTxnNJdyKxevZqkpP/vZfL9999z+/Zty/XU1FROnTr1TDuPj4+nTJkyjB8//pG3jxgxgjFjxjBx4kR27dqFq6srTZo0ITFR2lXYvTKvk+SRHx8lFp+jvxN+I1brREKIHGTZkassji3KEcJwa/Y16OQEhb1K9yv38Lh5zziO3iM1a9aMb7/9lrZt2z5yf6NGjeKLL76gdevWlC5dmj/++IMrV66kOXIj7JDecO9QLvCWfhm/rpBpLYQQWSPFZOaXNafYbi7JxppzcS3ZXOtI4gXYbAl67tw5rl27RsOGDS3LPD09qVKlCjt27Hjs/ZKSkoiJibG6CBtVoh1J3kXxUBIIC5/K/gt3tE4khMgB5u65SMStBHzdjLxRqwAoitaRxAtIdyGjKArKQy/2w9cz0rVr1wAICAiwWh4QEGC57VGGDRuGp6en5RISEpJpGcUL0ukwNv4agDf0q5i0bFuGHOkTQojHiU9KxWn1R7ynX8TAOkG4Gp95gHthY9L9CqqqSvfu3TEajQAkJibSu3dvXF1dAazaz2hp0KBBDBw40HI9JiZGihlbVqQZScGV2XfpLicvXmfjqUjqFfXXOpUQIpv6e9VqOpjXoHNQScnXV+s4IgOku5Dp1q2b1fXOnTunWScjZ70ODAwE4Pr16wQFBVmWX79+nbJlyz72fkaj0VJsCTugKBi7LWLz+kuc33yWH1adpHZhP/Q6OdQrhMhYt+KSCN7/EzpF5XLuZuQOKad1JJEB0l3ITJs2LTNzpJE/f34CAwNZv369pXCJiYlh165dvPPOO1maRWQyozvv1g1jzu4LnLwWy9KDl2lXPo/WqYQQ2cw/fy+ku7IfEzqC2nyrdRyRQTQ9ORgXF0d4eLjl+rlz5zh48CDe3t7kzZuX/v378+2331KoUCHy58/Pl19+SXBwMG3atNEutMgUXi6ODKjujbL5R5avakCL0m9iNMjgVEKIjHHxVjylTo4EHdwo2IEgv4JaRxIZRNNCZu/evdSrV89y/X7blm7dujF9+nQ+/vhj4uPjeeutt4iKiqJmzZqsWrUKJycnrSKLTNQ14Q8MhtUUvnuJP3c0ometAlpHEkJkE6sXT+dN3X8kKUaCWn2tdRyRgRQ1m3cTiYmJwdPTk+joaDw8PLSOI54k6gKmMeXRm1N4R/mCHz7pj4eTTOAmhHgxxy9HY5pUm1K6CG6UeRf/tsO0jiTSIb3f3zY7jozIgbzyolR6E4A+pj/59V+ZjkII8WJUVeX7lSfpk/I+2z2a49/0Y60jiQwmhYywKbraH5FqcKWkLoLIHbO4dEcmlBRCPL9N/0WyNfwm13RBhHSfCs65tI4kMpgUMsK2uPqgr/0BAAN0cxm98rDGgYQQ9irVZGbssl0AdKseSoi3i8aJRGaQQkbYHKXauyS7BpFHuUmuY9M5fClK60hCCDv09/ZDTIt5i/FOv9K3eqDWcUQmkUJG2B4HZxybDGVLrrYsNNXmu+UnZOoCIcQziU9KJfXf4XgoCVRxv4Wnp5fWkUQmkUJG2KbSr1Kg2wTiDLnYde42607c0DqREMKOzFu9gbbmtQB4tv4BdPJ1l13JKytsVm4vZ3rWzA/AzysOkmIya5xICGEPrkUnkmffDzgoJm4E1sGhYB2tI4lMJIWMsGnvllaZ7TSC/tE/Mmf3Ba3jCCHswMLF82ms7MGEDr92P2gdR2QyKWSETXMzKFTlME31e9i4ZinRCSlaRxJC2LCjl6KofnYUAHcKd0DxL6ZtIJHppJARts2/KJTvAkB/0zRGrTupcSAhhK1SVZUJS/4ljxJJkuKEb8tvtI4ksoAUMsLm6ep/QarBldK6c8Tv/pPwG3FaRxJC2KDlR66y/JKRpuZRxLabBe7S5TonkEJG2D43fwz1PgHgQ/1cfvpnr8aBhBC2JjHFxLAV947YdqlTEt9SDTVOJLKKFDLCPlTpTYpnPvyVKEqdm8qGU9IdWwjx/+as3U6FmHUEexh5u3aY1nFEFpJCRtgHgxGHZt8DUF93gO//OSLdsYUQwL3u1j47hzPGcTx/5l6Is6Ne60giC0khI+xHkeYktJ5Md8MITt9MZOaO81onEkLYgHmLF9JKtxUzCvkbvqV1HJHFpJAR9kNRcCnXnveblARg1Lr/uBWXpHEoIYSWDpy/Te2zvwAQVegVlNzlNE4kspoUMsLudKgUQslAFxqnrOfn1ce1jiOE0IjJrLJh/jjK6cJJUpzxbvWt1pGEBqSQEXZHr8BchyH85DAJ3f4ZHLoYpXUkIYQGFu04QefYqQCk1Bgg3a1zKClkhP1RFNwqdgTgQ8Nf/LhkO2azzI4tRE4SlZBM4trv8FeiiHbJi1vd/lpHEhqRQkbYp4pvkOJbHC8lnubXf2PBvktaJxJCZKGf1/zH0qTynNHlx7X1z2Awah1JaEQKGWGf9AYcWt5r4PeafiN/r1wm8zAJkUMcvRzNrF3n2asW5frrazAUaax1JKEhKWSE/QqthrlUe3SKyoepkxm55oTWiYQQmUxVVQYvPYxZhZdKB1G9oL/WkYTGpJARdk3XeCipDm6U1Z0hcc8fHL8So3UkIUQm+nvPaYZf68VAxyV83iS/1nGEDZBCRtg390AM9QZxyrkce82F+HLpUWn4K0Q2FX03hVsrhxGmu0p3l60EeThpHUnYAClkhP2r+g7ub63gikMo+87fYf6+i1onEkJkgulL19DZvBQA55eGg4OzxomELZBCRtg/nZ7gXC4MbFQYgB9XHOF2fLLGoYQQGenghTtUPv4tjoqJ27nr4VCildaRhI2QQkZkG90reDPGczZTTV/ww/IjWscRQmSQVJOZ9fNGU013nGTFiPcro0BRtI4lbIQUMiLbMJiTaa5upozuLC6HprHr7C2tIwkhMsDczYfpHjcFgJSaH0GufNoGEjZFChmRfbj5Y2g8BIAPDPMZtWgjyalmjUMJIV7EtehEtm1YgRuJRLkVxFVG8BUPkUJGZC/lu5EaXAk3JZEu0ROZsvWs1omEEC9gyLJjrEwuQ3+fCXh0nAp6B60jCRsjhYzIXnQ6DK1GYVb0NNfv5tD6eVy8naB1KiHEc9hw8gYrjlxDr1Po90oTdLnLah1J2CApZET2E1gSpeq7AHyhTGPwwt2oqowtI4Q9iU9KZfuCMZRX/qNH9XwUD/bQOpKwUVLIiGxJqTeIVPfcuCsJRJ49xOIDl7WOJIR4Br//vY4PUyaywDiYD0vIiN3i8aSQEdmToyuG12ayuPoiDqkFGbLsODfjkrROJYRIhwPnb1HpyDcYlRSiAmvglK+K1pGEDZNCRmRfuSvQuWFligV5EJWQwtBlx7VOJIR4iuRUM5vm/kxV3QmSFCe8O4yXMWPEE0khI7I1B72OH14uRSP9PtyO/MGGkze0jiSEeII/1+zgjYTfAUit+7mMGSOeSgoZke2VTj3KZIef+cowk4kLVxOXlKp1JCHEI4RfjyXvzq/wUO5yJ1cpXGv10TqSsANSyIjsL7QGpgL1MSopDEwax08r5RSTELbGbFaZNXcmDXV7SUWPV4eJoNNrHUvYASlkRPanKOhbjsKkd6aK7iTJe6bL9AVC2JgZOyKYdjUvn5t7E1djEEpgSa0jCTshhYzIGXKFom/4FQCDDLP5af56EpLlFJMQtiDiZjw/rDoJKBRt/i5ejT7SOpKwI1LIiJyjytuk5q6Eu3KXfnFj+HHVSa0TCZHjmc0qk+bMxzElluphPnSqnFfrSMLOSCEjcg6dHkPbCZj0Rmrrj3By5wp2n7utdSohcrS5mw4w8OaXrDF+ws/1nNDppKu1eDZSyIicxbcQ+uY/Mi30B3aYS/DRgkPcTTZpnUqIHCniZjyeGz7HT4nByT0XQfmKaR1J2CEpZETOU6EbL3fsSZCnE+dvJTBitZxiEiKrmc0qC//8lRa67ZjQ4fHaFDAYtY4l7JAUMiJH8nByYFi7Uvhzh7M7lkovJiGy2NxN++l2ZwwAcZX6octTXuNEwl5JISNyrLq5brPR5RPGOYxhxLy1xCamaB1JiBwh/HoMPhs+xVeJ4Y5bITybfK51JGHHpJAROZdvIRyDS+Cu3OXDhNEM/fuo1omEyPZSTGaWzBxNE93uewPfvS6nlMSLkUJG5Fz3ezEZXKimP477ocmsPnZN61RCZGtj159m5s3CrKYad2t+ghJcVutIws5JISNyNp8w9M2GAfCxYR5TFi4nMjZJ41BCZE/7L9xh3IZwonEjpe1U3OvLwHfixUkhI0T5bpgKNcGopDI4dTRfLtyLqqpapxIiW0lITmX0nH8wqyptygbzUpncoJOvIPHi5F0khKKgbz2OVCdviuvOE3p6JvP2XNQ6lRDZytQFfzM5oT+/u4xlcPMwreOIbEQKGSEA3PwxtB7LkTwdmW5qwpBlxzkbGad1KiGyhfWHz9Po5Fc4KibKBLvh6e6udSSRjUghI8R9xV6ixBsTKF8giIRkE+/NPUBSqoz6K8SLuBadSOSijyiqu0icIRc+r00ERaYhEBlHChkhHqDTKYzsUBYfZx25r67jJ5lYUojnZjKr/DljAq+xGgDHVyeBm5/GqUR2I4WMEA8JdHdkjf9YJjmOImrHdDb9F6l1JCHs0p9rd/DGrZ8AiCrzFo5FmmicSGRHUsgI8TCdDp+SDQD4xjCDMfOkS7YQz+rA+duEbfsIbyWOOx7F8Gr5rdaRRDZl04XMN998g6IoVpeiRYtqHUvkBDX6Y8pXG1clicEpI/n0rz2YzdIlW4j0iE1M4b15Bxmb0pZrjnnx6jpTRu8VmcamCxmAEiVKcPXqVctl69atWkcSOYFOj77db5icclFSF0HVc+OZsvWs1qmEsHmqqvLZ4qNcvH2XS57lce6/F8W3kNaxRDZm84WMwWAgMDDQcvH19dU6ksgpPILQt50AQC/DCnaunse+87c1DiWEbZu/5QjHD+9Br1MY07Esni5yJEZkLpsvZE6fPk1wcDAFChSgU6dOXLhw4YnrJyUlERMTY3UR4rkVaYZaqRcAQw1T6D9rN7fjkzUOJYRtOnopCu91/fnH8QsmVLhMhVBvrSOJHMCmC5kqVaowffp0Vq1axYQJEzh37hy1atUiNjb2sfcZNmwYnp6elktISEgWJhbZkdLkO1KKteMrl6+4GGNiwLyD0l5GiIfEJKawacbXNNTtw0Ex06haRa0jiRxCUe1oUpmoqChCQ0P55Zdf6Nmz5yPXSUpKIinp/3uYxMTEEBISQnR0NB4eHlkVVWRDJ6/F0HrcNpJSzXzUpAh96hXUOpIQNkFVVUZMmcnAS/1xUEzcbfQjzjXe0jqWsHMxMTF4eno+9fvbpo/IPMzLy4vChQsTHh7+2HWMRiMeHh5WFyEyQtFAD4a2KUk55TR71v7FzrO3tI4khE2Ys/EgnS99g4Ni4k6BVjhX76V1JJGD2FUhExcXx5kzZwgKCtI6isih2vueZ4FxCKMdxvL97NVcj0nUOpIQmtoXcYvgDf3Jrdwi2iWUXB1+lSkIRJay6ULmww8/ZNOmTURERLB9+3batm2LXq+nY8eOWkcTOVWeypC7HJ5KAkOTf+T9P3eSnGrWOpUQmrgRk8g/M0dSV3eQZMURj66zwCgTQoqsZdOFzKVLl+jYsSNFihShffv2+Pj4sHPnTvz8ZK4OoRGDI/pXp2My5qKM7iytr4xiyLJjWqcSIsslp5p5d9Z+ZsZXZp5jO8zNf0IJLKV1LJED2VVj3+eR3sZCQjyTM/+i/vkyimpmUEpPyrUdQPuK0kNO5BxfLz3KjB3ncTcaWNq3BgX83LSOJLKZbNnYVwibEVYfpf6XAAw2TGf+ksUcvhSlbSYhssiSXadx2z0aR1IY9VpZKWKEpqSQEeJ51RyAWqwVjoqJFmyh98x93IqTySVF9nb0UhT65e/zkcNfrAieRoNiAVpHEjmcFDJCPC9FQWnzK3eb/MQfnu9yJTqRd2btl8a/Itu6EZvIummDaanbhgkdBVp+pHUkIaSQEeKFGN1xrtaL37pVxN1oYPe5W3y55CjZvOmZyIESU0yMnzKZfqnTAEiuPwRd/poapxJCChkhMkRBf3fGtS/CBIfROBz4nalbz2kdSYgMo6oqP89ZzsCo79ErKrFF2+Ncq6/WsYQAwKB1ACGyizpJm0G/m0a6vfRYGUiY/xvUK+KvdSwhXtiUdQd5LfxjPHUJxPiWw+OVcTLonbAZckRGiIxSrgtq6Q4YFDPjHEbz8+zlnL7++AlOhbAHq49dY9m/m/FTool3CsSj2zwwGLWOJYSFFDJCZBRFQWk5BnOeSngqCYxWf+D96Ru5KT2ZhJ06ejmaAfMOckgtyLTiU3DtvgDcpZeSsC1SyAiRkRyc0L02G5NHHsJ0VxkUN5y3p+/kbrJJ62RCPJPLUXfpO20zCckmahb0pc8rzUBG7hU2SAoZITKamz/61+diNrhQS3+U1tfG8t7cA5jM0pNJ2IfouymMnzSBRSm9ae9zll87l8egl68LYZvknSlEZggshe7VaSQ7+/E3tVl7/DpD/jkm3bKFzUtKNTHs97l8njAcbyWOr/OfwMPJQetYQjyWFDJCZJYiTXEccIge7V8FYMaO80zZIt2yhe1SVZVhc9bR/8aXuCpJxOWuiWubUVrHEuKJpJARIjM5utKidBCfNy9GSeUs/65awD+HrmidSohHGr18H6+d/oBA5Q7xnoVw6zwLDI5axxLiiWQcGSGywJth0XR1/o5kE3T8yx0vl1eoVchP61hCWPy+6SQVdr1PUf1F7hp9ce2xGJy9tI4lxFPJERkhsoASUBzHkPK4K3eZahjO0JkrOHDhjtaxhABg4b5L3Fgzklr6o6TonHHuthC8QrSOJUS6SCEjRFYwGFFem4XZvzgBShST+ZYPf1/DfzJgntDY2uPX+XjhYaaamnPIpzmGTnMguKzWsYRINylkhMgqzrnQdVmM2SsfobobjDMP5d0p67l4O0HrZCKH2nn2Fn1m78dkVmldIR+l+85GCaundSwhnokUMkJkJfdAdF2XYHYNoJjuIj8kfUuvKZu4EZOodTKRwxy+FMWGGUP4jN9pUsyP4e1Kocj8ScIOSSEjRFbzzn+vmDF6kWjwIOL2XV6fskumMhBZ5ujlaP6aMoJBynS6G9YwtvxVGfBO2C155wqhhYDi6N5cS0jvxeTy9CT8Rhydp+zidnyy1slENnfyWgyzpvzEEPVXAJIrvo1jyVYapxLi+UkhI4RW/AqT19+T2b2q4u/mSMnIZXSbvI2oBClmROY4fT2Wab+NZKh5HDpFJblsVxxb/ABySknYMSlkhNBYfl9XVpdYy08Ok3j71jC6TdlB9N0UrWOJbOZMZBwTJ43hW9NoDIqZ5JIdcWw1WooYYfekkBHCBuQq0RBV58BL+l30jBxGtynb5ciMyDDhN2J5d9JqhppG46CYSC7+Co7txoNOvgKE/ZN3sRC2oHBjlA4zUXUOtNLvoMeN4XSatFUaAIsXdvxKDB0m7eRUnBM/uQ4kqdjLOL48CXR6raMJkSGkkBHCVhRphvLqdFSdgdb67fS7/T2dJ27munTNFs/p4MUouv62iVvxyZTM7UG/PgMxdvgd9DI7jcg+pJARwpYUewmlwyzMeiNN9Xv4MPo72k/czqU7MmieeDZ7Im7z15QfWGgeSOPcycx6syq5XGUCSJH9SCEjhK0p0hTd6/MwO7ix1bkB52/fpf3EHZyJjNM6mbATW05Hsvz37/he+fXeKNJFj+Hp7KB1LCEyhRQyQtiisHro+h+md5+PKODnypXoRF6ZsF0mmhRPtfTAJbbP+JJvdFMASK30Fo4NP9c4lRCZRwoZIWyVqw+Bnk7Mf7sa9YNSGJ0yhA8nL2PDqRtaJxM2asrmcG4u/JBPDHMASK3+PobmI6SLtcjWpMWXEDbOx83Ib7lmYrhzhFnql/T8I47b7VrycoU8WkcTNsJsVvlxxWGK7/qYload95Y1GoqhxnsaJxMi88kRGSHsgKH1aFS/ogQqd5hjGMyChbP5dWM4qqpqHU1oLCnVxAfzD/Hn1v8oqFzBpBhQ201GJ0WMyCGkkBHCHnjmQXljFWre6ngod5nu8AMn1kzj4wWHSU41a51OaORWXBKdp+xi8YHLJOhcOdtkBvoui1BKt9c6mhBZRgoZIeyFcy6ULouhWCuMSipjHceR+9AoOk/ZKZNN5kCnr8fy2dhpFLs4F3cnA9O6V6JFjfJQoI7W0YTIUlLICGFPHJzg1elQrS8ATfX7OBxxjTbjtxF+I1bbbCLLbDx1g99+/ZExiV8wxGEGq19KonZhP61jCaEJaewrhL3R6aHJdxBQEqNbOfwWXeHC7QTajt/O6I5lqV80QOuEIpOoqsrULWdIWPMdPxoWAZAc1pjgUvU0TiaEdhQ1m7cWjImJwdPTk+joaDw8PLSOI0SGuxWXxNsz91H00l8cNeenTv1mvN+gEDqddLnNTuKTUvn6r+00+G8IzfR7AEit1g9Do8Eyb5LIltL7/S1HZISwcz5uRmbXj8VxzjSSVT1DN57ljYuvM+q1cni5yJD02cGZyDiGT1/EoNjvKKC/hklxQNfyFwzlu2odTQjNSRsZIbIBx9BqUKwVjoqJoQ7TaXPuG14Zs46jl6O1jiZe0Kqj12g9bhvud45RQHeNJNdg9D1Xo0gRIwQgp5aEyD5UFXaMR137FYpq4j9zbt4zDaRD8wZ0r54PRUZ3tSuJKSaGrTjBjB3nAaic35upxQ7gXqEDuPponE6IzJfe7285IiNEdqEoUL0vSvdlmF0DKKy7zELDZxxa/htvTN/DzbgkrROKdDp1LZb3Rs+mwd7e+BDNW7ULMOvNKrjXfleKGCEeIoWMENlNaHV0vbeg5quFq5KEQa+w4VQkTUdtYdN/kVqnE0+gqiozt59j3vgvGBM7gNr6IywvuprPmhfDQS9/roV4FDm1JER2ZTbBf6s45VmLfnMP8N/1OFy5yyvVivJx06K4GqWtvy25Fp3IsAWbaRnxPQ31BwBIyt8A48sTwc1f43RCZL30fn9LISNEDpCYYmLk0h10P9KFFaYqzHXvyuCXK1O9oK/W0XI8VVWZv+cie1ZM4VP1d3yUWFJ1jugaDUFXtbfMXC1yLOl+LYSwcHLQMyjff3D0Nj0NK2kYv49Pf+/F8krNGNS8GG5ydEYTl6PuMmjREXKfmcuPDlNBgSTvohjbT4XAklrHE8IuyElXIXKKim9ApwWY3YMJ1d1gjuN3FN/3NW1+Xsmqo1dlJu0slGoyM3XrOZqM3Mzm/yJZpdQkyjkvpjqDML67RYoYIZ6BnFoSIqdJjIF1X8Pe3wG4qnrzbUpnYgu2ZHCrEuT3ddU4YPa26+wtfl+0nKpRyxiS2oVyeb0Z8UoZCno7gMGodTwhbIacWhJCPJqTB7w0Ekq0w/x3P4LunKOm/jiD/qtKk5Gbeat2Ad6tF4aLo/x5yEg3YhMZ+c9eCh0fy3j9GgwGM8XL1aBS25dkOgkhXoAckREiJ0u5Czt/5Xy+9ny19iqb/oskgNu4unnwZqNytK+YB4N0+30hcUmpTN50mptbp9NfmYOfcm+05eTCL+HYfDh4hWicUAjbJL2W/kcKGSHSR1VV1hy7Rq5Fr1HIFM741NZsydWGAU1L06REgIwM/IySU83M2XWeA+vn8k7qnxTRXQIgybMAxpY/QcEGGicUwrbJqSUhxDNRFIUm+R0xe99FdzOOLxxmcTl2FaPmvMzk4Jb0bVCUukX8pKB5iuRUM0sOXGbchnAu3I5nkeMCiugukezgiUPdDzFWeVvawgiRgeSIjBDCmtkEh+Zg3vA9upjLAJw252Z8amvOBDThnfpFaFoiUNp1PCQxxcS8PRfZtXEZO2J8uIMHfu5GvisfQwP9QfS1BoBzLq1jCmE35NTS/0ghI8RzSkmEPZMxb/4ZXeIdAN5Pfpel5pqE+bnyVu0CtC6bGycHvcZBtXU7Ppm5u89zfMsSuqQuoIruJFN1r2Cq+xmdq4ZKo2khnpMUMv8jhYwQLygxGvZMIfXoUsbl/5Xfd14mJjGV8sp/3HHKQ6NKJelcJZS8Pi5aJ81Shy9FMWvrfyjHFtJZWUVJXQQAJsUBtUpvDE2/1TagEHZOCpn/kUJGiAyiqqAoxCamMHfXOV7a2Bwf821WmKsw09QYz0I1eLlCCA2K+WfbozRRCcksP3KVv/ZeovaV3+lhWIW3EgdAqs4JpVIP9DXeA49gjZMKYf+ksa8QImP9r5Gvu5MDvcq5o/4XinI5kjb67bTRb+fYuVAWhdfiJ0MtKpcqTptyuamS39vu29IkpZrYcPIGy/eFs/q/WJJN9377dXCIwluJI9k1Nw5Ve2Eo3xVcfTROK0TOI0dkhBDP78oB2D0F85EF6EyJAJhUhaGpXZhuaoqfu5H6RfxpUMyfmoV87aa9yK24JDacimTj8Uskh2+miXkzTXW76Zb8CfGBlWlTNphXCyTjHX8WCjcFXfY8AiWElrLVqaXx48fz448/cu3aNcqUKcPYsWOpXLlyuu4rhYwQWSDhNhxdiHr4L5RLu/m1wK9MOOtLbGIqZZRwyunC2aJUICSsONUK+FA5vzclc3viYCOD7SUkp7L/fBS7I25z8L9zeF/ZSEPdfuroDuGu3LWsd6vsO/i0Ga5hUiFyjmxTyMybN4+uXbsyceJEqlSpwqhRo5g/fz6nTp3C39//qfeXQkaILHb7HOTKR7JJZde5Wzit/ohKNxcDEG4OZoe5OHvMRTmsL07u0DDKheSiaJA7xYI8yOfjij6TT0UlpZo4fT2Ok9diOXE1hv0RtzhyJZZUs0puItlkHIBBMVvWT3H2w1D8JZQyHSGksuUUmxAic2WbQqZKlSpUqlSJcePGAWA2mwkJCaFfv358+umnT72/FDJCaOzAn6iH5sD5HSiqyeqmi2Y/micPI5Z7PZ68DYnk9vcnr48ruXM5k9vLmWAvZwI8jHg4OeDuZMDdyQFHQ9ojOaqqkpRqJiYxhdjEVKLvpnAtOpHLd+5yOereJTLyOs63T1CUCIopFyihiyBczc37KX0J9nSicr5cDIt4FYObLw7FW0CR5hBcHnS2ceRIiJwkWzT2TU5OZt++fQwaNMiyTKfT0bBhQ3bs2PHI+yQlJZGUlGS5HhMTk+k5hRBPUK4zSrnOcDcKzm2GCztQz2+Ha4fJ5erAS2WLcPxqLP9di2UsP1Pq1lku3vTniurLZdWHPaoPN9Rc3MadzeYyABgNOoJ0d3AkFQX13sWUirM5Fg8lHoCN5nKWCL87jKCU7ix+Sgw4WMcLc4xj64C65PH+36zfCXvAxTsLnhghREaw6ULm5s2bmEwmAgICrJYHBARw8uTJR95n2LBhDB48OCviCSGehbMXFG8FxVuhACTF4hZ1kWEBxQEwmVXUn9/HEH+XEsp5SnDe6u4XVX9qJY0CICnVzETH7ymqu/j/Kzxw0OQyfrR3qk6Ah5HcuVwoeikZv/h7P2pSPfKgDyqNElgKAkvhFFyePJ6u/39nKWKEsCs2Xcg8j0GDBjFw4EDL9ZiYGEJCZHZZIWyO0R3+V8QA99rGDDgCt89A1EWIvgjRl+79Gx9JiKs/Z9o2Jy4xlZjEFPzn+WK+dfN/bVYU0DuCkyeKsxe5PfOw7bX6/7+vy+NA5wC5QjE4eWb9YxVCZBqbLmR8fX3R6/Vcv37davn169cJDAx85H2MRiNGo0zIJoRdMjiCf7F7l0fQA54uDni6OMA7G9O/3dwVMiSeEML22HQLNkdHRypUqMD69esty8xmM+vXr6datWoaJhNCCCGELbDpIzIAAwcOpFu3blSsWJHKlSszatQo4uPj6dGjh9bRhBBCCKExmy9kOnToQGRkJF999RXXrl2jbNmyrFq1Kk0DYCGEEELkPDY/jsyLknFkhBBCCPuT3u9vm24jI4QQQgjxJFLICCGEEMJuSSEjhBBCCLslhYwQQggh7JYUMkIIIYSwW1LICCGEEMJuSSEjhBBCCLslhYwQQggh7JYUMkIIIYSwW1LICCGEEMJu2fxcSy/q/gwMMTExGicRQgghRHrd/95+2kxK2b6QiY2NBSAkJETjJEIIIYR4VrGxsXh6ej729mw/aaTZbObKlSu4u7ujKIrWcTQXExNDSEgIFy9elEk0M5E8z1lDnuesIc9z1pDn2ZqqqsTGxhIcHIxO9/iWMNn+iIxOpyNPnjxax7A5Hh4e8kHJAvI8Zw15nrOGPM9ZQ57n//ekIzH3SWNfIYQQQtgtKWSEEEIIYbekkMlhjEYjX3/9NUajUeso2Zo8z1lDnuesIc9z1pDn+flk+8a+QgghhMi+5IiMEEIIIeyWFDJCCCGEsFtSyAghhBDCbkkhI4QQQgi7JYWMICkpibJly6IoCgcPHtQ6TrYSERFBz549yZ8/P87OzoSFhfH111+TnJysdTS7N378ePLly4eTkxNVqlRh9+7dWkfKdoYNG0alSpVwd3fH39+fNm3acOrUKa1jZXvDhw9HURT69++vdRS7IIWM4OOPPyY4OFjrGNnSyZMnMZvNTJo0iWPHjjFy5EgmTpzIZ599pnU0uzZv3jwGDhzI119/zf79+ylTpgxNmjThxo0bWkfLVjZt2kSfPn3YuXMna9euJSUlhcaNGxMfH691tGxrz549TJo0idKlS2sdxW5I9+scbuXKlQwcOJCFCxdSokQJDhw4QNmyZbWOla39+OOPTJgwgbNnz2odxW5VqVKFSpUqMW7cOODenGohISH069ePTz/9VON02VdkZCT+/v5s2rSJ2rVrax0n24mLi6N8+fL8+uuvfPvtt5QtW5ZRo0ZpHcvmyRGZHOz69ev06tWLmTNn4uLionWcHCM6Ohpvb2+tY9it5ORk9u3bR8OGDS3LdDodDRs2ZMeOHRomy/6io6MB5P2bSfr06UOLFi2s3tvi6bL9pJHi0VRVpXv37vTu3ZuKFSsSERGhdaQcITw8nLFjx/LTTz9pHcVu3bx5E5PJREBAgNXygIAATp48qVGq7M9sNtO/f39q1KhByZIltY6T7cydO5f9+/ezZ88eraPYHTkik818+umnKIryxMvJkycZO3YssbGxDBo0SOvIdim9z/ODLl++TNOmTXn11Vfp1auXRsmFeD59+vTh6NGjzJ07V+so2c7Fixd5//33mTVrFk5OTlrHsTvSRiabiYyM5NatW09cp0CBArRv355//vkHRVEsy00mE3q9nk6dOjFjxozMjmrX0vs8Ozo6AnDlyhXq1q1L1apVmT59Ojqd/IZ4XsnJybi4uLBgwQLatGljWd6tWzeioqJYunSpduGyqb59+7J06VI2b95M/vz5tY6T7SxZsoS2bdui1+sty0wmE4qioNPpSEpKsrpNWJNCJoe6cOECMTExlutXrlyhSZMmLFiwgCpVqpAnTx4N02Uvly9fpl69elSoUIE///xT/iBlgCpVqlC5cmXGjh0L3DvtkTdvXvr27SuNfTOQqqr069ePxYsXs3HjRgoVKqR1pGwpNjaW8+fPWy3r0aMHRYsW5ZNPPpFTeU8hbWRyqLx581pdd3NzAyAsLEyKmAx0+fJl6tatS2hoKD/99BORkZGW2wIDAzVMZt8GDhxIt27dqFixIpUrV2bUqFHEx8fTo0cPraNlK3369GH27NksXboUd3d3rl27BoCnpyfOzs4ap8s+3N3d0xQrrq6u+Pj4SBGTDlLICJGJ1q5dS3h4OOHh4WkKRDkY+vw6dOhAZGQkX331FdeuXaNs2bKsWrUqTQNg8WImTJgAQN26da2WT5s2je7du2d9ICEeQU4tCSGEEMJuSYtDIYQQQtgtKWSEEEIIYbekkBFCCCGE3ZJCRgghhBB2SwoZIYQQQtgtKWSEEEIIYbekkBFCCCGE3ZJCRgghhBB2SwoZIUSmmjp1Ko0bN86SfUVERKAoCgcPHnzienXr1qV///4Zuu9PP/2Ufv36Zeg2hRBPJyP7CiEyTWJiIgUKFGD+/PnUqFEDgG+++YbBgwcDoNfryZMnD23btmXo0KGWOb+el8lkIjIyEl9fXwwGAxs3bqRevXrcuXMHLy8vy3q3b9/GwcEBd3f3F9rfg27evEmBAgU4ePAgBQoUyLDtCiGeTI7ICCEyzYIFC/Dw8LAUMfeVKFGCq1evEhERwQ8//MBvv/3GBx988ML70+v1BAYGYjA8eRo5b2/vDC1iAHx9fWnSpIllfiIhRNaQQkYI8VSRkZEEBgby/fffW5Zt374dR0dH1q9f/9j7zZ07l5YtW6ZZbjAYCAwMJE+ePHTo0IFOnTrx999/A5CUlMR7772Hv78/Tk5O1KxZkz179ljue+fOHTp16oSfnx/Ozs4UKlSIadOmAdanliIiIqhXrx4AuXLlQlEUy0SHD59aunPnDl27diVXrly4uLjQrFkzTp8+bbl9+vTpeHl5sXr1aooVK4abmxtNmzbl6tWrVo+rZcuWzJ07N53PqhAiI0ghI4R4Kj8/P37//Xe++eYb9u7dS2xsLF26dKFv3740aNDgsffbunUrFStWfOr2nZ2dSU5OBuDjjz9m4cKFzJgxg/3791OwYEGaNGnC7du3Afjyyy85fvw4K1eu5MSJE0yYMAFfX9802wwJCWHhwoUAnDp1iqtXrzJ69OhH7r979+7s3buXv//+mx07dqCqKs2bNyclJcWyTkJCAj/99BMzZ85k8+bNXLhwgQ8//NBqO5UrV+bSpUtEREQ89TELITLGk4+/CiHE/zRv3pxevXrRqVMnKlasiKurK8OGDXvs+lFRUURHRxMcHPzE7e7bt4/Zs2dTv3594uPjmTBhAtOnT6dZs2YATJ48mbVr1zJ16lQ++ugjLly4QLly5SwFUr58+R65Xb1ej7e3NwD+/v5WbWQedPr0af7++2+2bdtG9erVAZg1axYhISEsWbKEV199FYCUlBQmTpxIWFgYAH379mXIkCFW27r/WM+fP//YXEKIjCWFjBAi3X766SdKlizJ/Pnz2bdvH0aj8bHr3r17FwAnJ6c0tx05cgQ3NzdMJhPJycm0aNGCcePGcebMGVJSUqza1Dg4OFC5cmVOnDgBwDvvvMPLL7/M/v37ady4MW3atLEUIM/jxIkTGAwGqlSpYlnm4+NDkSJFLPsEcHFxsRQxAEFBQdy4ccNqW87OzsC9ozdCiKwhp5aEEOl25swZrly5gtlsfurpEx8fHxRF4c6dO2luK1KkCAcPHuTEiRPcvXuXv//+m4CAgHRlaNasGefPn2fAgAFcuXKFBg0apDnFkxkcHBysriuKwsOdPu+f/vLz88v0PEKIe6SQEUKkS3JyMp07d6ZDhw4MHTqUN998M80RiQc5OjpSvHhxjh8//sjbChYsSL58+XB0dLQsDwsLw9HRkW3btlmWpaSksGfPHooXL25Z5ufnR7du3fjzzz8ZNWoUv/3222MzwL1u2Y9TrFgxUlNT2bVrl2XZrVu3OHXqlNU+0+Po0aM4ODhQokSJZ7qfEOL5SSEjhEiXzz//nOjoaMaMGcMnn3xC4cKFeeONN554nyZNmrB169Z078PV1ZV33nmHjz76iFWrVnH8+HF69epFQkICPXv2BOCrr75i6dKlhIeHc+zYMZYtW0axYsUeub3Q0FAURWHZsmVERkYSFxeXZp1ChQrRunVrevXqxdatWzl06BCdO3cmd+7ctG7dOt3ZAbZs2UKtWrUsp5iEEJlPChkhxFNt3LiRUaNGMXPmTDw8PNDpdMycOZMtW7Y8cdyUnj17smLFCqKjo9O9r+HDh/Pyyy/TpUsXypcvT3h4OKtXryZXrlzAvaMsgwYNonTp0tSuXRu9Xv/YLs+5c+dm8ODBfPrppwQEBNC3b99Hrjdt2jQqVKjASy+9RLVq1VBVlRUrVqQ5nfQ0c+fOpVevXs90HyHEi5GRfYUQmerVV1+lfPnyDBo0SOsomWrlypV88MEHHD58+KkD8gkhMo4ckRFCZKoff/zxhacesAfx8fFMmzZNihghspgckRFCCCGE3ZIjMkIIIYSwW1LICCGEEMJuSSEjhBBCCLslhYwQQggh7JYUMkIIIYSwW1LICCGEEMJuSSEjhBBCCLslhYwQQggh7JYUMkIIIYSwW/8HF5C6m63837MAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**FDM Validation**"
      ],
      "metadata": {
        "id": "PFlkccXfo_UF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Test function using FDM\n",
        "def validate_energy_grad_hess(energy_model, x_value, delta=1e-5):\n",
        "    \"\"\"\n",
        "    Validate the gradient and Hessian computed by the model using finite difference.\n",
        "\n",
        "    Parameters:\n",
        "        energy_model (ElasticEnergy): The neural network model.\n",
        "        x_value (float): The input value for which to validate.\n",
        "        delta (float): Small perturbation for finite difference.\n",
        "\n",
        "    Returns:\n",
        "        dict: Results containing analytical and FDM values for energy, gradient, and Hessian.\n",
        "    \"\"\"\n",
        "    # Compute analytical results\n",
        "    energy, grad_analytical, hess_analytical = energy_model.compute_energy_grad_hess(x_value)\n",
        "\n",
        "    # Finite difference for gradient\n",
        "    energy_plus = energy_model.compute_energy_grad_hess(x_value + delta)[0]\n",
        "    energy_minus = energy_model.compute_energy_grad_hess(x_value - delta)[0]\n",
        "    grad_fdm = (energy_plus - energy_minus) / (2 * delta)\n",
        "\n",
        "    # Finite difference for Hessian\n",
        "    grad_plus = (energy_model.compute_energy_grad_hess(x_value + delta)[1])\n",
        "    grad_minus = (energy_model.compute_energy_grad_hess(x_value - delta)[1])\n",
        "    hess_fdm = (grad_plus - grad_minus) / (2 * delta)\n",
        "\n",
        "    # Return results\n",
        "    results = {\n",
        "        \"x_value\": x_value,\n",
        "        \"energy_analytical\": energy,\n",
        "        \"grad_analytical\": grad_analytical,\n",
        "        \"hess_analytical\": hess_analytical,\n",
        "        \"grad_fdm\": grad_fdm,\n",
        "        \"hess_fdm\": hess_fdm\n",
        "    }\n",
        "    return results\n",
        "\n",
        "\n",
        "# Test inputs\n",
        "x_values = np.linspace(-1, 1, 5)  # Test over a range of inputs\n",
        "results = []\n",
        "\n",
        "for x in x_values:\n",
        "    res = validate_energy_grad_hess(energy_model, x)\n",
        "    results.append(res)\n",
        "    print(f\"x = {x}\")\n",
        "    print(f\"Energy (Analytical): {res['energy_analytical']}\")\n",
        "    print(f\"Gradient (Analytical): {res['grad_analytical']}, Gradient (FDM): {res['grad_fdm']}\")\n",
        "    print(f\"Hessian (Analytical): {res['hess_analytical']}, Hessian (FDM): {res['hess_fdm']}\")\n",
        "    print(\"-\" * 50)\n",
        "\n",
        "# Visualization\n",
        "analytical_grad = [res[\"grad_analytical\"] for res in results]\n",
        "fdm_grad = [res[\"grad_fdm\"] for res in results]\n",
        "analytical_hess = [res[\"hess_analytical\"] for res in results]\n",
        "fdm_hess = [res[\"hess_fdm\"] for res in results]\n",
        "\n",
        "plt.figure(figsize=(10, 5))\n",
        "\n",
        "# Gradient Comparison\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.plot(x_values, analytical_grad, 'ro-', label='Analytical Gradient')\n",
        "plt.plot(x_values, fdm_grad, 'b^--', label='FDM Gradient')\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"Gradient\")\n",
        "plt.title(\"Gradient Comparison\")\n",
        "plt.legend()\n",
        "\n",
        "# Hessian Comparison\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.plot(x_values, analytical_hess, 'ro-', label='Analytical Hessian')\n",
        "plt.plot(x_values, fdm_hess, 'b^--', label='FDM Hessian')\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"Hessian\")\n",
        "plt.title(\"Hessian Comparison\")\n",
        "plt.legend()\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 941
        },
        "id": "hnBtCFe5o-zu",
        "outputId": "fd601c27-82b0-4d7a-ec4c-24681fee0c79"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = -1.0\n",
            "Energy (Analytical): 0.9278690178289752\n",
            "Gradient (Analytical): -1.9778193194058233, Gradient (FDM): -1.9778193193875635\n",
            "Hessian (Analytical): 1.9666691569518076, Hessian (FDM): 1.9666691569719672\n",
            "--------------------------------------------------\n",
            "x = -0.5\n",
            "Energy (Analytical): 0.1847105024153135\n",
            "Gradient (Analytical): -0.9931189127380089, Gradient (FDM): -0.9931189127287964\n",
            "Hessian (Analytical): 1.9858295748313095, Hessian (FDM): 1.9858295748242936\n",
            "--------------------------------------------------\n",
            "x = 0.0\n",
            "Energy (Analytical): -0.06141740954951547\n",
            "Gradient (Analytical): 0.012324734468896592, Gradient (FDM): 0.01232473449963578\n",
            "Hessian (Analytical): 2.027779489190767, Hessian (FDM): 2.0277794891887524\n",
            "--------------------------------------------------\n",
            "x = 0.5\n",
            "Energy (Analytical): 0.19714227272239593\n",
            "Gradient (Analytical): 1.0174017585319457, Gradient (FDM): 1.017401758507397\n",
            "Hessian (Analytical): 1.9755948653174604, Hessian (FDM): 1.9755948652999675\n",
            "--------------------------------------------------\n",
            "x = 1.0\n",
            "Energy (Analytical): 0.9497266782873022\n",
            "Gradient (Analytical): 1.9894621253755438, Gradient (FDM): 1.9894621253291331\n",
            "Hessian (Analytical): 1.9385717953461659, Hessian (FDM): 1.9385717953790402\n",
            "--------------------------------------------------\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Neural Network Model: Comprehensive for 2D beams\n",
        "\n",
        "$$\n",
        "E = \\frac{1}{2} EA \\Delta l \\varepsilon^2\n",
        "+ \\frac{1}{2} \\frac{EI}{\\Delta l} \\kappa^2\n",
        "$$\n",
        "where $EI = Y \\pi h^4/4$ and $EA = Y \\pi h^2$. Here, $h$ is the cross-sectional radius and $Y$ is the Young's modulus.\n",
        "\n",
        "We can rewrite the above equations as\n",
        "$$\n",
        "E = \\frac{1}{2} EA \\Delta l\n",
        "\\left( \\varepsilon^2\n",
        "+ \\frac{1}{4} \\bar{\\kappa}^2\n",
        "\\right),\n",
        "$$\n",
        "where $\\bar{\\kappa} = \\kappa h / \\Delta l$.\n",
        "\n"
      ],
      "metadata": {
        "id": "QfNDD0M0axx5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the custom SquareActivation function\n",
        "class SquareActivation(nn.Module):\n",
        "    def forward(self, x):\n",
        "        return x**2\n",
        "\n",
        "class ElasticEnergyGeneric(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(ElasticEnergyGeneric, self).__init__()\n",
        "        self.layers = nn.Sequential(\n",
        "            SquareActivation(),\n",
        "            nn.Linear(2, 4, dtype=torch.float64),  # Initialize with float64\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(4, 4, dtype=torch.float64),\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(4, 1, dtype=torch.float64),\n",
        "        )\n",
        "\n",
        "    def forward(self, x):\n",
        "        return self.layers(x)\n",
        "\n",
        "    def compute_energy_grad_hess(self, x):\n",
        "        \"\"\"\n",
        "        Compute energy, gradient, and Hessian with respect to the input.\n",
        "\n",
        "        Parameters:\n",
        "            x (numpy.ndarray): Input vector (2D), shape (2,).\n",
        "\n",
        "        Returns:\n",
        "            tuple: (energy, gradient, Hessian), where:\n",
        "                - energy (float): Energy at the input.\n",
        "                - gradient (numpy.ndarray): Gradient vector, shape (2,).\n",
        "                - Hessian (numpy.ndarray): Hessian matrix, shape (2, 2).\n",
        "        \"\"\"\n",
        "\n",
        "        # Ensure the input is a 2D tensor of shape (1, 2)\n",
        "        if isinstance(x, torch.Tensor):\n",
        "            x_tensor = x.clone().detach().reshape(1, -1).requires_grad_(True)  # Safely copy the tensor\n",
        "        else:\n",
        "            x_tensor = torch.tensor(x.reshape(1, -1), requires_grad=True, dtype=torch.float64)\n",
        "\n",
        "        # Forward pass to compute energy (output is scalar)\n",
        "        energy = self.forward(x_tensor).squeeze()  # Remove batch dimension, if any\n",
        "\n",
        "        # Compute gradient (dE/dx)\n",
        "        grad = torch.autograd.grad(energy, x_tensor, create_graph=True)[0].squeeze()  # Shape: (2,)\n",
        "\n",
        "        # Compute Hessian (d²E/dx²)\n",
        "        hess = torch.zeros((2, 2), dtype=torch.float64)  # Initialize Hessian\n",
        "        for i in range(2):  # Iterate over each dimension\n",
