TF_PINN_PDE_System.ipynb

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  "metadata": {
    "colab": {
      "name": "TF_PINN_PDE_System",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPzSGgwKlCGOE5DDRiOkp2v",
      "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/kochlisGit/Physics-Informed-Neural-Network-PINN-/blob/main/TF_PINN_PDE_System.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "*PINNs* have the ability to solve **systems** of PDE equations. Solving a PDE System can be very difficult or time-consuming, because it includes many dependent variables and multiple functions that need to be approximated. For instance:\n",
        "\n",
        "1.   $\\frac{du_1}{dt}=\\frac{du^2_1}{dx^2} + u_3 sin(\\pi x)$\n",
        "\n",
        "2.   $\\frac{du_2}{dt}=\\frac{du^2_2}{dx^2} + u_3 cos(\\pi x)$\n",
        "\n",
        "3.   $𝑢_1 sin(𝜋𝑥) + 𝑢_2 cos(𝜋𝑥) − 𝑒^{-t} = 0$\n",
        "\n",
        "in domain $x \\in [0.0, 3.0], t \\in [0.0, 3.0]$ with boundary conditions:\n",
        "\n",
        "\n",
        "\n",
        "1.   $u_1(x, 0) = sin(\\pi x)$\n",
        "2.   $u_2(x, 0) = cos(\\pi x)$\n",
        "3.   $\\frac{du_1(x,0)}{dt} = -sin(\\pi x)$\n",
        "4.   $\\frac{du_2(x,0)}{dt} = -cos(\\pi x)$$\n",
        "\n",
        "In this system of equations, we are mainly interested in computing the function $u_1(x, t)$. However, $u_1(x, t)$ is dependent by functions $u_2(x, t), u_3(x, t)$\n",
        "This seems to be a very challenging PDE system. However, it is proved that PINNs can approximate the solution of the above system with very high accuracy. The solutions of the above system is:\n",
        "\n",
        "1.    $u_1(x, t) = e^{-t} sin(\\pi x)$\n",
        "2.    $u_2(x, t) = e^{-t} cos(\\pi x)$\n",
        "3.    $u_3(x, t) = e^{-t} (1+\\pi^2)$\n"
      ],
      "metadata": {
        "id": "-C5SH-6KUTwa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import tensorflow as tf\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "LVIhDfXTbYSc"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NbgfXrwlB947",
        "outputId": "862bee29-7058-4aa7-cd49-482de75d5446"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(TensorShape([4096, 2]), TensorShape([512, 2]))"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "num_domain = 4096\n",
        "num_test = 512\n",
        "minval = [0.0, 0.0]\n",
        "maxval = [3.0, 3.0]\n",
        "\n",
        "def generate_uniform_data(num_domain, minval, maxval):\n",
        "  data_init = tf.random_uniform_initializer(minval=minval, maxval=maxval, seed=0)\n",
        "  return tf.Variable(data_init(shape=[num_domain, 1]), dtype=tf.float32)\n",
        "\n",
        "x_train = generate_uniform_data(num_domain, minval, maxval)\n",
        "x_test = generate_uniform_data(num_test, minval, maxval)\n",
        "x_train.shape, x_test.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Like the previous examples, we will need to compute the Jacobian & Hessian matrix in order to compute the error of the above system. We may notice that by using the Jacobian matrix, we can compute any derivative with respect to every variable. For example:\n",
        "\n",
        "$\\frac{du_1}{dx} = J[0,0]$ and $\\frac{du_1}{dt} = J[0,1]$.\n",
        "\n",
