Untitled1.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/DeepaMahm/misc/blob/master/Untitled1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Trying to solve inverse problem for Lorenz System"
      ],
      "metadata": {
        "id": "IIOuWdFrXqEb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import solve_ivp\n",
        "\n",
        "\n",
        "def lorenz(t, u, sigma, rho, beta):\n",
        "    x, y, z = u\n",
        "    return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]\n",
        "\n",
        "\n",
        "sigma_true, rho_true, beta_true = 10.0, 15.0, 8.0 / 3.0\n",
        "u0 = [-8, 7, 27] #ic\n",
        "t_span = [0, 1] #taking 0-1 for now\n",
        "t_eval = np.linspace(t_span[0], t_span[1], 1001)\n",
        "\n",
        "sol = solve_ivp(lorenz, t_span, u0, args=(sigma_true, rho_true, beta_true), t_eval=t_eval) #generating data not using lorenz data now\n",
        "u_train = sol.y.T\n",
        "t_train = sol.t\n",
        "\n",
        "\n",
        "class model_arch(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(model_arch, self).__init__()\n",
        "        self.fc1 = nn.Linear(1, 50)\n",
        "        self.fc2 = nn.Linear(50, 50)\n",
        "        self.fc3 = nn.Linear(50, 50)\n",
        "        self.fc4 = nn.Linear(50, 50)\n",
        "        self.fc5 = nn.Linear(50, 3)\n",
        "\n",
        "    def forward(self, t):\n",
        "        x = torch.tanh(self.fc1(t))\n",
        "        x = torch.tanh(self.fc2(x))\n",
        "        x = torch.tanh(self.fc3(x))\n",
        "        x = torch.tanh(self.fc4(x))\n",
        "        x = self.fc5(x)\n",
        "        return x\n",
        "\n",
        "\n",
        "net = model_arch()\n",
        "\n",
        "\n",
        "sigma = torch.tensor([10.0], requires_grad=True)\n",
        "rho = torch.tensor([15.0], requires_grad=True)\n",
        "beta = torch.tensor([8.0 / 3.0], requires_grad=True)\n",
        "\n",
        "\n",
        "def loss_func(t, u, sigma, rho, beta):\n",
        "    u_pred = net(t)\n",
        "    x_pred, y_pred, z_pred = u_pred[:, 0], u_pred[:, 1], u_pred[:, 2]\n",
        "\n",
        "    x_t = torch.autograd.grad(x_pred, t, grad_outputs=torch.ones_like(x_pred), create_graph=True)[0]\n",
        "    y_t = torch.autograd.grad(y_pred, t, grad_outputs=torch.ones_like(y_pred), create_graph=True)[0]\n",
        "    z_t = torch.autograd.grad(z_pred, t, grad_outputs=torch.ones_like(z_pred), create_graph=True)[0]\n",
        "\n",
        "    loss_x = x_t - sigma * (y_pred - x_pred)\n",
        "    loss_y = y_t - (x_pred * (rho - z_pred) - y_pred)\n",
        "    loss_z = z_t - (x_pred * y_pred - beta * z_pred)\n",
        "\n",
        "    loss_data = torch.mean((x_pred - u[:, 0])**2 + (y_pred - u[:, 1])**2 + (z_pred - u[:, 2])**2)\n",
        "\n",
        "    loss_ic = torch.mean((x_pred[0] - u[0, 0])**2 + (y_pred[0] - u[0, 1])**2 + (z_pred[0] - u[0, 2])**2)\n",
        "\n",
        "    loss = torch.mean(loss_x**2 + loss_y**2 + loss_z**2) + loss_data + loss_ic\n",
        "    return loss\n",
        "\n",
        "\n",
        "optimizer = optim.Adam(list(net.parameters()) + [sigma, rho, beta], lr=0.001)\n",
        "\n",
        "\n",
        "num_epochs = 10000\n",
        "for epoch in range(num_epochs):\n",
        "    t_tensor = torch.tensor(t_train, dtype=torch.float32).view(-1, 1).requires_grad_(True)\n",
        "    u_tensor = torch.tensor(u_train, dtype=torch.float32)\n",
        "\n",
        "    optimizer.zero_grad()\n",
        "    loss = loss_func(t_tensor, u_tensor, sigma, rho, beta)\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    if epoch % 1000 == 0:\n",
        "        print(f'Epoch {epoch}, Loss: {loss.item()}, sigma: {sigma.item()}, rho: {rho.item()}, beta: {beta.item()}')\n",
        "\n",
