Burgers_discrete_identification.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Burgers_discrete_identification.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "machine_shape": "hm"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "nzRqrB2tCPJy"
      },
      "source": [
        "import torch\n",
        "import numpy as np"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pRSwnHfqCgbC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6ae891e9-6aee-4859-f76f-462c9fec48f1"
      },
      "source": [
        "np.random.seed(1234)\n",
        "torch.manual_seed(1234)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<torch._C.Generator at 0x7f64889e17d0>"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qAauKoFANT9d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1340e7be-0301-4f63-a6cc-7afa7b421e98"
      },
      "source": [
        "if torch.cuda.is_available():\n",
        "    device = torch.device(\"cuda:0\") \n",
        "    print(\"Running on the GPU\")\n",
        "else:\n",
        "    device = torch.device(\"cpu\")\n",
        "    print(\"Running on the CPU\")"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Running on the GPU\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aVzQS6uk_bpk"
      },
      "source": [
        "# **NEURAL NETWORK**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "10lIzpgQ_43-"
      },
      "source": [
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "from torch import autograd"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WmTWsvKS_f69"
      },
      "source": [
        "class PINN(nn.Module):\n",
        "    def __init__(self, input_dim, output_dim, layer_size):\n",
        "        super(PINN, self).__init__()\n",
        "        self.lambda_1 = nn.Parameter(torch.Tensor([0]), requires_grad=True)\n",
        "        self.lambda_2 = nn.Parameter(torch.Tensor([0]), requires_grad=True)\n",
        "\n",
        "        self.fc1 = nn.Linear(input_dim, layer_size)\n",
        "        self.fc2 = nn.Linear(layer_size, layer_size)\n",
        "        self.fc3 = nn.Linear(layer_size, layer_size)\n",
        "        self.fc4 = nn.Linear(layer_size, output_dim)\n",
        "\n",
        "        \n",
        "\n",
        "    def forward(self, input_0, input_1, dt, IRK_alpha, IRK_beta):\n",
        "        u_0 = self.forward_iteration(input_0, dt, IRK_alpha.T, True)\n",
        "        u_1 = self.forward_iteration(input_1, dt, (IRK_beta-IRK_alpha).T, False)\n",
        "        return u_0, u_1\n",
        "\n",
        "\n",
        "\n",
        "    def forward_iteration(self, x, dt, IRK_weights, flag_u0):\n",
        "        x.requires_grad_(True)\n",
        "\n",
        "        s = nn.Tanh()(self.fc1(x.float()))\n",
        "        s = nn.Tanh()(self.fc2(s))\n",
        "        s = nn.Tanh()(self.fc3(s))\n",
        "        u = self.fc4(s)\n",
        "        u_x = self.fwd_gradients(u, x)\n",
        "        u_xx = self.fwd_gradients(u_x, x)\n",
        "        f = - self.lambda_1*u*u_x + self.lambda_2*u_xx\n",
        "        \n",
        "        if flag_u0:\n",
        "            u_ = u - dt * torch.mm(f.double(), IRK_weights.double())\n",
        "        else: #flag_u1\n",
        "            u_ = u + dt * torch.mm(f.double(), IRK_weights.double())\n",
        "\n",
        "        return u_\n",
        "\n",
        "\n",
        "    def fwd_gradients(self, U, x):\n",
        "        z = torch.ones(U.shape).to(device).requires_grad_(True)\n",
        "        g = autograd.grad(U, x, grad_outputs=z, create_graph=True)[0]\n",
        "        return autograd.grad(g, z, grad_outputs=torch.ones(g.shape).to(device), create_graph=True)[0]"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "teTTflqiSFBB"
      },
      "source": [
        "# **OPTIMIZATION**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t78d2W1oSHyk"
      },
      "source": [
        "from torch.optim import LBFGS\n",
        "from time import time\n",
        "from tqdm.notebook import tqdm as tqdm"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TaJWr7CBSaTV"
      },
      "source": [