        "So we only need to compute the gradients for y=NN(x) once, where NN(x) is the forward output of our neural network! In this case, we will modify the functions *jacobian* and *hessian* in order to compute the gradients once and store them in a HashMap (**Dict**). This way, we can **re-use the gradients for each equation and optimize the training time**.\n",
        "\n",
        "# Jabocian Matrix\n",
        "\n",
        "![Jacobian-matrix-formula.png](data:image/png;base64,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)\n",
        "\n",
        "# Hessian Matrix\n",
        "\n",
        "![hessian-matrix-formula.png](data:image/png;base64,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)\n"
      ],
      "metadata": {
        "id": "en88m15MbmKF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Jacobian without Hashing\n",
        "\n",
        "```\n",
        "def jacobian(tape, y, x, i=0, j=0):\n",
        "  if y.shape[1] > 1:\n",
        "    y = y[:, i : i + 1]\n",
        "\n",
        "  grads = tape.gradient(y, x)\n",
        "  return grads[:, j : j + 1]\n",
        "  ```\n",
        "\n",
        "# Hessian without Hashing\n",
        "\n",
        "```\n",
        "def hessian(tape, y, x, i=0, j=0, component=0):\n",
        "  if y.shape[1] > 1:\n",
        "    y = y[:, i : i + 1]\n",
        "\n",
        "  jacobian_grads = tape.gradient(y, x)[:, i : i + 1]\n",
        "  hessian_grads = tape.gradient(jacobian_grads, x)\n",
        "  return hessian_grads[:, j : j + 1]\n",
        "```\n",
        "\n"
      ],
      "metadata": {
        "id": "x9KLDnyefZLh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's add some hashing, in order to re-use the gradients, if needed.\n",
        "\n",
        "**Params**\n",
        "- **tape**: The tf.GradientTape object that computes the gradients of the outputs with respects of inputs.\n",
        "- **y**: The outputs \"y\" of the operation `y = model(x)`.\n",
        "- **x**: The inputs \"x\" of the operation `y = model(x)`.\n",
        "- **i**: The row of the matrix (*Jacobian or Hessian*)\n",
        "- **j**: The column of the matrix (*Jacobian or Hessian*)\n",
        "- **component**: The function of which the gradients will be computed (`u1: 0, u2: 1`)\n",
        "- **key**: The hashing key, which is computed from the combination of y and x."
      ],
      "metadata": {
        "id": "2qluE5ryfpi4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "J = {}\n",
        "def jacobian(tape, y, x, i=0, j=0, key=None):\n",
        "  if key is None:\n",
        "    key = (y.ref(), x.ref())\n",
        "\n",
        "  if y.shape[1] > 1:\n",
        "    y = y[:, i : i + 1]\n",
        "\n",
        "  if not key in J:\n",
        "    J[key] = {}\n",
        "  if not i in J[key]:\n",
        "    grads = tape.gradient(y, x)\n",
        "    J[key][i] = grads\n",
        "  return J[key][i][:, j : j + 1]\n",
        "\n",
        "H = {}\n",
        "def hessian(tape, y, x, i=0, j=0, component=0):\n",
        "  key = (y.ref(), x.ref())\n",
        "  first_order_grads = jacobian(tape, y, x, component, i, key)\n",
        "\n",
        "  if key not in H:\n",
        "    H[key] = {}\n",
        "  if component not in H[key]:\n",
        "    H[key][component] = {}\n",
        "  if i not in H[key][component]:\n",