        "\n",
        "print(f'Final sigma: {sigma.item()}')\n",
        "print(f'Final rho: {rho.item()}')\n",
        "print(f'Final beta: {beta.item()}')\n",
        "\n",
        "\n",
        "t_tensor = torch.tensor(t_eval, dtype=torch.float32).view(-1, 1)\n",
        "u_pred = net(t_tensor).detach().numpy()\n",
        "x_pred, y_pred, z_pred = u_pred[:, 0], u_pred[:, 1], u_pred[:, 2]\n",
        "\n",
        "plt.figure(figsize=(10, 7))\n",
        "plt.plot(t_eval, u_train[:, 0], label='True x(t)', color='b')\n",
        "plt.plot(t_eval, x_pred, '--', label='Pred x(t)', color='b')\n",
        "plt.plot(t_eval, u_train[:, 1], label='True y(t)', color='r')\n",
        "plt.plot(t_eval, y_pred, '--', label='Pred y(t)', color='r')\n",
        "plt.plot(t_eval, u_train[:, 2], label='True z(t)', color='g')\n",
        "plt.plot(t_eval, z_pred, '--', label='Pred z(t)', color='g')\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('Values')\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 845
        },
        "id": "ADw_7WjHCf9b",
        "outputId": "becce6e6-047d-466a-ff1e-c3b73c4452bb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0, Loss: 1152.333740234375, sigma: 9.99899959564209, rho: 14.99899959564209, beta: 2.6656668186187744\n",
            "Epoch 1000, Loss: 253.972412109375, sigma: 8.771883964538574, rho: 14.761388778686523, beta: 1.432457685470581\n",
            "Epoch 2000, Loss: 192.27719116210938, sigma: 7.5575971603393555, rho: 15.015292167663574, beta: 0.7974898815155029\n",
            "Epoch 3000, Loss: 185.0603790283203, sigma: 6.2657670974731445, rho: 16.044185638427734, beta: 0.6528491973876953\n",
            "Epoch 4000, Loss: 178.41156005859375, sigma: 4.949809551239014, rho: 16.855222702026367, beta: 0.6144877076148987\n",
            "Epoch 5000, Loss: 168.67620849609375, sigma: 3.594346046447754, rho: 17.277462005615234, beta: 0.5808024406433105\n",
            "Epoch 6000, Loss: 154.54721069335938, sigma: 2.217806100845337, rho: 17.032127380371094, beta: 0.541670560836792\n",
            "Epoch 7000, Loss: 135.39761352539062, sigma: 0.9947434663772583, rho: 17.46202850341797, beta: 0.4959874153137207\n",
            "Epoch 8000, Loss: 110.80802917480469, sigma: 0.2743699848651886, rho: 17.663829803466797, beta: 0.28414350748062134\n",
            "Epoch 9000, Loss: 96.87574768066406, sigma: 0.20818603038787842, rho: 18.575448989868164, beta: -0.2164289653301239\n",
            "Final sigma: 0.1922706812620163\n",
            "Final rho: 19.98760223388672\n",
            "Final beta: -0.41512295603752136\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x700 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "from scipy.integrate import solve_ivp\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "############################# Generating data ##################################\n",
        "def lorenz_ode(t, y, sigma, rho, beta):\n",
        "    dydt = [\n",
        "        sigma * (y[1] - y[0]),\n",
        "        y[0] * (rho - y[2]) - y[1],\n",
        "        y[0] * y[1] - beta * y[2]\n",
        "    ]\n",
        "    return dydt\n",
        "\n",
        "t_span = [0, 1]  # Time span\n",
        "y0 = [1, 0, 0]  # Initial conditions\n",
        "sigma, rho, beta = 10, 28, 8/3  # Parameters\n",
        "\n",
        "sol = solve_ivp(lorenz_ode, t_span, y0, args=(sigma, rho, beta), dense_output=True)\n",
        "t = np.linspace(0, 1, 50)\n",
        "y_true = sol.sol(t)\n",
        "t_true = t\n",
        "\n",
        "t_tensor = torch.tensor(t_true, dtype=torch.float32).view(-1, 1).requires_grad_(True)\n",
        "y_true_tensor = torch.tensor(y_true.T, dtype=torch.float32)\n",
        "y_init = torch.tensor(y0, dtype=torch.float32).view(1, -1)\n",
        "\n",