        "class Train():\n",
        "    def __init__(self, network, input_0, target_0, input_1, target_1, dt, q):\n",
        "        self.net = network\n",
        "\n",
        "        self.lbfgs_optim = LBFGS(self.net.parameters(), lr=1, max_iter=50000, line_search_fn='strong_wolfe')\n",
        "\n",
        "        tmp = np.float32(np.loadtxt('/content/drive/My Drive/ETH/Private/Bachelor Thesis/Code/Paper 2/Utilities/IRK_weights/Butcher_IRK%d.txt' % (q), ndmin = 2))\n",
        "        weights = torch.from_numpy(np.reshape(tmp[0:q**2+q], (q+1, q)))\n",
        "        self.IRK_alpha = weights[0:-1, :].to(device)\n",
        "        self.IRK_beta = weights[-1:, :].to(device)\n",
        "        self.IRK_times = torch.from_numpy(tmp[q**2+q:]).to(device)\n",
        "\n",
        "        self.train_input_0, self.train_target_0,  = input_0.to(device), target_0.to(device)\n",
        "\n",
        "        self.train_input_1, self.train_target_1 = input_1.to(device), target_1.to(device)\n",
        "    \n",
        "        self.dt = torch.tensor(dt).to(device)\n",
        "        \n",
        "\n",
        "\n",
        "\n",
        "    def train(self): \n",
        "        start_time = time()\n",
        "\n",
        "        self.train_iteration(self.train_input_0, self.train_target_0, self.train_input_1, self.train_target_1)\n",
        "\n",
        "        end_time = time()\n",
        "        print('Time:', end_time - start_time)     \n",
        "\n",
        "\n",
        "\n",
        "    def train_iteration(self, input_0, target_0, input_1, target_1):\n",
        "        \n",
        "        def closure(): \n",
        "            if torch.is_grad_enabled():\n",
        "                self.lbfgs_optim.zero_grad()\n",
        "            predict_0, predict_1 = self.net(input_0, input_1, self.dt, self.IRK_alpha, self.IRK_beta)\n",
        "            loss = self.loss_function(predict_0, target_0, predict_1, target_1)\n",
        "            if loss.requires_grad:\n",
        "                loss.backward()\n",
        "            return loss\n",
        "        self.lbfgs_optim.step(closure)\n",
        "\n",
        "\n",
        "\n",
        "    def loss_function(self, predict_0, target_0, predict_1, target_1): #correct\n",
        "        loss = torch.sum(torch.square(predict_0 - target_0)) + torch.sum(torch.square(predict_1 - target_1))\n",
        "        return loss\n"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-70mDY_CAyRd"
      },
      "source": [
        "# **MAIN**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "huejQW71ywhO"
      },
      "source": [
        "## DATA PREPERATION"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9MzDySUNA132"
      },
      "source": [
        "import scipy.io"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xPVicEkoBVGo"
      },
      "source": [
        "COLLECTING THE DATA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wBQ47vBQBKsq"
      },
      "source": [
        "data = scipy.io.loadmat('/content/drive/My Drive/ETH/Private/Bachelor Thesis/Code/Paper 2/appendix/Data/burgers_shock.mat')\n",
        "\n",
        "t_data = data['t']  # SHAPE (100, 1)\n",
        "x_data = data['x']  # SHAPE (256,1)\n",
        "u_data = np.real(data['usol']).T  # SHAPE (100, 256)\n",
        "\n",
        "lb = np.array([-1.0])\n",
        "ub = np.array([1.0])\n",
        "N0 = 199\n",
        "N1 = 201 #number of x data points"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ftU2ZajqyjIV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "46264d24-377e-4936-daf6-318f57b38a07"
      },
      "source": [
        "idx_x0 = np.random.choice(u_data.shape[1], N0, replace=False) \n",
        "idx_t0 = 10\n",
        "\n",
        "x_0 = x_data[idx_x0, :]\n",
        "x_0 = torch.from_numpy(x_0)#.view(-1, 1)\n",
        "\n",
        "u_0 = u_data[idx_t0, idx_x0].T\n",
        "u_0 = torch.from_numpy(u_0).view(-1, 1)\n",
        "print('0 INPUT SHAPE:', x_0.shape)\n",
        "print('0 TARGET SHAPE:', u_0.shape)\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 INPUT SHAPE: torch.Size([199, 1])\n",