        "    second_order_grads = tape.gradient(first_order_grads, x)\n",
        "    H[key][component][i] = second_order_grads\n",
        "  return H[key][component][i][:, j : j + 1]"
      ],
      "metadata": {
        "id": "bCUQAriTbd6e"
      },
      "execution_count": 74,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def extract_input_vars(inputs):\n",
        "  x = inputs[:, 0: 1]\n",
        "  t = inputs[:, 1: 2]\n",
        "  return x, t\n",
        "\n",
        "def extract_output_functions(y):\n",
        "  u1 = y[:, 0: 1]\n",
        "  u2 = y[:, 1: 2]\n",
        "  u3 = y[:, 2: 3]\n",
        "  return u1, u2, u3\n",
        "\n",
        "def pde_system(tape, x, y):\n",
        "  u1, u2, u3 = extract_output_functions(y)\n",
        "  var_x, var_t = extract_input_vars(x)\n",
        "\n",
        "  du1_t = jacobian(tape, y, x, i=0, j=1)\n",
        "  du2_t = jacobian(tape, y, x, i=1, j=1)\n",
        "  du1_xx = hessian(tape, y, x, i=0, j=0, component=0)\n",
        "  du2_xx = hessian(tape, y, x, i=0, j=0, component=1)\n",
        "\n",
        "  eq1 = du1_t - du1_xx - u3*tf.math.sin(np.pi * var_x)\n",
        "  eq2 = du2_t - du2_xx - u3*tf.math.cos(np.pi * var_x)\n",
        "  eq3 = u1*tf.math.sin(np.pi * var_x) + u2*tf.math.cos(np.pi * var_x) - tf.math.exp(-var_t)\n",
        "  return tf.concat([eq1, eq2, eq3], axis=1)"
      ],
      "metadata": {
        "id": "I6pZxFBsgVup"
      },
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def bc_u1(x):\n",
        "  var_x, _ = extract_input_vars(x)\n",
        "  return tf.math.sin(np.pi*var_x)\n",
        "\n",
        "def bc_u2(x):\n",
        "  var_x, _ = extract_input_vars(x)\n",
        "  return tf.math.cos(np.pi*var_x)\n",
        "\n",
        "def bc_du1(x):\n",
        "  var_x, _ = extract_input_vars(x)\n",
        "  return -tf.math.sin(np.pi*var_x)\n",
        "\n",
        "def bc_du2(x):\n",
        "  var_x, _ = extract_input_vars(x)\n",
        "  return -tf.math.cos(np.pi*var_x)\n",
        "\n",
        "def solution(x):\n",
        "  var_x, var_t = extract_input_vars(x)\n",
        "  u1 = tf.math.exp(-var_t) * tf.math.sin(np.pi * var_x)\n",
        "  u2 = tf.math.exp(-var_t) * tf.math.cos(np.pi * var_x)\n",
        "  u3 = tf.math.exp(-var_t) * (1 + np.pi**2)\n",
        "  return tf.concat([u1, u2, u3], axis=1)\n",
        "\n",
        "x_bc = tf.Variable(x_train)\n",
        "x_bc[:, 1].assign(tf.zeros(shape=[x_bc.shape[0]]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ak7ZW_qXU38o",
        "outputId": "74236b7b-923b-4641-a3de-b5ad148694f9"
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'UnreadVariable' shape=(4096, 2) dtype=float32, numpy=\n",
              "array([[0.6330464 , 0.        ],\n",
              "       [2.11803   , 0.        ],\n",
              "       [2.40019   , 0.        ],\n",
              "       ...,\n",
              "       [2.7562017 , 0.        ],\n",
              "       [0.09513831, 0.        ],\n",
              "       [1.01101   , 0.        ]], dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n_inputs = 2\n",
        "n_outputs = 3\n",
        "hidden_units = [50, 50, 50, 50]\n",
        "activation = 'tanh'\n",
        "\n",
        "model = tf.keras.models.Sequential()\n",