        "            grad_i = torch.autograd.grad(grad[i], x_tensor, retain_graph=True)[0].squeeze()  # Shape: (2,)\n",
        "            hess[i, :] = grad_i  # Fill row i of the Hessian\n",
        "\n",
        "        return energy.item(), grad.detach().numpy(), hess.detach().numpy()"
      ],
      "metadata": {
        "id": "fTz27gqpdzLq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def train_elastic_energy_generic_model(model, x_train, y_train, E_train, epochs=10000, lr=0.01, verbose=True):\n",
        "    \"\"\"\n",
        "    Train the ElasticEnergyGeneric model to approximate the energy function.\n",
        "\n",
        "    Parameters:\n",
        "        model (nn.Module): The neural network model to train.\n",
        "        x_train (numpy.ndarray): Training inputs (x-coordinates), shape (n_samples, 1).\n",
        "        y_train (numpy.ndarray): Training inputs (y-coordinates), shape (n_samples, 1).\n",
        "        E_train (numpy.ndarray): Training outputs (energies), shape (n_samples, 1).\n",
        "        epochs (int): Number of training epochs.\n",
        "        lr (float): Learning rate for the optimizer.\n",
        "        verbose (bool): Whether to print training progress.\n",
        "\n",
        "    Returns:\n",
        "        model (nn.Module): Trained model.\n",
        "        losses (list): List of loss values for each epoch.\n",
        "    \"\"\"\n",
        "    # Combine x_train and y_train into a single input\n",
        "    inputs_train = np.hstack((x_train, y_train))  # Shape: (n_samples, 2)\n",
        "\n",
        "    # Convert training data to PyTorch tensors\n",
        "    inputs_tensor = torch.tensor(inputs_train, dtype=torch.float64)  # Shape: (n_samples, 2)\n",
        "    E_train_tensor = torch.tensor(E_train, dtype=torch.float64)      # Shape: (n_samples, 1)\n",
        "\n",
        "    # Define loss function and optimizer\n",
        "    criterion = nn.MSELoss()\n",
        "    optimizer = optim.Adam(model.parameters(), lr=lr)\n",
        "\n",
        "    # List to store loss values for plotting\n",
        "    losses = []\n",
        "\n",
        "    # Training loop\n",
        "    for epoch in range(epochs):\n",
        "        # Forward pass\n",
        "        predictions = model(inputs_tensor)\n",
        "        loss = criterion(predictions, E_train_tensor)\n",
        "\n",
        "        # Backward pass\n",
        "        optimizer.zero_grad()\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "        # Save loss for monitoring\n",
        "        losses.append(loss.item())\n",
        "\n",
        "        # Print progress\n",
        "        if verbose and (epoch + 1) % (epochs // 20) == 0:\n",
        "            print(f'Epoch [{epoch + 1}/{epochs}], Loss: {loss.item():.6f}')\n",
        "\n",
        "    return model, losses"
      ],
      "metadata": {
        "id": "qoEVEaVwgyLq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate training data\n",
        "x_train = np.linspace(-5, 5, 1000).reshape(-1, 1)  # Inputs (x-coordinates)\n",
        "y_train = np.linspace(-5, 5, 1000).reshape(-1, 1)  # Inputs (y-coordinates)\n",
        "E_train = x_train**2 + 0.25 * y_train**2                 # Outputs (energies)\n",
        "\n",
        "# Instantiate the model\n",
        "energy_model_generic = ElasticEnergyGeneric()\n",
        "\n",
        "# Train the model\n",
        "energy_model_generic, losses = train_elastic_energy_generic_model(\n",
        "    energy_model_generic, x_train, y_train, E_train, epochs=10000, lr=0.01\n",
        ")\n",
        "\n",
        "# Plot training loss\n",
        "plt.figure()\n",
        "plt.plot(losses, label='Training Loss')\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Loss')\n",
        "plt.title('Training Loss Over Epochs')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 819
        },
        "id": "vbKnOjgOg5vE",
        "outputId": "c05aa643-e282-466e-e809-bbce739269cd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch [500/10000], Loss: 0.000130\n",
            "Epoch [1000/10000], Loss: 0.000116\n",
            "Epoch [1500/10000], Loss: 0.000103\n",
            "Epoch [2000/10000], Loss: 0.000090\n",
            "Epoch [2500/10000], Loss: 0.000079\n",
            "Epoch [3000/10000], Loss: 0.000069\n",
            "Epoch [3500/10000], Loss: 0.000059\n",
            "Epoch [4000/10000], Loss: 0.000050\n",
            "Epoch [4500/10000], Loss: 0.000041\n",
            "Epoch [5000/10000], Loss: 0.000032\n",
            "Epoch [5500/10000], Loss: 0.000025\n",
            "Epoch [6000/10000], Loss: 0.000018\n",
            "Epoch [6500/10000], Loss: 0.000013\n",
            "Epoch [7000/10000], Loss: 0.000009\n",
            "Epoch [7500/10000], Loss: 0.000006\n",
            "Epoch [8000/10000], Loss: 0.000004\n",
            "Epoch [8500/10000], Loss: 0.000002\n",
            "Epoch [9000/10000], Loss: 0.000002\n",
            "Epoch [9500/10000], Loss: 0.000001\n",
            "Epoch [10000/10000], Loss: 0.000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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XJSQkGEkmPj7+vGX++9//msaNG5uiRYuaokWLmmrVqpmkpCSzefNmp8yFvifncqGp52d/f7Knnn/00Uemf//+JioqygQHB5s2bdrkmDpuzMU/i2wbNmwwHTp0MBERESYoKMhUrVrVDBgwIEf9fj+lfNy4cUaS2bZtmzHm1+9Xu3btTGxsrAkMDDSxsbGmW7du5vvvv7/kawFcDo8xBei/lAAKrPbt22vjxo05xoGg4FmwYIH+/Oc/a/LkybrzzjttVwewjjE7AHI4fvy4z/MtW7Zo5syZuuWWW+xUCAD+AMbsAMihYsWK6t69uypWrKgdO3ZozJgxCgwM1OOPP267agBw2Qg7AHJo2bKlPvroI6WkpMjr9SouLk7/+te/cixSBwBXAsbsAACAQo0xOwAAoFAj7AAAgEKNMTv69V42u3fvVmho6Dnv4AsAAAoeY4wOHz6s2NhY+fmdv/2GsCNp9+7dKlOmjO1qAACAXNi1a5euvfba8+4n7EgKDQ2V9OvFCgsLs1wbAABwKdLT01WmTBnn7/j5EHYkp+sqLCyMsAMAwBXmYkNQGKAMAAAKNcIOAAAo1Ag7AACgUGPMDgDAmszMTJ06dcp2NVBAFSlSRP7+/n/4OIQdAEC+M8YoJSVFaWlptquCAi4iIkIxMTF/aB08wg4AIN9lB52oqCiFhISwoCtyMMbo2LFjSk1NlSSVLl0618ci7AAA8lVmZqYTdEqUKGG7OijAgoODJUmpqamKiorKdZcWA5QBAPkqe4xOSEiI5ZrgSpD9PfkjY7sIOwAAK+i6wqXIi+8JYQcAABRqhB0AACwqX768Ro4cecnlFyxYII/Hw0y2y0DYAQDgEng8ngs+Bg0alKvjrlixQj179rzk8jfffLP27Nmj8PDwXL3fpSpMoYrZWC7am35CJ09nqVSoV0FF/viiSAAAe/bs2eP8/PHHH2vgwIHavHmzs61YsWLOz8YYZWZmKiDg4n9mS5UqdVn1CAwMVExMzGW95mpHy46Lur2xVE1GzNe6nw7ZrgoA4A+KiYlxHuHh4fJ4PM7z7777TqGhoZo1a5bq1asnr9erRYsW6YcfflC7du0UHR2tYsWK6cYbb9ScOXN8jvv7biyPx6O33npLHTp0UEhIiKpUqaLp06c7+3/f4jJ+/HhFREToiy++UPXq1VWsWDG1bNnSJ5ydPn1aDz/8sCIiIlSiRAk98cQTSkxMVPv27XN9PQ4ePKh77rlHxYsXV0hIiFq1aqUtW7Y4+3fs2KG2bduqePHiKlq0qGrUqKGZM2c6r01ISFCpUqUUHBysKlWqaNy4cbmuy8UQdtz02wByY4zdegBAAWeM0bGTp/P9kde/n5988kk9//zz2rRpk2rXrq0jR46odevWmjt3rlavXq2WLVuqbdu22rlz5wWPM3jwYHXu3Fnr1q1T69atlZCQoAMHDpy3/LFjx/Tiiy/q/fff18KFC7Vz507169fP2T98+HBNmDBB48aN0+LFi5Wenq5p06b9oXPt3r27Vq5cqenTp2vJkiUyxqh169bOFPGkpCRlZGRo4cKFWr9+vYYPH+60fg0YMEDffvutZs2apU2bNmnMmDEqWbLkH6rPhdCN5SK/36bLEXUA4MKOn8rU9QO/yPf3/XZIC4UE5t2fwiFDhujWW291nkdGRqpOnTrO82effVZTp07V9OnT1bt37/Mep3v37urWrZsk6V//+pdeeeUVLV++XC1btjxn+VOnTmns2LGqVKmSJKl3794aMmSIs3/UqFHq37+/OnToIEl69dVXnVaW3NiyZYumT5+uxYsX6+abb5YkTZgwQWXKlNG0adP017/+VTt37lSnTp1Uq1YtSVLFihWd1+/cuVN169ZV/fr1Jf3auuUmWnZclL0yQBYtOwBwVcj+453tyJEj6tevn6pXr66IiAgVK1ZMmzZtumjLTu3atZ2fixYtqrCwMOe2CecSEhLiBB3p11srZJc/dOiQ9u7dq5tuusnZ7+/vr3r16l3WuZ1t06ZNCggIUIMGDZxtJUqUUNWqVbVp0yZJ0sMPP6znnntOjRo10jPPPKN169Y5ZXv16qWJEyfqhhtu0OOPP67//e9/ua7LpaBlx0XOOkhkHQC4oOAi/vp2SAsr75uXihYt6vO8X79+Sk5O1osvvqjKlSsrODhYd955p06ePHnB4xQpUsTnucfjUVZW1mWVtz2E4u9//7tatGihzz//XF9++aWGDRumf//733rooYfUqlUr7dixQzNnzlRycrKaN2+upKQkvfjii67UhZYdF9GNBQCXxuPxKCQwIN8fbq/ivHjxYnXv3l0dOnRQrVq1FBMTo+3bt7v6nr8XHh6u6OhorVixwtmWmZmpb775JtfHrF69uk6fPq1ly5Y52/bv36/Nmzfr+uuvd7aVKVNGDzzwgKZMmaLHHntMb775prOvVKlSSkxM1AcffKCRI0fqjTfeyHV9LoaWnXxANxYAXJ2qVKmiKVOmqG3btvJ4PBowYMAFW2jc8tBDD2nYsGGqXLmyqlWrplGjRungwYOXFPbWr1+v0NBQ57nH41GdOnXUrl073X///Xr99dcVGhqqJ598Utdcc43atWsnSerTp49atWql6667TgcPHtT8+fNVvXp1SdLAgQNVr1491ahRQxkZGZoxY4azzw2EHRdlf4nIOgBwdXrppZd077336uabb1bJkiX1xBNPKD09Pd/r8cQTTyglJUX33HOP/P391bNnT7Vo0eKS7iLetGlTn+f+/v46ffq0xo0bp0ceeUS33367Tp48qaZNm2rmzJlOl1pmZqaSkpL0008/KSwsTC1bttTLL78s6de1gvr376/t27crODhYTZo00cSJE/P+xH/jMbY79QqA9PR0hYeH69ChQwoLC8uz47Z55Wtt3J2ud++9Sc2uu7xFowCgsDpx4oS2bdumChUqKCgoyHZ1rkpZWVmqXr26OnfurGeffdZ2dS7oQt+XS/37TcuOi7JbB+nGAgDYtGPHDn355Zdq1qyZMjIy9Oqrr2rbtm3629/+Zrtq+YIByi7yOKsK2q0HAODq5ufnp/Hjx+vGG29Uo0aNtH79es2ZM8fVcTIFCS07LvJzsg5pBwBgT5kyZbR48WLb1bCGlh03/daPZWHgPQAA+A1hx0WsKQgA58f8GFyKvPieEHZc5MeNQAEgh+ypyceOHbNcE1wJsr8nv18l+nIwZsdF2evsZJF1AMDh7++viIgI595NISEhrq9kjCuPMUbHjh1TamqqIiIiLmlNoPMh7LjozD9d0g4AnC0mJkaSLnhzS0CSIiIinO9LbhF2XOTHCsoAcE4ej0elS5dWVFSUTp06Zbs6KKCKFCnyh1p0slkNO8OGDdOUKVP03XffKTg4WDfffLOGDx+uqlWrOmVOnDihxx57TBMnTlRGRoZatGih1157TdHR0U6ZnTt3qlevXpo/f76KFSumxMREDRs2TAEBlrOcs6ig3WoAQEHl7++fJ3/MgAuxOkD5q6++UlJSkpYuXark5GSdOnVKt912m44ePeqUefTRR/XZZ59p8uTJ+uqrr7R792517NjR2Z+Zmak2bdro5MmT+t///qd3331X48eP18CBA22cko8zs7FIOwAA2FKg7o31yy+/KCoqSl999ZWaNm2qQ4cOqVSpUvrwww915513SpK+++47Va9eXUuWLFHDhg01a9Ys3X777dq9e7fT2jN27Fg98cQT+uWXXxQYGHjR93Xr3ljd3liqJT/u16huddW2TmyeHRcAAFz63+8CNfX80KFDkqTIyEhJ0qpVq3Tq1CnFx8c7ZapVq6ayZctqyZIlkqQlS5aoVq1aPt1aLVq0UHp6ujZu3JiPtc+Je2MBAGBfgRmgnJWVpT59+qhRo0aqWbOmJCklJUWBgYGKiIjwKRsdHa2UlBSnzNlBJ3t/9r5zycjIUEZGhvM8PT09r07DBzMpAQCwr8C07CQlJWnDhg2aOHGi6+81bNgwhYeHO48yZcq48j5+zjo7tOwAAGBLgQg7vXv31owZMzR//nxde+21zvaYmBidPHlSaWlpPuX37t3rzLmPiYnR3r17c+zP3ncu/fv316FDh5zHrl278vBsciLrAABgj9WwY4xR7969NXXqVM2bN08VKlTw2V+vXj0VKVJEc+fOdbZt3rxZO3fuVFxcnCQpLi5O69ev91mYKjk5WWFhYbr++uvP+b5er1dhYWE+Dzewzg4AAPZZHbOTlJSkDz/8UJ9++qlCQ0OdMTbh4eEKDg5WeHi47rvvPvXt21eRkZEKCwvTQw89pLi4ODVs2FCSdNttt+n666/X3XffrREjRiglJUVPP/20kpKS5PV6bZ4eA5QBACgArIadMWPGSJJuueUWn+3jxo1T9+7dJUkvv/yy/Pz81KlTJ59FBbP5+/trxowZ6tWrl+Li4lS0aFElJiZqyJAh+XUa58VdzwEAsM9q2LmUJX6CgoI0evRojR49+rxlypUrp5kzZ+Zl1fJEdjcWaQcAAHsKxADlwopuLAAA7CPsuOq3AcqWawEAwNWMsOMiv+xeLNIOAADWEHZcRDcWAAD2EXZc5KEbCwAA6wg7LvLLvrq07AAAYA1hx0XZLTtZZB0AAKwh7LjJGaBM2gEAwBbCjouce2NZrgcAAFczwo6Lsm8XQTcWAAD2EHZc5KEbCwAA6wg7LnLujQUAAKwh7LjoTDcWLTsAANhC2HETt4sAAMA6wo6LmI0FAIB9hB0X0Y0FAIB9hB0XeejGAgDAOsKOi5iNBQCAfYQdF2VnnSxWFQQAwBrCjqsYoAwAgG2EHRf5MWYHAADrCDsucrqxSDsAAFhD2HGRh24sAACsI+y4KLsbi34sAADsIey4yPNbPxaTsQAAsIewkw8MHVkAAFhD2HGRc28ssg4AANYQdlx0ZjaW3XoAAHA1I+y4yBmfTDcWAADWEHZc5OesKmi3HgAAXM0IOy7KbtlhUUEAAOwh7LiJ20UAAGAdYcdFzmwsy/UAAOBqRthxEd1YAADYR9hxkYduLAAArCPsuCi7GwsAANhD2HER3VgAANhH2HETt4sAAMA6wo6LzqwpSNoBAMAWwo6LPL91ZHFvLAAA7CHsuMiP2VgAAFhH2HHRmannpB0AAGwh7LjIwwBlAACsI+y4yMMAZQAArCPsuIgBygAA2EfYcRG3iwAAwD7CjotYZwcAAPsIOy7K7saiZQcAAHsIOy5i6jkAAPYRdlzkTD23XA8AAK5mhB0XnbnrudVqAABwVSPsuIhuLAAA7CPsuMiPbiwAAKwj7LiIlh0AAOwj7Lgoe8wOWQcAAHsIOy7iRqAAANhH2HFRdjdWFmkHAABrCDsuclZQtlwPAACuZoQdF/lxI1AAAKwj7LiI2VgAANhH2HER3VgAANhH2HERLTsAANhH2HFR9tRz7o0FAIA9hB0XOYsKWq0FAABXN8KOi/x+u7p0YwEAYA9hx0XOAGWyDgAA1hB2XOQMUKYjCwAAawg7LuLeWAAA2Gc17CxcuFBt27ZVbGysPB6Ppk2b5rO/e/fu8ng8Po+WLVv6lDlw4IASEhIUFhamiIgI3XfffTpy5Eg+nsX5ZQ9Q5t5YAADYYzXsHD16VHXq1NHo0aPPW6Zly5bas2eP8/joo4989ickJGjjxo1KTk7WjBkztHDhQvXs2dPtql8SD7eLAADAugCbb96qVSu1atXqgmW8Xq9iYmLOuW/Tpk2aPXu2VqxYofr160uSRo0apdatW+vFF19UbGxsntf5cvh5WEEZAADbCvyYnQULFigqKkpVq1ZVr169tH//fmffkiVLFBER4QQdSYqPj5efn5+WLVt23mNmZGQoPT3d5+EGZ50dmnYAALCmQIedli1b6r333tPcuXM1fPhwffXVV2rVqpUyMzMlSSkpKYqKivJ5TUBAgCIjI5WSknLe4w4bNkzh4eHOo0yZMq7Un24sAADss9qNdTFdu3Z1fq5Vq5Zq166tSpUqacGCBWrevHmuj9u/f3/17dvXeZ6enu5K4PHQjQUAgHUFumXn9ypWrKiSJUtq69atkqSYmBilpqb6lDl9+rQOHDhw3nE+0q/jgMLCwnwebmA2FgAA9l1RYeenn37S/v37Vbp0aUlSXFyc0tLStGrVKqfMvHnzlJWVpQYNGtiqpoN1dgAAsM9qN9aRI0ecVhpJ2rZtm9asWaPIyEhFRkZq8ODB6tSpk2JiYvTDDz/o8ccfV+XKldWiRQtJUvXq1dWyZUvdf//9Gjt2rE6dOqXevXura9eu1mdiSZKfs4IyAACwxWrLzsqVK1W3bl3VrVtXktS3b1/VrVtXAwcOlL+/v9atW6c77rhD1113ne677z7Vq1dPX3/9tbxer3OMCRMmqFq1amrevLlat26txo0b64033rB1Sj7ODFAm7gAAYIvVlp1bbrnlgkHgiy++uOgxIiMj9eGHH+ZltfIMNwIFAMC+K2rMzpWGG4ECAGAfYcdF2QOUs7IsVwQAgKsYYcdFzgrKVmsBAMDVjbDjIufeWAzaAQDAGsKOi7hdBAAA9hF2XHSmG4u0AwCALYQdFzkDlMk6AABYQ9hxEYsKAgBgH2HHRX7c9RwAAOsIOy5igDIAAPYRdlzkDFAm7QAAYA1hx0UeurEAALCOsOOi7G6sLFp2AACwhrDjojPdWFarAQDAVY2w46Izt4uwXBEAAK5ihB0Xsc4OAAD2EXZc5BEDlAEAsI2w4yLW2QEAwD7CjouYjQUAgH2EHRfRjQUAgH2EHRf5/XZ1adgBAMAewo6LnJYd0g4AANYQdlzkDFC2Ww0AAK5qhB0X+bHODgAA1hF2XPVr2ski6wAAYA1hx0WsoAwAgH2EHRc598ayXA8AAK5mhB0XcddzAADsI+y4iG4sAADsI+y4iG4sAADsI+zkA+6NBQCAPYQdF3HXcwAA7CPsuMhDNxYAANYRdlyUPRuLtAMAgD2EHReduTcWaQcAAFsIOy5yZmORdQAAsIaw46LsbixmYwEAYA9hx01ONxYAALCFsOMij+jGAgDANsKOizyei5cBAADuIuy46Oysw/2xAACwg7DjIs9ZTTtkHQAA7CDsuMinZcdaLQAAuLoRdlx09pgdurEAALCDsOOis7uxssg6AABYQdhxkU/LDh1ZAABYQdhxke9sLGvVAADgqkbYcZGHhXYAALCOsOMiWnYAALAvV2Fn165d+umnn5zny5cvV58+ffTGG2/kWcUKA8bsAABgX67Czt/+9jfNnz9fkpSSkqJbb71Vy5cv11NPPaUhQ4bkaQWvZB6xqCAAALblKuxs2LBBN910kyRp0qRJqlmzpv73v/9pwoQJGj9+fF7W74rm27IDAABsyFXYOXXqlLxeryRpzpw5uuOOOyRJ1apV0549e/Kudlc4FhUEAMC+XIWdGjVqaOzYsfr666+VnJysli1bSpJ2796tEiVK5GkFr2Rnd2OxqCAAAHbkKuwMHz5cr7/+um655RZ169ZNderUkSRNnz7d6d6Cb8sO/VgAANgRkJsX3XLLLdq3b5/S09NVvHhxZ3vPnj0VEhKSZ5W70vlmHdIOAAA25Kpl5/jx48rIyHCCzo4dOzRy5Eht3rxZUVFReVrBK9nZiwoyZAcAADtyFXbatWun9957T5KUlpamBg0a6N///rfat2+vMWPG5GkFr2T0YgEAYF+uws4333yjJk2aSJI++eQTRUdHa8eOHXrvvff0yiuv5GkFr2TMxgIAwL5chZ1jx44pNDRUkvTll1+qY8eO8vPzU8OGDbVjx448reCVzKcby2I9AAC4muUq7FSuXFnTpk3Trl279MUXX+i2226TJKWmpiosLCxPK3ily847NOwAAGBHrsLOwIED1a9fP5UvX1433XST4uLiJP3aylO3bt08reCVLrtth24sAADsyNXU8zvvvFONGzfWnj17nDV2JKl58+bq0KFDnlWuMPB4PJJh4jkAALbkKuxIUkxMjGJiYpy7n1977bUsKHgOZ1p2rFYDAICrVq66sbKysjRkyBCFh4erXLlyKleunCIiIvTss88qKysrr+t4RXPG7NC2AwCAFblq2Xnqqaf09ttv6/nnn1ejRo0kSYsWLdKgQYN04sQJDR06NE8reSX79f5YhpYdAAAsyVXYeffdd/XWW285dzuXpNq1a+uaa67Rgw8+SNg5m9OyAwAAbMhVN9aBAwdUrVq1HNurVaumAwcOXPJxFi5cqLZt2yo2NlYej0fTpk3z2W+M0cCBA1W6dGkFBwcrPj5eW7ZsyVGXhIQEhYWFKSIiQvfdd5+OHDmSm9NyBbOxAACwK1dhp06dOnr11VdzbH/11VdVu3btSz7O0aNHVadOHY0ePfqc+0eMGKFXXnlFY8eO1bJly1S0aFG1aNFCJ06ccMokJCRo48aNSk5O1owZM7Rw4UL17Nnz8k/KJX6/Ddoh6wAAYEeuurFGjBihNm3aaM6cOc4aO0uWLNGuXbs0c+bMSz5Oq1at1KpVq3PuM8Zo5MiRevrpp9WuXTtJ0nvvvafo6GhNmzZNXbt21aZNmzR79mytWLFC9evXlySNGjVKrVu31osvvqjY2NjcnF6eYlFBAADsylXLTrNmzfT999+rQ4cOSktLU1pamjp27KiNGzfq/fffz5OKbdu2TSkpKYqPj3e2hYeHq0GDBlqyZImkXwNWRESEE3QkKT4+Xn5+flq2bFme1OOPcrqxGLUDAIAVuV5nJzY2NsdA5LVr1+rtt9/WG2+88YcrlpKSIkmKjo722R4dHe3sS0lJUVRUlM/+gIAARUZGOmXOJSMjQxkZGc7z9PT0P1zf8/HQjQUAgFW5atm50g0bNkzh4eHOo0yZMq6915mWHQAAYEOBDTsxMTGSpL179/ps37t3r7MvJiZGqampPvtPnz6tAwcOOGXOpX///jp06JDz2LVrVx7X/izOmB3iDgAANhTYsFOhQgXFxMRo7ty5zrb09HQtW7bMGRQdFxentLQ0rVq1yikzb948ZWVlqUGDBuc9ttfrVVhYmM/DLbTsAABg12WN2enYseMF96elpV3Wmx85ckRbt251nm/btk1r1qxRZGSkypYtqz59+ui5555TlSpVVKFCBQ0YMECxsbFq3769JKl69epq2bKl7r//fo0dO1anTp1S79691bVr1wIxE0tizA4AALZdVtgJDw+/6P577rnnko+3cuVK/fnPf3ae9+3bV5KUmJio8ePH6/HHH9fRo0fVs2dPpaWlqXHjxpo9e7aCgoKc10yYMEG9e/dW8+bN5efnp06dOumVV165nNNyVfbUc9p2AACww2MYTKL09HSFh4fr0KFDed6l9adnk3Xg6EklP9pUVaJD8/TYAABczS7173eBHbNTWGQ37GRd9ZESAAA7CDsuc1ZQphsLAAArCDuuY4AyAAA2EXZcxr2xAACwi7DjMu6NBQCAXYQdl9GyAwCAXYQdl3mcth0AAGADYcdlfrTsAABgFWHHZdm3i8gi7QAAYAVhJ58QdQAAsIOw47IzA5SJOwAA2EDYcdmZFZQBAIANhB2XeVhBGQAAqwg7LvM4M89JOwAA2EDYcZmzgjJZBwAAKwg7LvP7rWmHrAMAgB2EHbf91rSTlUXcAQDABsKOy87cCBQAANhA2HFZ9grKjNkBAMAOwo7LzrTskHYAALCBsOMyD/1YAABYRdhxmbOooOV6AABwtSLsuOzMvbHs1gMAgKsVYSefMGYHAAA7CDsu82M2FgAAVhF2XJbdjZVF2gEAwArCjsucMTt2qwEAwFWLsOOy7NlYpB0AAOwg7LjsTMsOaQcAABsIOy5z1hQk6wAAYAVhx23MxgIAwCrCjsu4WwQAAHYRdlzm56ygTNwBAMAGwo7LPL91Y2WRdQAAsIKw4zKP8xNpBwAAGwg7LuNGoAAA2EXYcVn2ooJkHQAA7CDsuI2WHQAArCLsuOzM1HPSDgAANhB2XMaYHQAA7CLsuMzPw5gdAABsIuy4zMOiggAAWEXYcZkzG4usAwCAFYQdlzktO3RkAQBgBWEnn9CyAwCAHYQdl2XfG4uwAwCAHYQdl51ZZwcAANhA2HEZs7EAALCLsOMyWnYAALCLsOMyZ1FBWnYAALCCsOMybhcBAIBdhB3XcbsIAABsIuy4jJYdAADsIuy47MwAZdIOAAA2EHZcRssOAAB2EXZc5mHMDgAAVhF2XOZx+rGIOwAA2EDYcZmzzo7legAAcLUi7Ljtt5adrCziDgAANhB2XMbtIgAAsIuw4zKPc7sIyxUBAOAqRdhxGS07AADYRdhx2Zl1dog7AADYQNhxmefiRQAAgIsIOy5jzA4AAHYRdlzmdGMxagcAACsIOy7Lvl0Ey+wAAGAHYcdl3AgUAAC7CnTYGTRokDwej8+jWrVqzv4TJ04oKSlJJUqUULFixdSpUyft3bvXYo1zOjP1nLQDAIANBTrsSFKNGjW0Z88e57Fo0SJn36OPPqrPPvtMkydP1ldffaXdu3erY8eOFmubEy07AADYFWC7AhcTEBCgmJiYHNsPHTqkt99+Wx9++KH+8pe/SJLGjRun6tWra+nSpWrYsGF+V/WcPEw+BwDAqgLfsrNlyxbFxsaqYsWKSkhI0M6dOyVJq1at0qlTpxQfH++UrVatmsqWLaslS5Zc8JgZGRlKT0/3ebiFRQUBALCrQIedBg0aaPz48Zo9e7bGjBmjbdu2qUmTJjp8+LBSUlIUGBioiIgIn9dER0crJSXlgscdNmyYwsPDnUeZMmVcOwe6sQAAsKtAd2O1atXK+bl27dpq0KCBypUrp0mTJik4ODjXx+3fv7/69u3rPE9PT3cx8Py2qKBLRwcAABdWoFt2fi8iIkLXXXedtm7dqpiYGJ08eVJpaWk+Zfbu3XvOMT5n83q9CgsL83m4xe+3lp0smnYAALDiigo7R44c0Q8//KDSpUurXr16KlKkiObOnevs37x5s3bu3Km4uDiLtfRFNxYAAHYV6G6sfv36qW3btipXrpx2796tZ555Rv7+/urWrZvCw8N13333qW/fvoqMjFRYWJgeeughxcXFFZiZWNKZ2VhkHQAA7CjQYeenn35St27dtH//fpUqVUqNGzfW0qVLVapUKUnSyy+/LD8/P3Xq1EkZGRlq0aKFXnvtNcu19uVxVhUk7gAAYEOBDjsTJ0684P6goCCNHj1ao0ePzqcaXb4zKygDAAAbrqgxO1ciz29NOzTsAABgB2Enn3BvLAAA7CDsuIzZWAAA2EXYcZmfh9lYAADYRNhxWfYAZRYVBADADsKOyzxMxwIAwCrCjss8dGMBAGAVYcdlZ9YUJO4AAGADYcdtzMYCAMAqwo7LuDcWAAB2EXZcxjo7AADYRdhxmV922KFtBwAAKwg7LnO6scg6AABYQdhx2ZluLNIOAAA2EHZcxpqCAADYRdhxm4duLAAAbCLsuOxMyw5pBwAAGwg7LmPqOQAAdhF2XMaiggAA2EXYcZkfLTsAAFhF2HEZU88BALCLsOMyD7OxAACwirCTT5iNBQCAHYQdlzEbCwAAuwg7LmM2FgAAdhF2XEbLDgAAdhF2XMYKygAA2EXYcZmHO4ECAGAVYcdlfr+lnSz6sQAAsIKwk0+IOgAA2EHYcRmLCgIAYBdhx2UM2QEAwC7Cjsu4NxYAAHYRdlxGyw4AAHYRdlzmcZp27NYDAICrFWHHZWeyDmkHAAAbCDsuYzYWAAB2EXZclj1mh0UFAQCwg7DjMm4ECgCAXYQdl3l+a9sh6wAAYAdhx2W07AAAYBdhx2Ue5yfSDgAANhB2XEbLDgAAdhF2XMaYHQAA7CLsuIx7YwEAYBdhx2XZiwpmkXUAALCCsOMybgQKAIBdhB2X0Y0FAIBdhB2XeTwXLwMAANxD2HGZMxuLhh0AAKwg7LjM6cZi1A4AAFYQdvIJLTsAANhB2HFZ9tRzwg4AAHYQdlzm91s3VhZpBwAAKwg7LuN2EQAA2EXYcZmHVQUBALCKsOOyM1mHtAMAgA2EHZedWUHZbj0AALhaEXZcx5gdAABsIuy4jHtjAQBgF2HHZdljdr7ZmUbgAQDAAsKOy/zOuhPo9LW7LdYEAICrE2HHZWff9XzbvqP2KgIAwFWKsOOys8NOFr1YAADkO8KOyzw6k3YYswMAQP4j7LjNp2WHsAMAQH4j7OSjzCzbNQAA4OpD2HHZ6Uxz1s+kHQAA8luhCTujR49W+fLlFRQUpAYNGmj58uW2qyRJOnVWwDlJ2AEAIN8VirDz8ccfq2/fvnrmmWf0zTffqE6dOmrRooVSU1NtV02ZZ03B2rH/mMWaAABwdQqwXYG88NJLL+n+++9Xjx49JEljx47V559/rnfeeUdPPvmk1bqdPfX8q+9/0SerflKDCpE59gEAUJhFhwWpiL+dNpYrPuycPHlSq1atUv/+/Z1tfn5+io+P15IlS875moyMDGVkZDjP09PTXavf7z/YfpPXuvZeAAAUVPMea6aKpYpZee8rPuzs27dPmZmZio6O9tkeHR2t77777pyvGTZsmAYPHpwf1VOz60qpeEgRHTx2SpIUWTRQJ05lXpHT0K/AKgMACgiPxe6MKz7s5Eb//v3Vt29f53l6errKlCnjynsFFfHX6oG3uXJsAABwcVd82ClZsqT8/f21d+9en+179+5VTEzMOV/j9Xrl9Xrzo3oAAMCyK342VmBgoOrVq6e5c+c627KysjR37lzFxcVZrBkAACgIrviWHUnq27evEhMTVb9+fd10000aOXKkjh496szOAgAAV69CEXa6dOmiX375RQMHDlRKSopuuOEGzZ49O8egZQAAcPXxGG7FrfT0dIWHh+vQoUMKCwuzXR0AAHAJLvXv9xU/ZgcAAOBCCDsAAKBQI+wAAIBCjbADAAAKNcIOAAAo1Ag7AACgUCPsAACAQo2wAwAACjXCDgAAKNQKxe0i/qjsRaTT09Mt1wQAAFyq7L/bF7sZBGFH0uHDhyVJZcqUsVwTAABwuQ4fPqzw8PDz7ufeWJKysrK0e/duhYaGyuPx5Nlx09PTVaZMGe3atYt7brmI65x/uNb5g+ucP7jO+cPN62yM0eHDhxUbGys/v/OPzKFlR5Kfn5+uvfZa144fFhbGP6R8wHXOP1zr/MF1zh9c5/zh1nW+UItONgYoAwCAQo2wAwAACjXCjou8Xq+eeeYZeb1e21Up1LjO+YdrnT+4zvmD65w/CsJ1ZoAyAAAo1GjZAQAAhRphBwAAFGqEHQAAUKgRdgAAQKFG2HHR6NGjVb58eQUFBalBgwZavny57SoVWMOGDdONN96o0NBQRUVFqX379tq8ebNPmRMnTigpKUklSpRQsWLF1KlTJ+3du9enzM6dO9WmTRuFhIQoKipK//znP3X69GmfMgsWLNCf/vQneb1eVa5cWePHj3f79Aqs559/Xh6PR3369HG2cZ3zxs8//6y77rpLJUqUUHBwsGrVqqWVK1c6+40xGjhwoEqXLq3g4GDFx8dry5YtPsc4cOCAEhISFBYWpoiICN133306cuSIT5l169apSZMmCgoKUpkyZTRixIh8Ob+CIDMzUwMGDFCFChUUHBysSpUq6dlnn/W5TxLXOXcWLlyotm3bKjY2Vh6PR9OmTfPZn5/XdfLkyapWrZqCgoJUq1YtzZw58/JPyMAVEydONIGBgeadd94xGzduNPfff7+JiIgwe/futV21AqlFixZm3LhxZsOGDWbNmjWmdevWpmzZsubIkSNOmQceeMCUKVPGzJ0716xcudI0bNjQ3Hzzzc7+06dPm5o1a5r4+HizevVqM3PmTFOyZEnTv39/p8yPP/5oQkJCTN++fc23335rRo0aZfz9/c3s2bPz9XwLguXLl5vy5cub2rVrm0ceecTZznX+4w4cOGDKlStnunfvbpYtW2Z+/PFH88UXX5itW7c6ZZ5//nkTHh5upk2bZtauXWvuuOMOU6FCBXP8+HGnTMuWLU2dOnXM0qVLzddff20qV65sunXr5uw/dOiQiY6ONgkJCWbDhg3mo48+MsHBweb111/P1/O1ZejQoaZEiRJmxowZZtu2bWby5MmmWLFi5j//+Y9ThuucOzNnzjRPPfWUmTJlipFkpk6d6rM/v67r4sWLjb+/vxkxYoT59ttvzdNPP22KFCli1q9ff1nnQ9hxyU033WSSkpKc55mZmSY2NtYMGzbMYq2uHKmpqUaS+eqrr4wxxqSlpZkiRYqYyZMnO2U2bdpkJJklS5YYY379x+nn52dSUlKcMmPGjDFhYWEmIyPDGGPM448/bmrUqOHzXl26dDEtWrRw+5QKlMOHD5sqVaqY5ORk06xZMyfscJ3zxhNPPGEaN2583v1ZWVkmJibGvPDCC862tLQ04/V6zUcffWSMMebbb781ksyKFSucMrNmzTIej8f8/PPPxhhjXnvtNVO8eHHnume/d9WqVfP6lAqkNm3amHvvvddnW8eOHU1CQoIxhuucV34fdvLzunbu3Nm0adPGpz4NGjQw//jHPy7rHOjGcsHJkye1atUqxcfHO9v8/PwUHx+vJUuWWKzZlePQoUOSpMjISEnSqlWrdOrUKZ9rWq1aNZUtW9a5pkuWLFGtWrUUHR3tlGnRooXS09O1ceNGp8zZx8guc7V9LklJSWrTpk2Oa8F1zhvTp09X/fr19de//lVRUVGqW7eu3nzzTWf/tm3blJKS4nONwsPD1aBBA5/rHBERofr16ztl4uPj5efnp2XLljllmjZtqsDAQKdMixYttHnzZh08eNDt07Tu5ptv1ty5c/X9999LktauXatFixapVatWkrjObsnP65pXv0sIOy7Yt2+fMjMzff4YSFJ0dLRSUlIs1erKkZWVpT59+qhRo0aqWbOmJCklJUWBgYGKiIjwKXv2NU1JSTnnNc/ed6Ey6enpOn78uBunU+BMnDhR33zzjYYNG5ZjH9c5b/z4448aM2aMqlSpoi+++EK9evXSww8/rHfffVfSmet0od8RKSkpioqK8tkfEBCgyMjIy/osCrMnn3xSXbt2VbVq1VSkSBHVrVtXffr0UUJCgiSus1vy87qer8zlXnfueo4CJykpSRs2bNCiRYtsV6XQ2bVrlx555BElJycrKCjIdnUKraysLNWvX1//+te/JEl169bVhg0bNHbsWCUmJlquXeExadIkTZgwQR9++KFq1KihNWvWqE+fPoqNjeU6wwctOy4oWbKk/P39c8xg2bt3r2JiYizV6srQu3dvzZgxQ/Pnz9e1117rbI+JidHJkyeVlpbmU/7saxoTE3POa56970JlwsLCFBwcnNenU+CsWrVKqamp+tOf/qSAgAAFBAToq6++0iuvvKKAgABFR0dznfNA6dKldf311/tsq169unbu3CnpzHW60O+ImJgYpaam+uw/ffq0Dhw4cFmfRWH2z3/+02ndqVWrlu6++249+uijTqsl19kd+Xldz1fmcq87YccFgYGBqlevnubOnetsy8rK0ty5cxUXF2exZgWXMUa9e/fW1KlTNW/ePFWoUMFnf7169VSkSBGfa7p582bt3LnTuaZxcXFav369zz+w5ORkhYWFOX944uLifI6RXeZq+VyaN2+u9evXa82aNc6jfv36SkhIcH7mOv9xjRo1yrF0wvfff69y5cpJkipUqKCYmBifa5Senq5ly5b5XOe0tDStWrXKKTNv3jxlZWWpQYMGTpmFCxfq1KlTTpnk5GRVrVpVxYsXd+38Copjx47Jz8/3z5i/v7+ysrIkcZ3dkp/XNc9+l1zWcGZcsokTJxqv12vGjx9vvv32W9OzZ08TERHhM4MFZ/Tq1cuEh4ebBQsWmD179jiPY8eOOWUeeOABU7ZsWTNv3jyzcuVKExcXZ+Li4pz92VOib7vtNrNmzRoze/ZsU6pUqXNOif7nP/9pNm3aZEaPHn1VTYk+l7NnYxnDdc4Ly5cvNwEBAWbo0KFmy5YtZsKECSYkJMR88MEHTpnnn3/eREREmE8//dSsW7fOtGvX7pxTd+vWrWuWLVtmFi1aZKpUqeIzdTctLc1ER0ebu+++22zYsMFMnDjRhISEFOop0WdLTEw011xzjTP1fMqUKaZkyZLm8ccfd8pwnXPn8OHDZvXq1Wb16tVGknnppZfM6tWrzY4dO4wx+XddFy9ebAICAsyLL75oNm3aZJ555hmmnhc0o0aNMmXLljWBgYHmpptuMkuXLrVdpQJL0jkf48aNc8ocP37cPPjgg6Z48eImJCTEdOjQwezZs8fnONu3bzetWrUywcHBpmTJkuaxxx4zp06d8ikzf/58c8MNN5jAwEBTsWJFn/e4Gv0+7HCd88Znn31matasabxer6lWrZp54403fPZnZWWZAQMGmOjoaOP1ek3z5s3N5s2bfcrs37/fdOvWzRQrVsyEhYWZHj16mMOHD/uUWbt2rWncuLHxer3mmmuuMc8//7zr51ZQpKenm0ceecSULVvWBAUFmYoVK5qnnnrKZyoz1zl35s+ff87fyYmJicaY/L2ukyZNMtddd50JDAw0NWrUMJ9//vlln4/HmLOWmgQAAChkGLMDAAAKNcIOAAAo1Ag7AACgUCPsAACAQo2wAwAACjXCDgAAKNQIOwAAoFAj7ADAOXg8Hk2bNs12NQDkAcIOgAKne/fu8ng8OR4tW7a0XTUAV6AA2xUAgHNp2bKlxo0b57PN6/Vaqg2AKxktOwAKJK/Xq5iYGJ9H9p2QPR6PxowZo1atWik4OFgVK1bUJ5984vP69evX6y9/+YuCg4NVokQJ9ezZU0eOHPEp884776hGjRryer0qXbq0evfu7bN/37596tChg0JCQlSlShVNnz7d3ZMG4ArCDoAr0oABA9SpUyetXbtWCQkJ6tq1qzZt2iRJOnr0qFq0aKHixYtrxYoVmjx5subMmeMTZsaMGaOkpCT17NlT69ev1/Tp01W5cmWf9xg8eLA6d+6sdevWqXXr1kpISNCBAwfy9TwB5IHLvnUoALgsMTHR+Pv7m6JFi/o8hg4daowxRpJ54IEHfF7ToEED06tXL2OMMW+88YYpXry4OXLkiLP/888/N35+fiYlJcUYY0xsbKx56qmnzlsHSebpp592nh85csRIMrNmzcqz8wSQPxizA6BA+vOf/6wxY8b4bIuMjHR+jouL89kXFxenNWvWSJI2bdqkOnXqqGjRos7+Ro0aKSsrS5s3b5bH49Hu3bvVvHnzC9ahdu3azs9FixZVWFiYUlNTc3tKACwh7AAokIoWLZqjWymvBAcHX1K5IkWK+Dz3eDzKyspyo0oAXMSYHQBXpKVLl+Z4Xr16dUlS9erVtXbtWh09etTZv3jxYvn5+alq1aoKDQ1V+fLlNXfu3HytMwA7aNkBUCBlZGQoJSXFZ1tAQIBKliwpSZo8ebLq16+vxo0ba8KECVq+fLnefvttSVJCQoKeeeYZJSYmatCgQfrll1/00EMP6e6771Z0dLQkadCgQXrggQcUFRWlVq1a6fDhw1q8eLEeeuih/D1RAK4j7AAokGbPnq3SpUv7bKtataq+++47Sb/OlJo4caIefPBBlS5dWh999JGuv/56SVJISIi++OILPfLII7rxxhsVEhKiTp066aWXXnKOlZiYqBMnTujll19Wv379VLJkSd155535d4IA8o3HGGNsVwIALofH49HUqVPVvn1721UBcAVgzA4AACjUCDsAAKBQY8wOgCsOve8ALgctOwAAoFAj7AAAgEKNsAMAAAo1wg4AACjUCDsAAKBQI+wAAIBCjbADAAAKNcIOAAAo1Ag7AACgUPt/Vvo4I9ptYsYAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test input\n",
        "# x_input = np.array([1.0, -1.0])  # 2D input vector\n",
        "x_input = np.random.rand(2)\n",
        "\n",
        "# Compute energy, gradient, and Hessian\n",
        "energy, grad, hess = energy_model_generic.compute_energy_grad_hess(x_input)\n",
        "\n",
        "print(f'x = {x_input[0]} and {x_input[1]}')\n",
        "print(\"Energy:\", energy)        # Scalar\n",
        "print(\"Gradient:\", grad)        # 2x1 vector\n",
        "print(\"Hessian:\\n\", hess)       # 2x2 matrix"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QLTxntmkf4Ji",
        "outputId": "77bfc808-d040-4e98-84e6-398454b4153f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.27230489765106847 and 0.46230977235684834\n",
            "Energy: 0.21519334818903638\n",
            "Gradient: [0.22209338 0.79105191]\n",
            "Hessian:\n",
            " [[0.81560554 0.        ]\n",
            " [0.         1.71108629]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate test data\n",
        "x_test = np.linspace(-5, 5, 500)\n",
        "y_test = np.linspace(-5, 5, 500)\n",
        "x_grid, y_grid = np.meshgrid(x_test, y_test)\n",
        "\n",
        "# Flatten the grid for input into NN\n",
        "input_data = np.vstack([x_grid.ravel(), y_grid.ravel()]).T\n",
        "\n",
        "# Convert to PyTorch tensor\n",
        "input_tensor = torch.tensor(input_data, dtype=torch.float64)\n",
        "\n",
        "# True function: E(x, y) = x^2 + 0.25*y^2\n",
        "true_energy = input_data[:, 0]**2 + 0.25 * input_data[:, 1]**2\n",
        "\n",
        "# NN prediction\n",
        "with torch.no_grad():\n",
        "    predicted_energy = energy_model_generic(input_tensor).numpy().flatten()\n",
        "\n",
        "# Reshape for plotting\n",
        "true_energy_grid = true_energy.reshape(x_grid.shape)\n",
        "predicted_energy_grid = predicted_energy.reshape(x_grid.shape)\n",
        "\n",
        "# Plotting\n",
        "fig, axes = plt.subplots(1, 2, figsize=(12, 6))\n",
        "\n",
        "# True energy\n",
        "im1 = axes[0].imshow(\n",
        "    true_energy_grid, extent=[-5, 5, -5, 5], origin=\"lower\", cmap=\"viridis\"\n",
        ")\n",