        "########################## Plotting the true solution ##########################\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(t_true, y_true[0, :], label='True x')\n",
        "plt.plot(t_true, y_true[1, :], label='True y')\n",
        "plt.plot(t_true, y_true[2, :], label='True z')\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('State')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.title('Lorenz System: True Solution')\n",
        "plt.show()\n",
        "\n",
        "############################## Neural Network ##################################\n",
        "class ModelArch(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(ModelArch, self).__init__()\n",
        "        self.net = nn.Sequential(\n",
        "            nn.Linear(1, 64),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(64, 64),\n",
        "            nn.Tanh(),\n",
        "            nn.Linear(64, 3)\n",
        "        )\n",
        "\n",
        "    def forward(self, t):\n",
        "        return self.net(t)\n",
        "\n",
        "model = ModelArch()\n",
        "criterion = nn.MSELoss()\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)\n",
        "\n",
        "################################ Loss Function #################################\n",
        "def loss_func(t, u, u_init, sigma, rho, beta, y_true_tensor):\n",
        "    u_pred = model(t)\n",
        "    x_pred, y_pred, z_pred = u_pred[:, 0], u_pred[:, 1], u_pred[:, 2]\n",
        "\n",
        "    x_t = torch.autograd.grad(x_pred, t, grad_outputs=torch.ones_like(x_pred), create_graph=True)[0]\n",
        "    y_t = torch.autograd.grad(y_pred, t, grad_outputs=torch.ones_like(y_pred), create_graph=True)[0]\n",
        "    z_t = torch.autograd.grad(z_pred, t, grad_outputs=torch.ones_like(z_pred), create_graph=True)[0]\n",
        "\n",
        "    loss_x = x_t - sigma * (y_pred - x_pred)\n",
        "    loss_y = y_t - (x_pred * (rho - z_pred) - y_pred)\n",
        "    loss_z = z_t - (x_pred * y_pred - beta * z_pred)\n",
        "\n",
        "    loss_obs = criterion(u_pred, y_true_tensor)\n",
        "\n",
        "    loss_ic = torch.mean((x_pred[0] - u_init[0, 0])**2 + (y_pred[0] - u_init[0, 1])**2 + (z_pred[0] - u_init[0, 2])**2)\n",
        "\n",
        "    loss_ode = torch.mean(loss_x**2 + loss_y**2 + loss_z**2)\n",
        "\n",
        "    lambda1 = 1e-4\n",
        "    lambda2 = 1\n",
        "    lambda3 = 1e-2\n",
        "\n",
        "    loss = lambda1 * loss_ode + lambda2 * loss_obs + lambda3 * loss_ic\n",
        "    return loss, loss_ic, loss_obs, loss_ode, x_t, y_t, z_t, loss_x, loss_y, loss_z\n",
        "\n",
        "################################ Training loop #################################\n",
        "epochs = 1\n",
        "loss_ic_list = []\n",
        "loss_obs_list = []\n",
        "loss_ode_list = []\n",
        "loss_total_list = []\n",
        "\n",
        "for epoch in range(epochs):\n",
        "    # optimizer.zero_grad()  # Moved before model prediction for consistency\n",
        "\n",
        "    loss, loss_ic, loss_obs, loss_ode, x_t, y_t, z_t, loss_x, loss_y, loss_z = loss_func(t_tensor, y_true_tensor, y_init, sigma, rho, beta, y_true_tensor)\n",
        "    # y_pred = model(t_tensor.unsqueeze(1))\n",
        "    # loss = criterion(y_pred, y_true_tensor)\n",
        "\n",
        "    # print(f\"x_t: {x_t}\")\n",
        "    # print(f\"y_t: {y_t}\")\n",
        "    # print(f\"z_t: {z_t}\")\n",
        "    # print(f\"loss_x: {loss_x}\")\n",
        "    # print(f\"loss_y: {loss_y}\")\n",
        "    # print(f\"loss_z: {loss_z}\")\n",
        "\n",
        "\n",
        "    if torch.isnan(loss):\n",
        "        print(f'NaN loss encountered at epoch {epoch+1}. Exiting training loop.')\n",
        "        break\n",
        "    optimizer.zero_grad()\n",
        "    loss_ic.backward()\n",