        "model.add(tf.keras.layers.Input((n_inputs,)))\n",
        "\n",
        "for units in hidden_units:\n",
        "  model.add(tf.keras.layers.Dense(units=units, activation=activation))\n",
        "\n",
        "model.add(tf.keras.layers.Dense(units=n_outputs))\n",
        "model.summary()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UaNmqU3RUxL9",
        "outputId": "1d5f56dd-f292-474a-ab1d-72f627c7fc09"
      },
      "execution_count": 75,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential_4\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense_20 (Dense)            (None, 50)                150       \n",
            "                                                                 \n",
            " dense_21 (Dense)            (None, 50)                2550      \n",
            "                                                                 \n",
            " dense_22 (Dense)            (None, 50)                2550      \n",
            "                                                                 \n",
            " dense_23 (Dense)            (None, 50)                2550      \n",
            "                                                                 \n",
            " dense_24 (Dense)            (None, 3)                 153       \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 7,953\n",
            "Trainable params: 7,953\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def test_inputs():\n",
        "  y_train = model(x_train)\n",
        "  y_test = model(x_test)\n",
        "\n",
        "  print('\\n--- Testing inputs ---')\n",
        "  print('\\nTraining inputs:', x_train)\n",
        "  print('\\nTraining outputs:', y_train)\n",
        "  print('\\nEvaluation inputs:', x_test)\n",
        "  print('\\nEvaluation outputs:', y_test)\n",
        "\n",
        "def test_bcs():\n",
        "  with tf.GradientTape(persistent=True) as tape:\n",
        "    y = model(x_bc, training=True)\n",
        "    u1_bc = y[:, 0: 1]\n",
        "    u2_bc = y[:, 1: 2]\n",
        "    du1_t_bc = jacobian(tape, y, x_bc, i=0, j=1)\n",
        "    du2_t_bc = jacobian(tape, y, x_bc, i=1, j=1)\n",
        "\n",
        "  print('\\n--- Testing boundary conditions ---')\n",
        "  print('\\nBC input:', x_bc)\n",
        "  print('\\nBC output', y)\n",
        "  print('\\nBC of u1:', u1_bc)\n",
        "  print('\\nBC of u2:', u1_bc)\n",
        "  print('\\nBC of du1_t:', du1_t_bc)\n",
        "  print('\\nBC of du2_t:', du2_t_bc)\n",
        "\n",
        "def test_losses():\n",
        "  with tf.GradientTape(persistent=True) as tape_domain:\n",
        "    y_train = model(x_train, training=True)\n",
        "    errors = pde_system(tape_domain, x_train, y_train)\n",
        "\n",
        "  with tf.GradientTape(persistent=True) as tape_bc:\n",
        "    y_bc = model(x_bc, training=True)\n",
        "    u1_bc = y_bc[:, 0: 1]\n",
        "    u2_bc = y_bc[:, 1: 2]\n",
        "    du1_t_bc = jacobian(tape_bc, y_bc, x_bc, i=0, j=1)\n",
        "    du2_t_bc = jacobian(tape_bc, y_bc, x_bc, i=1, j=1)\n",
        "\n",
        "  domain_mean_losses = tf.math.reduce_mean(tf.math.square(errors), axis=0)\n",
        "  domain_total_mean_loss = tf.math.reduce_mean(domain_mean_losses, axis=0)\n",