        "axes[0].set_title(\"True Energy\")\n",
        "axes[0].set_xlabel(\"x\")\n",
        "axes[0].set_ylabel(\"y\")\n",
        "fig.colorbar(im1, ax=axes[0])\n",
        "\n",
        "# Predicted energy\n",
        "im2 = axes[1].imshow(\n",
        "    predicted_energy_grid, extent=[-5, 5, -5, 5], origin=\"lower\", cmap=\"viridis\"\n",
        ")\n",
        "axes[1].set_title(\"Predicted Energy (NN)\")\n",
        "axes[1].set_xlabel(\"x\")\n",
        "axes[1].set_ylabel(\"y\")\n",
        "fig.colorbar(im2, ax=axes[1])\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "VtwJ8Yp5mRSR",
        "outputId": "ab0493b3-5183-4b11-ec94-ab42dad2be3f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x600 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of Elastic Energy - Stretching Energy in NN-based (Linear Elastic) Formulation"
      ],
      "metadata": {
        "id": "k3i8HXDTtGXc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_energy_stretch_nn(node0, node1, node2=None, l_eff=None, EA=None, nn_model=None):\n",
        "    \"\"\"\n",
        "    Compute the energy using the NN-based solution for strain stretch.\n",
        "\n",
        "    Parameters:\n",
        "        node0 (array-like): Coordinates of node 0.\n",
        "        node1 (array-like): Coordinates of node 1.\n",
        "        node2 (array-like, optional): Coordinates of node 2.\n",
        "        l_eff (float): Effective length.\n",
        "        EA (float): Axial stiffness (Young's modulus * Area).\n",
        "        nn_model (ElasticEnergy): Trained neural network for energy computation.\n",
        "\n",
        "    Returns:\n",
        "        float: Energy computed using the NN-based solution.\n",
        "    \"\"\"\n",
        "    # Compute strain stretch using the existing function\n",
        "    strain_stretch = get_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "\n",
        "    # Use the NN model to compute energy instead of strain_stretch**2.0\n",
        "    strain_tensor = torch.tensor([[strain_stretch]], dtype=torch.float64)\n",
        "    nn_energy_output = nn_model.forward(strain_tensor).item()\n",
        "    # nn_energy_output, grad, hess = nn_model.compute_energy_grad_hess(strain_tensor)\n",
        "\n",
        "    # Scale by EA and l_eff as in the original function\n",
        "    E_s = 0.5 * EA * nn_energy_output * l_eff\n",
        "    return E_s"
      ],
      "metadata": {
        "id": "rfOcZcexkaRE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_energy_stretch_nn(node0, node1, node2 = None, l_eff = None, EA = None, nn_model=None):\n",
        "\n",
        "    strain_stretch = get_strain_stretch2D(node0, node1, node2, l_eff, l_eff) # Geometry, no ML\n",
        "    G_strain, H_strain = grad_and_hess_strain_stretch2D(node0, node1, node2, l_eff, l_eff) # Geometry, no ML\n",
        "\n",
        "    # Use NN module\n",
        "    strain_tensor = torch.tensor([[strain_stretch]], dtype=torch.float64)\n",
        "    _, gradE_strain, hessE_strain = nn_model.compute_energy_grad_hess(strain_tensor)\n",
        "\n",
        "    # Scale\n",
        "    gradE_strain = (0.5 * EA * l_eff) * gradE_strain\n",
        "    hessE_strain = (0.5 * EA * l_eff) * hessE_strain\n",
        "\n",
        "    G = gradE_strain * G_strain\n",
        "    H = gradE_strain * H_strain + hessE_strain * np.outer(G_strain, G_strain)\n",
        "\n",
        "    return G, H"
      ],
      "metadata": {
        "id": "2qfKip3WlI6a"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Define input values for evaluation\n",
        "x_values = [0.1, 1.0]\n",
        "\n",
        "# Evaluate and print gradient and Hessian for each input\n",
        "for x in x_values:\n",
        "    energy, grad, hess = energy_model.compute_energy_grad_hess(x)\n",
        "    print(f\"x = {x}\")\n",
        "    print(f\"Energy (E): {energy}\")\n",
        "    print(f\"Gradient (dE/dx): {grad}\")\n",
        "    print(f\"Hessian (d²E/dx²): {hess}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YKtMryIkMqxS",
        "outputId": "5271cf5f-f1ef-4d89-f200-d4d3b26c6d6b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.1\n",
            "Energy (E): -0.05004644208822895\n",
            "Gradient (dE/dx): 0.21506999400613203\n",
            "Hessian (d²E/dx²): 2.026295641117421\n",
            "x = 1.0\n",
            "Energy (E): 0.9497266782873022\n",
            "Gradient (dE/dx): 1.9894621253755438\n",
            "Hessian (d²E/dx²): 1.9385717953461659\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def test_energy_stretch_nn():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_energy_stretch_nn() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Stretching stiffness\n",
        "  EA = np.random.rand()\n",
        "\n",
        "  # Undeformed configuration (2 nodes, 1 edge)\n",
        "  x0 = np.random.rand(6)\n",
        "  l_0 = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "  l_1 = np.linalg.norm(x0[2:4] - x0[4:6])\n",
        "  l_eff = 0.5 * (l_0 + l_1)\n",
        "\n",
        "  # Deformed configuration (2 nodes, 1 edge)\n",
        "  x = np.random.rand(6)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "  node2 = x[4:6]\n",
        "\n",
        "  # Stretching force and Jacobian\n",
        "  grad, hess = grad_and_hess_energy_stretch_nn(node0, node1, node2, l_eff, EA, energy_model)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-3\n",
        "  # change = np.sqrt(np.finfo(float).eps)  # Optimal perturbation size\n",
        "  energy_ground = get_energy_stretch_nn(node0, node1, node2, l_eff, EA, energy_model)\n",
        "  grad_fdm = np.zeros(6)\n",
        "  hess_fdm = np.zeros((6,6))\n",
        "  for c in range(6):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    node2_plus = x_plus[4:6]\n",
        "    energy_plus = get_energy_stretch_nn(node0_plus, node1_plus, node2_plus, \\\n",
        "                                          l_eff, EA, energy_model)\n",
        "    grad_fdm[c] = (energy_plus - energy_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_energy_stretch_nn(node0_plus, node1_plus, \\\n",
        "                                                  node2_plus, l_eff, EA, energy_model)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "test_energy_stretch_nn()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 927
        },
        "id": "5mn_btTvhXtG",
        "outputId": "ea48ba59-870a-4c93-b3e7-e15cfa573892"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Compare with analytical solution**"
      ],
      "metadata": {
        "id": "WCzch8DbkWxL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example nodes\n",
        "node0 = [0.0, 0.0]\n",
        "node1 = [1.0, 0.1]\n",
        "node2 = [2.0, 0.3]\n",
        "\n",
        "# Parameters\n",
        "l_eff = 2.0\n",
        "EA = 100.0\n",
        "# Compare outputs of both functions\n",
        "energy_linear = get_energy_stretch_linear_elastic(node0, node1, node2, l_eff, EA)\n",
        "energy_nn = get_energy_stretch_nn(node0, node1, node2, l_eff, EA, energy_model)\n",
        "\n",
        "print(f\"Linear Elastic Energy: {energy_linear}\")\n",
        "print(f\"NN-Based Energy: {energy_nn}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5C7lh5a9nvlm",
        "outputId": "a7472a24-65fb-41d2-ce95-76ffd5a1e5c6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Linear Elastic Energy: 24.38405473378666\n",
            "NN-Based Energy: 17.85934298553482\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of Elastic Energy - Bending Energy in NN-based (Linear Elastic) Formulation"
      ],
      "metadata": {
        "id": "BxIwLqv37ems"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_energy_bending_nn(node0, node1, node2 = None, l_eff = None, EA = None, h = None, nn_model=None):\n",
        "\n",
        "  if node2 is None:\n",
        "    return 0\n",
        "\n",
        "  # Get curvature given three nodes\n",
        "  strain_curvature = get_strain_curvature2D(node0, node1, node2)\n",
        "\n",
        "  # Scale strain before passing onto the nn_model\n",
        "  strain_curvature = strain_curvature / l_eff * h\n",
        "  strain_tensor = torch.tensor([[strain_curvature]], dtype=torch.float64)\n",
        "\n",
        "  nn_energy_output = nn_model.forward(strain_tensor).item()\n",
        "\n",
        "  E_b = (0.5 * 0.25 * EA * l_eff) * nn_energy_output\n",
        "  # Note that EI / EA = 1/4 * h^2.\n",
        "  # Eb = 0.5 * EI / l_eff * kappa^2 = (0.5 * 0.25 * EA * l_eff) * (kappa*h/l_eff)^2\n",
        "  return E_b"
      ],
      "metadata": {
        "id": "B4km0k9eEByY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_energy_bending_nn(node0, node1, node2 = None, l_eff = None, EA = None, h = None, nn_model=None):\n",
        "\n",
        "  if node2 is None:\n",
        "    return 0, 0\n",
        "\n",
        "  strain_curvature = get_strain_curvature2D(node0, node1, node2)\n",
        "  G_strain, H_strain = grad_and_hess_strain_curvature2D(node0, node1, node2)\n",
        "\n",
        "  # Use NN module\n",
        "  # Scale strain before passing onto the nn_model\n",
        "  strain_curvature = strain_curvature / l_eff * h\n",
        "  strain_tensor = torch.tensor([[strain_curvature]], dtype=torch.float64)\n",
        "  _, gradE_strain, hessE_strain = nn_model.compute_energy_grad_hess(strain_tensor)\n",
        "  # Scale back\n",
        "  gradE_strain = gradE_strain * h / l_eff\n",
        "  hessE_strain = hessE_strain * h**2 / l_eff**2\n",
        "\n",
        "  G = gradE_strain * G_strain\n",
        "  H = gradE_strain * H_strain + hessE_strain * np.outer(G_strain, G_strain)\n",
        "\n",
        "  G = (0.5 * 0.25 * EA * l_eff) * G\n",
        "  H = (0.5 * 0.25 * EA * l_eff) * H\n",
        "\n",
        "  return G, H"
      ],
      "metadata": {
        "id": "XDLZ09HoEBya"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Parameters\n",
        "EA = np.random.rand()  # Stretching stiffness\n",
        "h = 0.01               # Radius\n",
        "\n",
        "# Undeformed configuration (2 nodes, 1 edge)\n",
        "x0 = np.random.rand(6)\n",
        "l_0 = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "l_1 = np.linalg.norm(x0[2:4] - x0[4:6])\n",
        "l_eff = 0.5 * (l_0 + l_1)\n",
        "\n",
        "# Deformed configuration (2 nodes, 1 edge)\n",
        "x = np.random.rand(6)\n",
        "node0 = x[0:2]\n",
        "node1 = x[2:4]\n",
        "node2 = x[4:6]\n",
        "\n",
        "# Analytical gradient and Hessian\n",
        "grad, hess = grad_and_hess_energy_bending_nn(node0, node1, node2, l_eff, EA, h, energy_model)\n",
        "\n",
        "# Finite difference method\n",
        "perturbation = 1e-3\n",
        "energy_original = get_energy_bending_nn(node0, node1, node2, l_eff, EA, h, energy_model)\n",
        "\n",
        "grad_fdm = np.zeros(6)\n",
        "for c in range(len(x)):\n",
        "    x_perturbed = x.copy()\n",
        "    x_perturbed[c] += perturbation\n",
        "    node0_perturbed = x_perturbed[0:2]\n",
        "    node1_perturbed = x_perturbed[2:4]\n",
        "    node2_perturbed = x_perturbed[4:6]\n",
        "    energy_perturbed = get_energy_bending_nn(node0_perturbed, node1_perturbed, node2_perturbed, l_eff, EA, h, energy_model)\n",
        "    grad_fdm[c] = (energy_perturbed - energy_original) / perturbation\n",
        "\n",
        "# Results comparison\n",
        "print(\"Analytical Gradient:\", grad)\n",
        "print(\"Finite Difference Gradient:\", grad_fdm)\n",
        "\n",
        "# Visualization\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(grad, 'ro-', label='Analytical Gradient')\n",
        "plt.plot(grad_fdm, 'b^--', label='FDM Gradient')\n",
        "plt.xlabel(\"Index\")\n",
        "plt.ylabel(\"Gradient\")\n",
        "plt.legend()\n",
        "plt.title(\"Comparison of Analytical and FDM Gradients\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 556
        },
        "id": "_u0XRI9tnorP",
        "outputId": "9f4a0c2d-86ab-4331-93e8-a46a9f9427b4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Analytical Gradient: [-1.23567813e-03 -3.19130973e-05 -4.03550094e-04 -5.50009159e-04\n",
            "  1.63922822e-03  5.81922257e-04]\n",
            "Finite Difference Gradient: [-1.22884589e-03 -3.18715822e-05 -4.01960782e-04 -5.49498936e-04\n",