        "    loss_obs.backward()\n",
        "    loss_ode.backward()\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    if (epoch + 1) % 100 == 0 or epoch == 0:\n",
        "        loss_ic_list.append(loss_ic.item())\n",
        "        loss_obs_list.append(loss_obs.item())\n",
        "        loss_ode_list.append(loss_ode.item())\n",
        "        loss_total_list.append(loss.item())\n",
        "\n",
        "    if (epoch + 1) % 1000 == 0 or epoch == 0:\n",
        "        print(f\"Epoch: {epoch+1}\")\n",
        "        print(f\"Observational Loss: {loss_obs.item()}\")\n",
        "        print(f\"IC Loss: {loss_ic.item()}\")\n",
        "        print(f\"ODE Loss: {loss_ode.item()}\")\n",
        "        print(f\"Total Loss: {loss.item()}\")\n",
        "\n",
        "        with torch.no_grad():\n",
        "            y_pred = model(t_tensor).numpy()\n",
        "        plt.figure(figsize=(10, 6))\n",
        "        plt.plot(t, y_true[0, :], label='True x')\n",
        "        plt.plot(t, y_true[1, :], label='True y')\n",
        "        plt.plot(t, y_true[2, :], label='True z')\n",
        "        plt.plot(t, y_pred[:, 0], '--', label='Predicted x')\n",
        "        plt.plot(t, y_pred[:, 1], '--', label='Predicted y')\n",
        "        plt.plot(t, y_pred[:, 2], '--', label='Predicted z')\n",
        "        plt.xlabel('Time')\n",
        "        plt.ylabel('State')\n",
        "        plt.title(f'Lorenz System: True vs Predicted, Epoch {epoch+1}')\n",
        "        plt.legend()\n",
        "        plt.grid(True)\n",
        "        plt.show()\n",
        "\n",
        "########################## Ploting the final results ###########################\n",
        "with torch.no_grad():\n",
        "    y_pred = model(t_tensor).numpy()\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(t, y_true[0, :], label='True x')\n",
        "plt.plot(t, y_true[1, :], label='True y')\n",
        "plt.plot(t, y_true[2, :], label='True z')\n",
        "plt.plot(t, y_pred[:, 0], '--', label='Predicted x')\n",
        "plt.plot(t, y_pred[:, 1], '--', label='Predicted y')\n",
        "plt.plot(t, y_pred[:, 2], '--', label='Predicted z')\n",
        "plt.xlabel('Time')\n",
        "plt.ylabel('State')\n",
        "plt.title('Lorenz System: True vs Predicted')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "\n",
        "############################ Ploting the losses ################################\n",
        "epochs_range = range(0, (epochs // 100) * 100 + 1, 100)\n",
        "\n",
        "plt.figure(figsize=(12, 8))\n",
        "\n",
        "plt.subplot(2, 2, 1)\n",
        "plt.plot(epochs_range, loss_ic_list, label='IC Loss')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Loss')\n",
        "plt.title('IC Loss vs Epochs')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot(2, 2, 2)\n",
        "plt.plot(epochs_range, loss_obs_list, label='Observational Loss')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Loss')\n",
        "plt.title('Observational Loss vs Epochs')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot(2, 2, 3)\n",
        "plt.plot(epochs_range, loss_ode_list, label='ODE Loss')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Loss')\n",
        "plt.title('ODE Loss vs Epochs')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "\n",
        "plt.subplot(2, 2, 4)\n",
        "plt.plot(epochs_range, loss_total_list, label='Total Loss')\n",
        "plt.xlabel('Epochs')\n",
        "plt.ylabel('Loss')\n",
        "plt.title('Total Loss vs Epochs')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "sZr46MpZUd1B"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "e87K-wUGUd3w"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "RUciZQ4I-Job"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}