        "  loss_u1 = tf.math.reduce_mean(tf.math.square(u1_bc - bc_u1(x_bc)), axis=0)[0]\n",
        "  loss_u2 = tf.math.reduce_mean(tf.math.square(u2_bc - bc_u2(x_bc)), axis=0)[0]\n",
        "  loss_du1 = tf.math.reduce_mean(tf.math.square(du1_t_bc - bc_du1(x_bc)), axis=0)[0]\n",
        "  loss_du2 = tf.math.reduce_mean(tf.math.square(du2_t_bc - bc_du2(x_bc)), axis=0)[0]\n",
        "  total_loss = domain_total_mean_loss + loss_u1 + loss_u2 + loss_du1 + loss_du2\n",
        "\n",
        "  print('\\n--- Testing losses ---')\n",
        "  print('\\nTesting domain errors:', errors)\n",
        "  print('\\nTesting domain mean losses:', domain_mean_losses)\n",
        "  print('\\nTesting total domain mean loss:', domain_total_mean_loss)\n",
        "  print('\\nTesting loss of u1-bcs:', loss_u1)\n",
        "  print('\\nTesting loss of u2-bcs:', loss_u2)\n",
        "  print('\\nTesting loss of du1-bcs:', loss_du1)\n",
        "  print('\\nTesting loss of du2_t-bcs:', loss_du2)\n",
        "  print('\\nTesting total loss:', total_loss)\n",
        "\n",
        "def test_solution():\n",
        "  print('\\n--- Testing solution ---')\n",
        "  print('\\nTesting domain errors:', solution(x_train))\n",
        "\n",
        "test_inputs()\n",
        "test_bcs()\n",
        "test_losses()\n",
        "test_solution()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N7wfZ_XEZ2On",
        "outputId": "0a04e809-97ec-44d4-c627-df9f7b1c4eea"
      },
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "--- Testing inputs ---\n",
            "\n",
            "Training inputs: <tf.Variable 'Variable:0' shape=(4096, 2) dtype=float32, numpy=\n",
            "array([[0.6330464 , 0.6330464 ],\n",
            "       [2.11803   , 2.11803   ],\n",
            "       [2.40019   , 2.40019   ],\n",
            "       ...,\n",
            "       [2.7562017 , 2.7562017 ],\n",
            "       [0.09513831, 0.09513831],\n",
            "       [1.01101   , 1.01101   ]], dtype=float32)>\n",
            "\n",
            "Training outputs: tf.Tensor(\n",
            "[[-0.16319206  0.08628783  0.18769218]\n",
            " [-0.3748796   0.22495344  0.32350507]\n",
            " [-0.39366317  0.24881688  0.3225546 ]\n",
            " ...\n",
            " [-0.4122589   0.27803248  0.31710514]\n",
            " [-0.02594845  0.01412409  0.03171227]\n",
            " [-0.24094753  0.12638244  0.2581645 ]], shape=(4096, 3), dtype=float32)\n",
            "\n",
            "Evaluation inputs: <tf.Variable 'Variable:0' shape=(512, 2) dtype=float32, numpy=\n",
            "array([[0.6330464 , 0.6330464 ],\n",
            "       [2.11803   , 2.11803   ],\n",
            "       [2.40019   , 2.40019   ],\n",
            "       ...,\n",
            "       [0.23787296, 0.23787296],\n",
            "       [0.4770459 , 0.4770459 ],\n",
            "       [1.925     , 1.925     ]], dtype=float32)>\n",
            "\n",
            "Evaluation outputs: tf.Tensor(\n",
            "[[-0.16319206  0.08628783  0.18769218]\n",
            " [-0.3748796   0.22495344  0.32350507]\n",
            " [-0.39366317  0.24881688  0.3225546 ]\n",
            " ...\n",
            " [-0.0644148   0.03488423  0.07806579]\n",
            " [-0.12598804  0.06725508  0.14852689]\n",
            " [-0.3593397   0.20837668  0.3215768 ]], shape=(512, 3), dtype=float32)\n",