            "  1.65236132e-03  5.82558980e-04]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Example nodes\n",
        "node0 = [0.0, 0.0]\n",
        "node1 = [1.0, 0.0]\n",
        "node2 = [2.0, 1.0]\n",
        "\n",
        "# Parameters\n",
        "Y = 5.0 # Young's Modulus\n",
        "h = 1.0\n",
        "l_eff = 2.0\n",
        "EA = Y * np.pi * h**2\n",
        "EI = Y * np.pi * h**4 / 4.0\n",
        "\n",
        "# Compare outputs of both functions\n",
        "energy_linear = get_energy_bending_linear_elastic(node0, node1, node2, l_eff, EI)\n",
        "energy_nn = get_energy_bending_nn(node0, node1, node2, l_eff, EA, h, energy_model)\n",
        "\n",
        "print(f\"Linear Elastic Energy: {energy_linear}\")\n",
        "print(f\"NN-Based Energy: {energy_nn}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wu0245GzEFzW",
        "outputId": "ece69135-cfce-4643-ca28-7433ed348a62"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Linear Elastic Energy: 0.673765105565809\n",
            "NN-Based Energy: 0.4600519479067172\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def test_energy_bending_nn():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_energy_stretch_nn() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Stretching stiffness\n",
        "  EA = np.random.rand()\n",
        "  # Radius\n",
        "  h = 0.01\n",
        "\n",
        "  # Undeformed configuration (2 nodes, 1 edge)\n",
        "  x0 = np.random.rand(6)\n",
        "  l_0 = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "  l_1 = np.linalg.norm(x0[2:4] - x0[4:6])\n",
        "  l_eff = 0.5 * (l_0 + l_1)\n",
        "\n",
        "  # Deformed configuration (2 nodes, 1 edge)\n",
        "  x = np.random.rand(6)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "  node2 = x[4:6]\n",
        "\n",
        "  # Stretching force and Jacobian\n",
        "  grad, hess = grad_and_hess_energy_bending_nn(node0, node1, node2, l_eff, EA, h, energy_model)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-6\n",
        "  # change = np.sqrt(np.finfo(float).eps)  # Optimal perturbation size\n",
        "  energy_ground = get_energy_bending_nn(node0, node1, node2, l_eff, EA, h, energy_model)\n",
        "  grad_fdm = np.zeros(6)\n",
        "  hess_fdm = np.zeros((6,6))\n",
        "  for c in range(6):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    node2_plus = x_plus[4:6]\n",
        "    energy_plus = get_energy_bending_nn(node0_plus, node1_plus, node2_plus, \\\n",
        "                                          l_eff, EA, h, energy_model)\n",
        "    grad_fdm[c] = (energy_plus - energy_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_energy_bending_nn(node0_plus, node1_plus, \\\n",
        "                                                  node2_plus, l_eff, EA, h, energy_model)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "test_energy_bending_nn()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 927
        },
        "id": "jVgYgNRFlwX7",
        "outputId": "6b3e57d9-89c8-48c4-f031-cc1b0ef74c1d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Gradient and Hessian of GENERAL Elastic Energy (Bending+Stretching) in NN-based Formulation"
      ],
      "metadata": {
        "id": "24QqW0t0qpW1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def get_energy_elastic_nn_generic(node0, node1, node2=None, l_eff=None, EA=None, h = None, nn_model_generic=None):\n",
        "    \"\"\"\n",
        "    Compute the energy using the NN-based solution for elastic energy.\n",
        "\n",
        "    Parameters:\n",
        "        node0 (array-like): Coordinates of node 0.\n",
        "        node1 (array-like): Coordinates of node 1.\n",
        "        node2 (array-like, optional): Coordinates of node 2.\n",
        "        l_eff (float): Effective length.\n",
        "        EA (float): Axial stiffness (Young's modulus * Area).\n",
        "        nn_model (ElasticEnergy): Trained neural network for energy computation.\n",
        "\n",
        "    Returns:\n",
        "        float: Energy computed using the NN-based solution.\n",
        "    \"\"\"\n",
        "    # Compute stretch and curvature using the existing function\n",
        "    strain_stretch = get_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "    strain_curvature = get_strain_curvature2D(node0, node1, node2)\n",
        "    strain_curvature = strain_curvature / l_eff * h # Scale strain before passing onto the nn_model\n",
        "\n",
        "    # Use the NN model to compute energy\n",
        "    strain_tensor = torch.tensor([[strain_stretch, strain_curvature]], dtype=torch.float64)\n",
        "    nn_energy_output = nn_model_generic(strain_tensor).item()\n",
        "\n",
        "    # Scale by EA and l_eff as in the original function\n",
        "    E_elastic = (0.5 * EA * l_eff) * nn_energy_output\n",
        "\n",
        "    return E_elastic"
      ],
      "metadata": {
        "id": "YsLTjZcXrCdu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def grad_and_hess_energy_elastic_nn_generic(node0, node1, node2 = None, l_eff = None, EA = None, h = None, nn_model_generic=None):\n",
        "\n",
        "    if node2 is None:\n",
        "      # Edge case handling with zero curvature and two nodes\n",
        "      # It should return gradient of size 4 and Hessian of size 4x4\n",
        "      if node2 is None:\n",
        "        # Compute stretch and curvature using the existing function\n",
        "        strain_stretch = get_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "        strain_curvature = 0.0\n",
        "\n",
        "        # Compute gradient and hessian of strains\n",
        "        G_strain_stretch, H_strain_stretch = grad_and_hess_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "\n",
        "        # Use NN module\n",
        "        strain_tensor = torch.tensor([[strain_stretch, strain_curvature]], dtype=torch.float64)\n",
        "        _, gradE_strain, hessE_strain = nn_model_generic.compute_energy_grad_hess(strain_tensor)\n",
        "\n",
        "        # Scale\n",
        "        gradE_strain = (0.5 * EA * l_eff) * gradE_strain\n",
        "        hessE_strain = (0.5 * EA * l_eff) * hessE_strain\n",
        "\n",
        "        G = gradE_strain[0] * G_strain_stretch\n",
        "        H = gradE_strain[0] * H_strain_stretch + \\\n",
        "        hessE_strain[0,0] * np.outer(G_strain_stretch, G_strain_stretch)\n",
        "\n",
        "      return G, H\n",
        "\n",
        "    # Compute stretch and curvature using the existing function\n",
        "    strain_stretch = get_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "    strain_curvature = get_strain_curvature2D(node0, node1, node2)\n",
        "    strain_curvature = strain_curvature / l_eff * h # Scale strain before passing onto the nn_model\n",
        "\n",
        "    # Compute gradient and hessian of strains\n",
        "    G_strain_stretch, H_strain_stretch = grad_and_hess_strain_stretch2D(node0, node1, node2, l_eff, l_eff)\n",
        "    G_strain_curvature, H_strain_curvature = grad_and_hess_strain_curvature2D(node0, node1, node2)\n",
        "    # Scale back\n",
        "    G_strain_curvature = G_strain_curvature * h / l_eff\n",
        "    H_strain_curvature = H_strain_curvature * h**2 / l_eff**2\n",
        "\n",
        "    # Use NN module\n",
        "    strain_tensor = torch.tensor([[strain_stretch, strain_curvature]], dtype=torch.float64)\n",
        "    _, gradE_strain, hessE_strain = nn_model_generic.compute_energy_grad_hess(strain_tensor)\n",
        "\n",
        "    # Scale\n",
        "    gradE_strain = (0.5 * EA * l_eff) * gradE_strain\n",
        "    hessE_strain = (0.5 * EA * l_eff) * hessE_strain\n",
        "\n",
        "    G = gradE_strain[0] * G_strain_stretch + gradE_strain[1] * G_strain_curvature\n",
        "    H = gradE_strain[0] * H_strain_stretch + \\\n",
        "    hessE_strain[0,0] * np.outer(G_strain_stretch, G_strain_stretch) + \\\n",
        "    hessE_strain[0,1] * np.outer(G_strain_stretch, G_strain_curvature) + \\\n",
        "    gradE_strain[1] * H_strain_curvature + \\\n",
        "    hessE_strain[1,1] * np.outer(G_strain_curvature, G_strain_curvature) + \\\n",
        "    hessE_strain[1,0] * np.outer(G_strain_curvature, G_strain_stretch)\n",
        "\n",
        "    return G, H"
      ],
      "metadata": {
        "id": "RrfqK7VarN60"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_energy_elastic_nn_generic():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  grad_and_hess_energy_stretch_nn() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Stretching stiffness\n",
        "  EA = np.random.rand()\n",
        "\n",
        "  # Undeformed configuration (2 nodes, 1 edge)\n",
        "  x0 = np.random.rand(6)\n",
        "  l_0 = np.linalg.norm(x0[0:2] - x0[2:4])\n",
        "  l_1 = np.linalg.norm(x0[2:4] - x0[4:6])\n",
        "  l_eff = 0.5 * (l_0 + l_1)\n",
        "\n",
        "  h = 0.001 # radius\n",
        "\n",
        "  # Deformed configuration (2 nodes, 1 edge)\n",
        "  x = np.random.rand(6)\n",
        "  node0 = x[0:2]\n",
        "  node1 = x[2:4]\n",
        "  node2 = x[4:6]\n",
        "\n",
        "  # Force and Jacobian\n",
        "  grad, hess = grad_and_hess_energy_elastic_nn_generic(node0, node1, node2, l_eff, EA, h, energy_model_generic)\n",
        "\n",
        "  # Use FDM to compute Fs and Js\n",
        "  change = 1e-3\n",
        "  # change = np.sqrt(np.finfo(float).eps)  # Optimal perturbation size\n",
        "  energy_ground = get_energy_elastic_nn_generic(node0, node1, node2, l_eff, EA, h, energy_model_generic)\n",
        "  grad_fdm = np.zeros(6)\n",
        "  hess_fdm = np.zeros((6,6))\n",
        "  for c in range(6):\n",
        "    x_plus = x.copy()\n",
        "    x_plus[c] += change\n",
        "    node0_plus = x_plus[0:2]\n",
        "    node1_plus = x_plus[2:4]\n",
        "    node2_plus = x_plus[4:6]\n",
        "    energy_plus = get_energy_elastic_nn_generic(node0_plus, node1_plus, node2_plus, \\\n",
        "                                          l_eff, EA, h, energy_model_generic)\n",
        "    grad_fdm[c] = (energy_plus - energy_ground) / change\n",
        "\n",
        "    grad_change, _ = grad_and_hess_energy_elastic_nn_generic(node0_plus, node1_plus, \\\n",
        "                                                  node2_plus, l_eff, EA, h, energy_model_generic)\n",
        "    hess_fdm[:,c] = (grad_change - grad) / change\n",
        "\n",
        "  # First plot: Forces (Gradients)\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(1)\n",
        "  plt.plot(grad, 'ro', label='Analytical')  # Plot analytical forces\n",
        "  plt.plot(grad_fdm, 'b^', label='Finite Difference')  # Plot finite difference forces\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Gradient')  # Y-axis label\n",
        "  plt.title('Forces (Gradients) Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "\n",
        "  # Second plot: Hessians\n",
        "  plt.figure(2)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(hess.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(hess_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "test_energy_elastic_nn_generic()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 927
        },
        "id": "4MirHLlbrUil",
        "outputId": "8ef71f91-dcaf-4754-e061-dddd32aeb521"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Compute the elastic force, given the DOF vector"
      ],
      "metadata": {
        "id": "bUNRNfKpwFZb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class ElasticForce():\n",
        "  def __init__(self, l_eff_vector, EA, EI = 1.0, h = 1.0, model_choice = 1, nn_model = None):\n",
        "    self.l_eff_vector = l_eff_vector\n",
        "    self.EA = EA\n",
        "    self.EI = EI\n",
        "    self.h = h\n",
        "    self.N = len( l_eff_vector ) # Number of nodes\n",
        "    self.ndof = int(self.N * 2) # Number of DOFs\n",
        "    self.model_choice = model_choice # 1 for linear elastic, 2 for NN\n",
        "    self.nn_model = nn_model\n",
        "\n",
        "  def computeGradientHessian(self, q):\n",
        "    G = np.zeros( self.ndof )\n",
        "    H = np.zeros( (self.ndof, self.ndof) )\n",
        "\n",
        "    for i in range( self.N ):\n",
        "      l_eff = self.l_eff_vector[i]\n",
        "\n",
        "      if i == 0:\n",
        "        node0 = q[2*i:2*i+2]\n",