            "0 TARGET SHAPE: torch.Size([199, 1])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qm0-vOhX_Alf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dc8f0bdf-9f5d-4ef4-ae4b-0ff2b78992cb"
      },
      "source": [
        "idx_x1 = np.random.choice(u_data.shape[1], N1, replace=False) \n",
        "idx_t1 = 90\n",
        "\n",
        "x_1 = x_data[idx_x1, :]\n",
        "x_1 = torch.from_numpy(x_1)\n",
        "\n",
        "u_1 = u_data[idx_t1, idx_x1].T\n",
        "u_1 = torch.from_numpy(u_1).view(-1, 1)\n",
        "print('1 INPUT SHAPE:', x_1.shape)\n",
        "print('1 TARGET SHAPE:', u_1.shape)\n",
        "\n",
        "dt = t_data[idx_t1] - t_data[idx_t0]\n",
        "print('dt:', dt.item())"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 INPUT SHAPE: torch.Size([201, 1])\n",
            "1 TARGET SHAPE: torch.Size([201, 1])\n",
            "dt: 0.8\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uXdPaKLP3zdk"
      },
      "source": [
        "## TRAINING"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zTWHRZHg4F0o"
      },
      "source": [
        "INITIALIZE NETWORK"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0PoaulQu3vcK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7ed6e2e5-d16d-4165-8efd-3aa5f0e8f67c"
      },
      "source": [
        "q = int(np.ceil(0.5*np.log(np.finfo(float).eps)/np.log(dt)))\n",
        "input_dim, output_dim, layer_size = 1, q, 100\n",
        "net = PINN(input_dim, output_dim, layer_size).to(device)\n",
        "print('q:', q)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q: 81\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "reqmFvCM81Ee"
      },
      "source": [
        "TRAINING NETWORK"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xjiHR9islT_f"
      },
      "source": [
        "train = Train(net, x_0.to(device), u_0.to(device), x_1.to(device), u_1.to(device), dt, q)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HLaDmNYqmrrc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2f196b77-fcc0-49be-9bf8-668a432423af"
      },
      "source": [
        "train.train()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time: 363.1729054450989\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p74P_4EUBwJ0"
      },
      "source": [
        "## PLOTTING"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "szwo5Ln4P2fp"
      },
      "source": [
        "u0_pred, u1_pred = net.forward(x_0.to(device), x_1.to(device), train.dt, train.IRK_alpha, train.IRK_beta)"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2PnxxeKM8TMc"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.gridspec as gridspec"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "166W0HLl5lL0"
      },
      "source": [
        "def plot_grid(u_plot, t_data, X_grid, T_grid, string_title, t_index_low=None, t_index_high=None):\n",
        "    fig = plt.subplots(figsize=(8, 4))\n",
        "    plt.contourf(T_grid, X_grid, u_plot, 1000, cmap=plt.get_cmap('Spectral'))\n",
        "    plt.colorbar()\n",
        "    plt.ylabel(r'$x$')\n",
        "    plt.xlabel(r'$t$')\n",
        "    plt.title(string_title, fontsize = 15) \n",
        "\n",
        "    try:\n",
        "        line = np.linspace(x_data.min(), x_data.max(), 2)[:,None]\n",
        "        fig[1].plot(t_data[t_index_low]*np.ones((2,1)), line, 'k--', linewidth = 1)\n",
        "        fig[1].plot(t_data[t_index_high]*np.ones((2,1)), line, 'k--', linewidth = 1)\n",
        "    except Exception:\n",
        "        pass    \n",
        "    \n",
        "\n",
        "    plt.show()\n",
        "    plt.draw()\n",
        "    #fig[0].savefig('/content/drive/My Drive/ETH/Private/Bachelor Thesis/Images/Burgers_Discrete_Identification/' + string_title.format(1000), bbox_inches='tight')\n",
        "    plt.close()\n",
        "\n",
        "def plot_time_step(x_data, x_input, t_data, u_data, u_pred, t_index, x_lb, x_ub, y_lb, y_ub):\n",
        "    fig = plt.subplots(figsize=(2.6,2.6))\n",
        "    fig[1].plot(x_data, u_data[t_index,:].T, 'b-', linewidth = 2, label = 'Exact') \n",