            "\n",
            "--- Testing boundary conditions ---\n",
            "\n",
            "BC input: <tf.Variable 'Variable:0' shape=(4096, 2) dtype=float32, numpy=\n",
            "array([[0.6330464 , 0.        ],\n",
            "       [2.11803   , 0.        ],\n",
            "       [2.40019   , 0.        ],\n",
            "       ...,\n",
            "       [2.7562017 , 0.        ],\n",
            "       [0.09513831, 0.        ],\n",
            "       [1.01101   , 0.        ]], dtype=float32)>\n",
            "\n",
            "BC output tf.Tensor(\n",
            "[[-0.1764651   0.24935566  0.02372235]\n",
            " [-0.4306767   0.60458106  0.02183342]\n",
            " [-0.4552589   0.6415223   0.01883256]\n",
            " ...\n",
            " [-0.4786142   0.67962474  0.0157775 ]\n",
            " [-0.02779831  0.03936598  0.0042846 ]\n",
            " [-0.26425982  0.37214625  0.02927235]], shape=(4096, 3), dtype=float32)\n",
            "\n",
            "BC of u1: tf.Tensor(\n",
            "[[-0.1764651 ]\n",
            " [-0.4306767 ]\n",
            " [-0.4552589 ]\n",
            " ...\n",
            " [-0.4786142 ]\n",
            " [-0.02779831]\n",
            " [-0.26425982]], shape=(4096, 1), dtype=float32)\n",
            "\n",
            "BC of u2: tf.Tensor(\n",
            "[[-0.1764651 ]\n",
            " [-0.4306767 ]\n",
            " [-0.4552589 ]\n",
            " ...\n",
            " [-0.4786142 ]\n",
            " [-0.02779831]\n",
            " [-0.26425982]], shape=(4096, 1), dtype=float32)\n",
            "\n",
            "BC of du1_t: tf.Tensor(\n",
            "[[0.01606014]\n",
            " [0.00239742]\n",
            " [0.00143011]\n",
            " ...\n",
            " [0.00107838]\n",
            " [0.0193252 ]\n",
            " [0.0120025 ]], shape=(4096, 1), dtype=float32)\n",
            "\n",
            "BC of du2_t: tf.Tensor(\n",
            "[[-0.24491107]\n",
            " [-0.14949614]\n",
            " [-0.13635491]\n",
            " ...\n",
            " [-0.12239864]\n",
            " [-0.26494905]\n",
            " [-0.21985996]], shape=(4096, 1), dtype=float32)\n",
            "\n",
            "--- Testing losses ---\n",
            "\n",
            "Testing domain errors: tf.Tensor(\n",
            "[[-0.24058372 -0.09427004 -0.7151402 ]\n",
            " [-0.15299062 -0.40150797 -0.04644613]\n",
            " [-0.3342196  -0.18265924 -0.38842207]\n",
            " ...\n",
            " [-0.2385615   0.16358656 -0.5497006 ]\n",
            " [-0.00919089 -0.27491248 -0.90338993]\n",
            " [-0.06534408  0.10044232 -0.48182562]], shape=(4096, 3), dtype=float32)\n",
            "\n",
            "Testing domain mean losses: tf.Tensor([0.03974378 0.05398791 0.2575662 ], shape=(3,), dtype=float32)\n",
            "\n",
            "Testing total domain mean loss: tf.Tensor(0.11709931, shape=(), dtype=float32)\n",
            "\n",
            "Testing loss of u1-bcs: tf.Tensor(0.7326865, shape=(), dtype=float32)\n",
            "\n",
            "Testing loss of u2-bcs: tf.Tensor(0.75586855, shape=(), dtype=float32)\n",
            "\n",
            "Testing loss of du1-bcs: tf.Tensor(0.51718557, shape=(), dtype=float32)\n",
            "\n",