        "        node1 = q[2*i+2:2*i+4]\n",
        "        node2 = None\n",
        "        ind = np.array([2*i, 2*i+1, 2*i+2, 2*i+3])\n",
        "      elif i == self.N - 1:\n",
        "        node0 = q[2*i-2:2*i  ]\n",
        "        node1 = q[2*i  :2*i+2]\n",
        "        node2 = None\n",
        "        ind = np.array([2*i-2, 2*i-1, 2*i, 2*i+1])\n",
        "      else:\n",
        "        node0 = q[2*i-2:2*i  ]\n",
        "        node1 = q[2*i  :2*i+2]\n",
        "        node2 = q[2*i+2:2*i+4]\n",
        "        ind = np.array([2*i-2, 2*i-1, 2*i, 2*i+1,2*i+2, 2*i+3])\n",
        "\n",
        "      if self.model_choice == 1: # Linear Elastic\n",
        "        dG1, dH1 = grad_and_hess_energy_stretch_linear_elastic(node0, node1, node2, l_eff, self.EA)\n",
        "        dG2, dH2 = grad_and_hess_energy_bending_linear_elastic(node0, node1, node2, l_eff, self.EI)\n",
        "        dG = dG1 + dG2\n",
        "        dH = dH1 + dH2\n",
        "      elif self.model_choice == 2: # NN-based (separable and simplified)\n",
        "        dG1, dH1 = grad_and_hess_energy_stretch_nn(node0, node1, node2, l_eff, self.EA, self.nn_model)\n",
        "        dG2, dH2 = grad_and_hess_energy_bending_nn(node0, node1, node2, l_eff, self.EA, self.h, self.nn_model)\n",
        "        dG = dG1 + dG2\n",
        "        dH = dH1 + dH2\n",
        "      else: # NN-based GENERIC (allows coupling between stretching and bending)\n",
        "        dG, dH = grad_and_hess_energy_elastic_nn_generic(node0, node1, node2, l_eff, self.EA, self.h, self.nn_model)\n",
        "\n",
        "      G[ind] = G[ind] + dG\n",
        "      H[np.ix_(ind, ind)] = H[np.ix_(ind, ind)] + dH\n",
        "\n",
        "    return G, H"
      ],
      "metadata": {
        "id": "2h0riRBOwEpx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def computeReferenceLength(q):\n",
        "  ndof = len( q )\n",
        "  N = ndof // 2\n",
        "  l_eff_vector = np.zeros(N)\n",
        "  for i in range( N):\n",
        "    if i == 0:\n",
        "      node0 = q[2*i:2*i+2]\n",
        "      node1 = q[2*i+2:2*i+4]\n",
        "      l_eff_vector[i] = np.linalg.norm(node0 - node1)\n",
        "    elif i == N - 1:\n",
        "      node0 = q[2*i-2: 2*i]\n",
        "      node1 = q[2*i  : 2*i+2]\n",
        "      l_eff_vector[i] = np.linalg.norm(node0 - node1)\n",
        "    else:\n",
        "      node0 = q[2*i-2:2*i]\n",
        "      node1 = q[2*i:2*i+2]\n",
        "      node2 = q[2*i+2:2*i+4]\n",
        "      l_eff_vector[i] = 0.5 * (np.linalg.norm(node0 - node1) + np.linalg.norm(node1 - node2))\n",
        "\n",
        "  return l_eff_vector"
      ],
      "metadata": {
        "id": "GSX44kE-1gMY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def test_ElasticForce():\n",
        "  # Define a test q vector (4 nodes with 2 DOFs each)\n",
        "  q = np.array([0.0, 0.0,   # Node 0\n",
        "    1.0, 0.0,   # Node 1\n",
        "    2.0, 0.0,   # Node 2\n",
        "    3.0, 0.0])  # Node 3\n",
        "  l_eff_vector = computeReferenceLength(q)\n",
        "  print(l_eff_vector)\n",
        "\n",
        "  Y = 5.0\n",
        "  h = 0.01\n",
        "  EA = Y * np.pi * h**2.0\n",
        "  EI = Y * np.pi / 4.0 * h**4.0\n",
        "  model_choice = 3\n",
        "\n",
        "  if model_choice == 1 or model_choice == 2: # Linear elastic\n",
        "    elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice)\n",
        "  elif model_choice == 2: # NN-based (simplified)\n",
        "    elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice, energy_model)\n",
        "  else: # Generic NN-based with coupling allowed\n",
        "    elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice, energy_model_generic)\n",
        "\n",
        "  F_elastic, J_elastic = elForce.computeGradientHessian(q)\n",
        "  print(F_elastic)\n",
        "  print(J_elastic)\n",
        "\n",
        "  return\n",
        "\n",
        "test_ElasticForce()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AlNxNbU_1JSd",
        "outputId": "41f22b9c-0e05-40e4-c83d-b8a615116d8a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1. 1. 1. 1.]\n",
            "[0. 0. 0. 0. 0. 0. 0. 0.]\n",
            "[[-2.64693195e-06  0.00000000e+00  1.32346597e-06  0.00000000e+00\n",
            "   1.32346597e-06  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
            " [ 0.00000000e+00  4.89399556e-10  0.00000000e+00 -9.78799112e-10\n",
            "   0.00000000e+00  4.89399556e-10  0.00000000e+00  0.00000000e+00]\n",
            " [ 1.32346597e-06  0.00000000e+00 -2.64693195e-06  0.00000000e+00\n",
            "   0.00000000e+00  0.00000000e+00  1.32346597e-06  0.00000000e+00]\n",
            " [ 0.00000000e+00 -9.78799112e-10  0.00000000e+00  2.44699778e-09\n",
            "   0.00000000e+00 -1.95759822e-09  0.00000000e+00  4.89399556e-10]\n",
            " [ 1.32346597e-06  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
            "  -2.64693195e-06  0.00000000e+00  1.32346597e-06  0.00000000e+00]\n",
            " [ 0.00000000e+00  4.89399556e-10  0.00000000e+00 -1.95759822e-09\n",
            "   0.00000000e+00  2.44699778e-09  0.00000000e+00 -9.78799112e-10]\n",
            " [ 0.00000000e+00  0.00000000e+00  1.32346597e-06  0.00000000e+00\n",
            "   1.32346597e-06  0.00000000e+00 -2.64693195e-06  0.00000000e+00]\n",
            " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  4.89399556e-10\n",
            "   0.00000000e+00 -9.78799112e-10  0.00000000e+00  4.89399556e-10]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Finite Difference Validation**"
      ],
      "metadata": {
        "id": "kA9TUGj97m-l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def FDM_ElasticForce():\n",
        "  '''\n",
        "  This function tests the outputs (gradient and hessian) of\n",
        "  computeGradientHessian() of theElasticForce() against their finite difference\n",
        "  approximations.\n",
        "  '''\n",
        "\n",
        "  # Define a test q vector (4 nodes with 2 DOFs each)\n",
        "  q = np.array([0.0, 0.0,   # Node 0\n",
        "    1.0, 0.0,   # Node 1\n",
        "    2.0, 0.2,   # Node 2\n",
        "    3.0, 0.5])  # Node 3\n",
        "\n",
        "\n",
        "  # Create reference lengths: Intentionally perturb it so that axial stretch is not all 0's.\n",
        "  l_eff_vector = computeReferenceLength(q)\n",
        "  random_factors = np.random.uniform(0.9, 1.1, size=l_eff_vector.shape)\n",
        "  l_eff_vector = l_eff_vector * random_factors\n",
        "\n",
        "  ndof = len(q)\n",
        "\n",
        "  Y = 5.0\n",
        "  h = 0.01\n",
        "  EA = Y * np.pi * h**2.0\n",
        "  EI = Y * np.pi / 4.0 * h**4.0\n",
        "  model_choice = 3\n",
        "  if model_choice == 1: # Linear Elastic\n",
        "    elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice, energy_model)\n",
        "  elif model_choice == 2: # NN-based (simplified, separable)\n",
        "    elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice, energy_model)\n",
        "  else: # Generic NN-based (coupled)\n",
        "    elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice, energy_model_generic)\n",
        "\n",
        "  # Gradient and Hessian and Jacobian\n",
        "  F_elastic, J_elastic = elForce.computeGradientHessian(q)\n",
        "\n",
        "  change = 1.0e-5\n",
        "  J_fdm = np.zeros((ndof,ndof))\n",
        "  for c in range(ndof):\n",
        "    q_plus = q.copy()\n",
        "    q_plus[c] += change\n",
        "    F_change, _ = elForce.computeGradientHessian(q_plus)\n",
        "    J_fdm[:,c] = (F_change - F_elastic) / change\n",
        "\n",
        "  # Plot: Hessians\n",
        "  plt.figure(1)  # Equivalent to MATLAB's figure(2)\n",
        "  plt.plot(J_elastic.flatten(), 'ro', label='Analytical')  # Flatten and plot analytical Hessian\n",
        "  plt.plot(J_fdm.flatten(), 'b^', label='Finite Difference')  # Flatten and plot finite difference Hessian\n",
        "  plt.legend(loc='best')  # Display the legend\n",
        "  plt.xlabel('Index')  # X-axis label\n",
        "  plt.ylabel('Hessian')  # Y-axis label\n",
        "  plt.title('Hessian Comparison')  # Optional title\n",
        "  plt.show()  # Show the plot\n",
        "  return\n",
        "\n",
        "FDM_ElasticForce()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "NUMg9O-1KAEK",
        "outputId": "c7386344-ce8f-4e61-d7ab-d9bd99942ddf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Boundary Condition\n",
        "**This should provide an interface to set and release boundary conditions. This class is passed onto the timeStepper. The class \"timeStepper\" uses fixedDOFs and fixedIndices during it's linear system solve.**"
      ],
      "metadata": {
        "id": "PbquShrePtCG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class BoundaryConditions:\n",
        "    def __init__(self, ndof):\n",
        "        \"\"\"\n",
        "        Initialize boundary conditions.\n",
        "\n",
        "        Parameters:\n",
        "            ndof (int): Total number of degrees of freedom (DOFs).\n",
        "        \"\"\"\n",
        "        self.ndof = ndof\n",
        "        self.fixedIndices = []  # List for fixed DOFs\n",
        "        self.fixedDOFs = []  # List for fixed boundary condition values\n",
        "        self.freeIndices = list(range(ndof))  # Initialize free DOFs (0 to ndof-1)\n",
        "\n",
        "    def setBoundaryConditionNode(self, i, x):\n",
        "        \"\"\"\n",
        "        Add or update boundary conditions for a node.\n",
        "\n",
        "        Parameters:\n",
        "            i (int): Node index.\n",
        "            x (numpy.ndarray): Array of size 2 representing boundary condition values.\n",
        "        \"\"\"\n",
        "        if not isinstance(x, np.ndarray) or x.shape != (2,):\n",
        "            raise ValueError(\"x must be a numpy array of size 2.\")\n",
        "\n",
        "        # Calculate the DOFs for this node\n",
        "        dof_1, dof_2 = 2 * i, 2 * i + 1\n",
        "\n",
        "        # Check if DOFs are already in fixedDOFs\n",
        "        if dof_1 in self.fixedIndices and dof_2 in self.fixedIndices:\n",
        "            # Find their indices in fixedDOFs\n",
        "            index_1 = self.fixedIndices.index(dof_1)\n",
        "            index_2 = self.fixedIndices.index(dof_2)\n",
        "\n",
        "            # Update corresponding values in fixedIndices\n",
        "            self.fixedDOFs[index_1] = x[0]\n",
        "            self.fixedDOFs[index_2] = x[1]\n",
        "        else:\n",
        "            # Add new DOFs and corresponding values\n",
        "            self.fixedIndices.extend([dof_1, dof_2])\n",
        "            self.fixedDOFs.extend(x.copy().tolist())  # Convert NumPy array to list for storage\n",
        "\n",
        "            # Remove the DOFs from freeIndices\n",
        "            self.freeIndices.remove(dof_1)\n",
        "            self.freeIndices.remove(dof_2)\n",
        "\n",
        "    def releaseBoundaryConditionNode(self, i):\n",
        "        \"\"\"\n",
        "        Release the boundary conditions for a node.\n",
        "\n",
        "        Parameters:\n",
        "            i (int): Node index to release.\n",
        "        \"\"\"\n",
        "        # Calculate the DOFs for this node\n",
        "        dof_1, dof_2 = 2 * i, 2 * i + 1\n",
        "\n",
        "        # Remove DOFs and corresponding indices if they exist\n",
        "        if dof_1 in self.freeIndices and dof_2 in self.freeIndices:\n",
        "            # Find their indices in fixedDOFs\n",
        "            index_1 = self.freeIndices.index(dof_1)\n",
        "            index_2 = self.freeIndices.index(dof_2)\n",
        "\n",
        "            # Remove the DOFs from fixedDOFs and corresponding values from fixedIndices\n",
        "            del self.freeIndices[index_2]  # Remove larger index first\n",
        "            del self.freeIndices[index_1]\n",
        "            del self.fixedDOFs[index_2]\n",
        "            del self.fixedDOFs[index_1]\n",
        "\n",
        "            # Add the DOFs back to freeIndices\n",
        "            self.freeIndices.append(dof_1)\n",
        "            self.freeIndices.append(dof_2)\n",