        "    fig[1].plot(x_input, u_pred[: ,-1].cpu().detach().numpy(), 'rx', linewidth = 2, label = 'Prediciton')      \n",
        "    fig[1].set_xlabel('$x$')\n",
        "    fig[1].set_ylabel('$u(t,x)$')    \n",
        "    fig[1].set_title('$t = %.2f$' % (t_data[t_index]), fontsize = 15)\n",
        "    fig[1].set_xlim([x_lb, x_ub])\n",
        "    fig[1].set_ylim([y_lb, y_ub])\n",
        "    fig[1].legend(loc='upper center', bbox_to_anchor=(0.5, -0.25), ncol=5, frameon=False)\n",
        "    plt.show()\n",
        "    #fig[1].figure.savefig('/content/drive/My Drive/ETH/Private/Bachelor Thesis/Images/Burgers_Discrete_Identification/target_v_pred_t%.2f' % t_data[t_index].item() + 'testtesttesttest.png', bbox_inches='tight')"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uKN2Z0585dEr",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "outputId": "e3b09b47-d22a-42f3-dcb2-854b2fdf80b2"
      },
      "source": [
        "X, T = np.meshgrid(x_data, t_data)\n",
        "plot_grid(u_data, t_data, X, T, 'u(t,x)', idx_t0, idx_t1)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Locator attempting to generate 1001 ticks ([-1.0, ..., 1.0]), which exceeds Locator.MAXTICKS (1000).\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o4JV63G_x98B",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "outputId": "b00ee18e-bbf9-42bf-93b6-caf8c7c8665b"
      },
      "source": [
        "plot_time_step(x_data, x_0.cpu().detach().numpy(), t_data, u_data, u0_pred, idx_t0, x_data.min(), x_data.max(), u_data.min()*1.05, u_data.max()*1.05)\n",
        "plot_time_step(x_data, x_1.cpu().detach().numpy(), t_data, u_data, u1_pred, idx_t1, x_data.min(), x_data.max(), u_data.min()*1.05, u_data.max()*1.05)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 187.2x187.2 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 187.2x187.2 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PZ7i9fzgBO_h"
      },
      "source": [
        "## SOLUTION"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zwn06JcJ9v7B",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3fe40ee7-29a0-4ee1-8810-1145f9457962"
      },
      "source": [
        "print('TARGET LAMBDA 1:', 1.,'\\nTARGET LAMBDA 2', '%.6f' % (0.01/np.pi))\n",
        "print('\\nPREDICTED LAMBDA 1:', net.lambda_1.item(), '\\nPREDICTED LAMBDA 2:', net.lambda_2.item(), '=', net.lambda_2.item() * np.pi, '/ pi')\n",
        "\n",
        "print('\\nLAMBDA 1 ABSOLUTE ERROR:', np.abs((net.lambda_1.item() - 1)))\n",
        "print('LAMBDA 2 ABSOLUTE ERROR:', np.abs((net.lambda_2.item() - 0.01/np.pi) ))\n",
        "\n",
        "print('\\nLAMBDA 1 RELATIVE ERROR:', np.abs((net.lambda_1.item() - 1)/1))\n",
        "print('LAMBDA 2 RELATIVE ERROR:', np.abs((net.lambda_2.item() - 0.01/np.pi) /(0.01/np.pi)))"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "TARGET LAMBDA 1: 1.0 \n",
            "TARGET LAMBDA 2 0.003183\n",
            "\n",
            "PREDICTED LAMBDA 1: 0.998324990272522 \n",
            "PREDICTED LAMBDA 2: 0.0036664134822785854 = 0.011518377660948976 / pi\n",
            "\n",
            "LAMBDA 1 ABSOLUTE ERROR: 0.0016750097274780273\n",
            "LAMBDA 2 ABSOLUTE ERROR: 0.0004833146204406783\n",
            "\n",
            "LAMBDA 1 RELATIVE ERROR: 0.0016750097274780273\n",
            "LAMBDA 2 RELATIVE ERROR: 0.1518377660948974\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2fnUaWe3x8hV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3ad3d2aa-bdcd-4c4e-d215-2d282bea07c6"
      },
      "source": [
        "criterion = nn.MSELoss()\n",
        "Error = criterion(u0_pred[:, -1].view(-1, 1).cpu(), u_0) + criterion( u1_pred[:, -1].view(-1, 1).cpu(), u_1)\n",
        "\n",
        "print('L2 Norm Error:', Error.item())\n",
        "\n",
        "Error_relative = Error / (torch.mean(torch.abs(u_0)) + torch.mean(torch.abs(u_1)))\n",
        "print('Relative L2 Norm Error:', Error_relative.item())"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "L2 Norm Error: 4.2679053209780995e-06\n",
            "Relative L2 Norm Error: 4.17212961323647e-06\n"
          ]
        }
      ]
    }
  ]
}