            "Testing loss of du2_t-bcs: tf.Tensor(0.5182947, shape=(), dtype=float32)\n",
            "\n",
            "Testing total loss: tf.Tensor(2.6411347, shape=(), dtype=float32)\n",
            "\n",
            "--- Testing solution ---\n",
            "\n",
            "Testing domain errors: tf.Tensor(\n",
            "[[ 0.48526132 -0.21552834  5.771453  ]\n",
            " [ 0.04358086  0.1120945   1.307269  ]\n",
            " [ 0.08627824  0.0279765   0.9858808 ]\n",
            " ...\n",
            " [ 0.04404061 -0.04579104  0.6905744 ]\n",
            " [ 0.26773295  0.8689358   9.883157  ]\n",
            " [-0.01258279 -0.36363366  3.9549193 ]], shape=(4096, 3), dtype=float32)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "epochs = 20000\n",
        "learning_rate = 0.0005\n",
        "\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate=learning_rate)\n",
        "\n",
        "for i in range(epochs + 1):\n",
        "  with tf.GradientTape() as tape_model:\n",
        "    with tf.GradientTape(persistent=True) as tape_domain:\n",
        "      y_train = model(x_train, training=True)\n",
        "      domain_errors = pde_system(tape_domain, x_train, y_train)\n",
        "\n",
        "    with tf.GradientTape(persistent=True) as tape_bcs:\n",
        "      y_bc = model(x_bc, training=True)\n",
        "      du1_t_bc = jacobian(tape_bcs, y_bc, x_bc, i=0, j=1)\n",
        "      du2_t_bc = jacobian(tape_bcs, y_bc, x_bc, i=1, j=1)\n",
        "    u1_bc = y_bc[:, 0: 1]\n",
        "    u2_bc = y_bc[:, 1: 2]\n",
        "\n",
        "    domain_mean_losses = tf.math.reduce_mean(tf.math.square(domain_errors), axis=0)\n",
        "    domain_total_mean_loss = tf.math.reduce_mean(domain_mean_losses, axis=0)\n",
        "    loss_u1 = tf.math.reduce_mean(tf.math.square(u1_bc - bc_u1(x_bc)), axis=0)[0]\n",
        "    loss_u2 = tf.math.reduce_mean(tf.math.square(u2_bc - bc_u2(x_bc)), axis=0)[0]\n",
        "    loss_du1 = tf.math.reduce_mean(tf.math.square(du1_t_bc - bc_du1(x_bc)), axis=0)[0]\n",
        "    loss_du2 = tf.math.reduce_mean(tf.math.square(du2_t_bc - bc_du2(x_bc)), axis=0)[0]\n",
        "    total_train_mse_loss = domain_total_mean_loss + loss_u1 + loss_u2 + loss_du1 + loss_du2\n",
        "\n",
        "  model_update_gradients = tape_model.gradient(total_train_mse_loss, model.trainable_variables)\n",
        "  optimizer.apply_gradients(\n",
        "    zip(model_update_gradients, model.trainable_variables)\n",
        "  )\n",
        "\n",
        "  del tape_domain, tape_bcs\n",
        "\n",
        "  if i % 1000 == 0:\n",
        "    y_preds = model(x_test)\n",
        "    y_true = solution(x_test)\n",
        "    errors = y_preds - y_true\n",
        "    test_mse_mean_losses = tf.math.reduce_mean(tf.math.square(errors), axis=0)\n",
        "    print('Epoch: {}\\tTrain Loss = {},\\tTest Loss = {}'.format(i, domain_mean_losses.numpy(), test_mse_mean_losses.numpy()))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fVVgKpKNXE4q",
        "outputId": "b4cef3a1-ae0c-4a4e-c050-ddb2b01cd23e"
      },
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch: 0\tTrain Loss = [0.03974378 0.05398791 0.2575662 ],\tTest Loss = [ 0.14426956  0.10616456 19.06314   ]\n",