        "\n",
        "            # Keep freeIndices sorted\n",
        "            self.freeIndices.sort()\n",
        "\n",
        "    def getBoundaryConditions(self):\n",
        "        \"\"\"\n",
        "        Returns the current boundary conditions as a tuple.\n",
        "\n",
        "        Returns:\n",
        "            tuple: (fixedDOFs, fixedIndices, freeIndices)\n",
        "        \"\"\"\n",
        "        return self.fixedDOFs, np.array(self.fixedIndices), self.freeIndices"
      ],
      "metadata": {
        "id": "H9rMdk1oPsgr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Test Function**"
      ],
      "metadata": {
        "id": "B7mTHoY0Ryeg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Initialize with 6 DOFs\n",
        "bc = BoundaryConditions(ndof=6)\n",
        "\n",
        "# Add boundary conditions for node 0\n",
        "x0 = np.array([1.0, 2.0])\n",
        "bc.setBoundaryConditionNode(0, x0)\n",
        "\n",
        "# Add boundary conditions for node 1\n",
        "x1 = np.array([3.0, 4.0])\n",
        "bc.setBoundaryConditionNode(1, x1)\n",
        "\n",
        "# Check boundary conditions and free DOFs\n",
        "print(\"After adding boundary conditions:\")\n",
        "fixedDOFs, fixedIndices, freeIndices = bc.getBoundaryConditions()\n",
        "print(\"Fixed DOFs:\", fixedDOFs)        # Expected: [0, 1, 2, 3]\n",
        "print(\"Fixed Indices:\", fixedIndices)  # Expected: [1.0, 2.0, 3.0, 4.0]\n",
        "print(\"Free DOFs:\", freeIndices)       # Expected: [4, 5]\n",
        "\n",
        "# Release boundary conditions for node 0\n",
        "bc.releaseBoundaryConditionNode(0)\n",
        "\n",
        "# Check boundary conditions and free DOFs after releasing\n",
        "print(\"\\nAfter releasing boundary conditions for node 0:\")\n",
        "fixedDOFs, fixedIndices, freeIndices = bc.getBoundaryConditions()\n",
        "print(\"Fixed DOFs:\", fixedDOFs)        # Expected: [2, 3]\n",
        "print(\"Fixed Indices:\", fixedIndices)  # Expected: [3.0, 4.0]\n",
        "print(\"Free DOFs:\", freeIndices)       # Expected: [0, 1, 4, 5]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mImcBbWkQPf1",
        "outputId": "fbe9530d-bb93-4e17-d3ee-5a90500e62d1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "After adding boundary conditions:\n",
            "Fixed DOFs: [1.0, 2.0, 3.0, 4.0]\n",
            "Fixed Indices: [0 1 2 3]\n",
            "Free DOFs: [4, 5]\n",
            "\n",
            "After releasing boundary conditions for node 0:\n",
            "Fixed DOFs: [1.0, 2.0, 3.0, 4.0]\n",
            "Fixed Indices: [0 1 2 3]\n",
            "Free DOFs: [4, 5]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Objective Function"
      ],
      "metadata": {
        "id": "iSDGzfyztOBW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class timeStepper:\n",
        "  def __init__(self, massVector, dt, qtol, maxIter, g, boundaryCondition, elasticModel):\n",
        "    self.massVector = massVector\n",
        "    self.ndof = len(massVector) # Number of degrees of freedom\n",
        "    if self.ndof % 2 == 1:\n",
        "      raise ValueError(\"Constructor of timeStepper: Number of degrees of freedom must be even.\")\n",
        "    self.N = self.ndof // 2 # Number of nodes\n",
        "\n",
        "    self.dt = dt # Time step size\n",
        "    self.qtol = qtol # Tolerance on position\n",
        "    self.maxIter = maxIter # Maximum iterations\n",
        "    self.g = g # Gravity\n",
        "\n",
        "    self.Fg = np.zeros(self.ndof)\n",
        "    self.makeWeight()\n",
        "\n",
        "    # Make a diagonal mass matrix\n",
        "    self.massMatrix = np.zeros((self.ndof, self.ndof))\n",
        "    self.makeMassMatrix()\n",
        "\n",
        "    # Boundary Condition (BC)\n",
        "    self.bc = boundaryCondition\n",
        "\n",
        "    # Model for elastic force\n",
        "    self.elasticModel = elasticModel\n",
        "\n",
        "  def makeMassMatrix(self):\n",
        "    '''\n",
        "    Compute the mass matrix.\n",
        "    '''\n",
        "    for i in range(self.ndof):\n",
        "      self.massMatrix[i,i] = self.massVector[i]\n",
        "\n",
        "  def makeWeight(self):\n",
        "    '''\n",
        "      Compute the weight vector.\n",
        "    '''\n",
        "    if len(g) != 2:\n",
        "      raise ValueError(\"makeWeight of timeStepper: Gravity vector must be of length 2.\")\n",
        "    for i in range(self.N):\n",
        "      self.Fg[2*i:2*i+2] = self.massVector[2*i:2*i+2] * self.g\n",
        "\n",
        "  def beforeTimeStep(self) -> None:\n",
        "    '''\n",
        "    Take care of any business that should be done BEFORE a time step.\n",
        "    '''\n",
        "    pass\n",
        "\n",
        "\n",
        "  def afterTimeStep(self) -> None:\n",
        "    '''\n",
        "    Take care of any business that should be done AFTER a time step.\n",
        "      '''\n",
        "    return\n",
        "\n",
        "  def simulate(self, q_guess, q_old, u_old, a_old):\n",
        "    '''\n",
        "    The main simulation loop that takes in the OLD state (DOFs, their first\n",
        "    and second derivatives, i.e., velocities and accelerations) and outputs\n",
        "    the NEW state.\n",
        "    '''\n",
        "\n",
        "    q_new = q_guess.copy()\n",
        "\n",
        "    # Impose boundary conditions\n",
        "    for k in range(len(bc.fixedIndices)):\n",
        "      q_new[bc.fixedIndices[k]] = bc.fixedDOFs[k]\n",
        "\n",
        "    error = 10 * self.qtol # Initialize error to a value larger than tolerance\n",
        "    iter = 0 # Iteration number\n",
        "\n",
        "    while error > self.qtol and iter < self.maxIter:\n",
        "      #\n",
        "      # Personal notes: I want it to quit without linear solve when steady\n",
        "      # state is achieved. Perhaps, set a utol or ftol for that.\n",
        "      # Right now, it executes linear solve no matter what.\n",
        "      #\n",
        "\n",
        "      gradE, hessE = self.elasticModel.computeGradientHessian(q_new)\n",
        "      inertiaF = (massVector / dt) * (((q_new - q_old) / dt) - u_old)\n",
        "\n",
        "      # Compute the force and Jacobian\n",
        "      force = inertiaF + gradE - self.Fg\n",
        "      J = (self.massMatrix / dt**2) + hessE\n",
        "\n",
        "      # Extract the free components\n",
        "      freeIndex = self.bc.freeIndices\n",
        "      f_free = force[freeIndex]\n",
        "      J_free = J[np.ix_(freeIndex, freeIndex)]\n",
        "      dq_free = np.linalg.solve(J_free, f_free)\n",
        "\n",
        "      # Update error and iteration number\n",
        "      error = np.linalg.norm(dq_free)\n",
        "      iter += 1\n",
        "\n",
        "      print(f'iter={iter} error={error}')\n",
        "\n",
        "      # Update the DOFs\n",
        "      q_new[freeIndex] = q_new[freeIndex] - dq_free\n",
        "\n",
        "\n",
        "    u_new = (q_new - q_old) / dt\n",
        "    a_new = force / self.massVector\n",
        "\n",
        "    if error < self.qtol:\n",
        "      flag = True # Simulation converged successfully\n",
        "    else:\n",
        "      flag = False # Simulation did not converge\n",
        "\n",
        "    return q_new, u_new, a_new, flag"
      ],
      "metadata": {
        "id": "-4bvVB76tcrd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Main Function"
      ],
      "metadata": {
        "id": "0Ig9ZyLuZ4jn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Geometry\n",
        "N = 10 # Number of nodes\n",
        "ndof = N * 2 # Number of DOFs\n",
        "RodLength = 0.1 # Length of rod in meter\n",
        "q = np.zeros(ndof)\n",
        "for k in range(N):\n",
        "  q[2*k] = k * RodLength / (N-1.0)\n",
        "  q[2*k+1] = 0\n",
        "\n",
        "# Compute l_eff\n",
        "# TODO: Should be delegated to elastic energy model\n",
        "l_eff_vector = computeReferenceLength(q)\n",
        "\n",
        "# Set up boundary condition\n",
        "bc = BoundaryConditions(ndof)\n",
        "\n",
        "# Set up elastic energy model\n",
        "Y = 10.0e8\n",
        "h = 0.001\n",
        "EA = Y * np.pi * h**2.0\n",
        "EI = Y * np.pi / 4.0 * h**4.0\n",
        "model_choice = 1 # 1 is analytical, 2 is separable (simplified) NN, and 3 is generic\n",
        "if model_choice == 1 or model_choice == 2:\n",
        "  elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice, energy_model)\n",
        "else:\n",
        "  elForce = ElasticForce(l_eff_vector, EA, EI, h, model_choice, energy_model_generic)\n",
        "\n",
        "# Mass Vector\n",
        "totalMass = 0.2\n",
        "massVector = np.zeros(ndof)\n",
        "massVector[:] = totalMass / N\n",
        "\n",
        "# Define timeStepper\n",
        "dt = 0.01 # Time step size in second\n",
        "qtol = 0.001 # Tolerance on position change\n",
        "maxIter = 10 # Maximum number of iterations\n",
        "g = np.array([0.0, -9.81])\n",
        "stepper = timeStepper(massVector, dt, qtol, maxIter, g, bc, elForce)"
      ],
      "metadata": {
        "id": "_R-kpgDyYRqV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import clear_output\n",
        "\n",
        "# Boundary conditions\n",
        "bc.setBoundaryConditionNode(0, q[0:2])\n",
        "bc.setBoundaryConditionNode(1, q[2:4])\n",
        "\n",
        "# Main simulation loop\n",
        "totalTime = 10.0 # Total Simulation Time\n",
        "q_old = q.copy()\n",
        "u_old = np.zeros(ndof)\n",
        "a_old = np.zeros(ndof)\n",
        "\n",
        "time_iter = 0\n",
        "for t in np.arange(0, totalTime, dt):\n",
        "\n",
        "  # Slowly move the last node\n",
        "  targetNodeLocation = np.array([RodLength - 0.05 * t * RodLength, 0.0])\n",
        "  bc.setBoundaryConditionNode(N-1, targetNodeLocation)\n",
        "\n",
        "  q_new, u_new, a_new, flag = stepper.simulate(q_old, q_old, u_old, a_old)\n",
        "\n",
        "  if flag == False:\n",
        "    print(f\"Simulation did not converge at time {t} seconds.\")\n",
        "    break\n",
        "\n",
        "  q_old = q_new.copy()\n",
        "  u_old = u_new.copy()\n",
        "  a_old = a_new.copy()\n",
        "\n",
        "  # Plot\n",
        "  if time_iter % 10 == 0 or time_iter == 0:\n",
        "    clear_output()\n",
        "    x = q_old[0:ndof:2]\n",
        "    y = q_old[1:ndof:2]\n",
        "    plt.figure(1)\n",
        "    plt.plot(x, y, 'ro-')\n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('y')\n",
        "    plt.title(f'Time={t} seconds')\n",
        "    plt.xlim([0, 2.0*RodLength])\n",
        "    plt.ylim([-RodLength, RodLength])\n",
        "    plt.show()\n",
        "\n",
        "  time_iter += 1"
      ],
      "metadata": {
        "id": "PUw1SLtzbCJh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 628
        },
        "outputId": "df10ef2b-35d7-4beb-df30-0b6714e53419"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iter=1 error=4.479409856542352e-05\n",
            "iter=1 error=4.478968452707367e-05\n",
            "iter=1 error=4.4785506847293084e-05\n",
            "iter=1 error=4.4781567110968866e-05\n",
            "iter=1 error=4.477786691346357e-05\n",
            "iter=1 error=4.4774407860675946e-05\n",
            "iter=1 error=4.4771191569021885e-05\n",
            "iter=1 error=4.476821966553883e-05\n",
            "iter=1 error=4.4765493787821994e-05\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a_old"
      ],
      "metadata": {
        "id": "VbiTVbV5WPWf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dd17b084-d51c-4fc1-8952-0d3a60e03758"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 3.14896387e+01, -2.68603920e+02,  8.93450267e+01,  3.86575185e+02,\n",
              "        2.24654401e-02,  2.73982052e-02,  6.03625260e-02,  4.04365123e-02,\n",
              "        7.33223483e-02,  5.63655053e-02,  3.83034800e-02,  2.56588411e-02,\n",
              "        7.38767666e-02, -1.03907661e-01,  7.34132918e+00, -8.06902415e+01,\n",
              "        6.87496537e+01, -6.19443977e+01, -1.96345222e+02,  1.22675085e+02])"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "0L4fzGg49Bni"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}