            "Epoch: 1000\tTrain Loss = [0.00044387 0.00033955 0.00051211],\tTest Loss = [6.0356776e-03 1.1616416e-02 1.4600947e+01]\n",
            "Epoch: 2000\tTrain Loss = [4.4964185e-05 4.0343097e-05 1.3704150e-04],\tTest Loss = [3.6434918e-03 5.4735313e-03 1.4164449e+01]\n",
            "Epoch: 3000\tTrain Loss = [1.0556585e-05 1.8312225e-05 7.2138711e-05],\tTest Loss = [3.2672051e-03 4.2237067e-03 1.4013189e+01]\n",
            "Epoch: 4000\tTrain Loss = [1.1765272e-05 5.6781930e-05 4.6417932e-05],\tTest Loss = [3.0861616e-03 3.6608034e-03 1.3869204e+01]\n",
            "Epoch: 5000\tTrain Loss = [2.5159237e-05 2.0179452e-05 3.3210163e-05],\tTest Loss = [2.8973864e-03 3.3252102e-03 1.3700095e+01]\n",
            "Epoch: 6000\tTrain Loss = [2.3197922e-06 5.5363284e-06 2.2426013e-05],\tTest Loss = [2.6315937e-03 3.0213839e-03 1.3513732e+01]\n",
            "Epoch: 7000\tTrain Loss = [6.3152806e-06 8.4911098e-06 1.9736670e-05],\tTest Loss = [2.4272972e-03 2.7676784e-03 1.3336361e+01]\n",
            "Epoch: 8000\tTrain Loss = [1.8216383e-06 2.9768369e-06 1.5802263e-05],\tTest Loss = [2.2883138e-03 2.5374040e-03 1.3154322e+01]\n",
            "Epoch: 9000\tTrain Loss = [8.372078e-06 8.172202e-06 1.438901e-05],\tTest Loss = [2.1626500e-03 2.3401254e-03 1.2975323e+01]\n",
            "Epoch: 10000\tTrain Loss = [4.12261907e-05 1.06000356e-04 1.62896249e-05],\tTest Loss = [2.0668122e-03 2.1684682e-03 1.2812875e+01]\n",
            "Epoch: 11000\tTrain Loss = [2.6732030e-06 5.6455997e-06 1.2763173e-05],\tTest Loss = [1.9783317e-03 2.0365224e-03 1.2645886e+01]\n",
            "Epoch: 12000\tTrain Loss = [1.8927103e-05 2.1169306e-05 1.3533332e-05],\tTest Loss = [1.9574403e-03 1.9389968e-03 1.2487029e+01]\n",
            "Epoch: 13000\tTrain Loss = [3.6131652e-05 2.8031704e-05 1.5817452e-05],\tTest Loss = [1.8828129e-03 1.8379826e-03 1.2338890e+01]\n",
            "Epoch: 14000\tTrain Loss = [3.64818952e-05 1.08173284e-04 2.14328229e-05],\tTest Loss = [1.9188834e-03 1.7888822e-03 1.2183121e+01]\n",
            "Epoch: 15000\tTrain Loss = [1.04922165e-05 1.59236424e-05 1.08997183e-05],\tTest Loss = [1.8561631e-03 1.7548254e-03 1.2026764e+01]\n",
            "Epoch: 16000\tTrain Loss = [2.5782206e-06 2.0562586e-06 1.0645050e-05],\tTest Loss = [1.8343062e-03 1.7176595e-03 1.1882441e+01]\n",
            "Epoch: 17000\tTrain Loss = [2.3974842e-05 1.7992523e-05 1.3107186e-05],\tTest Loss = [1.8605168e-03 1.7193848e-03 1.1737818e+01]\n",
            "Epoch: 18000\tTrain Loss = [6.6027474e-06 5.7070001e-06 9.3740246e-06],\tTest Loss = [1.8428876e-03 1.6738016e-03 1.1597012e+01]\n",
            "Epoch: 19000\tTrain Loss = [7.9372308e-05 1.4552911e-04 1.9006951e-05],\tTest Loss = [1.9253306e-03 1.7035021e-03 1.1456088e+01]\n",
            "Epoch: 20000\tTrain Loss = [1.2177767e-05 1.6581735e-05 1.5292097e-05],\tTest Loss = [1.8790207e-03 1.7360847e-03 1.1326667e+01]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x_eval = np.linspace([0.0, 0.0], [3.0, 3.0], 100)\n",
        "y_true = solution(x_eval)\n",
        "y_pred = model(x_eval)\n",
        "\n",
        "plt.plot(y_true[:, 0: 1])\n",
        "plt.plot(y_pred[:, 0: 1])\n",
        "plt.title('Evaluation of u1(x,t)')\n",
        "plt.legend(['Real', 'Predicted'])\n",
        "plt.show()\n",
        "\n",
        "plt.plot(y_true[:, 1: 2])\n",
        "plt.plot(y_pred[:, 1: 2])\n",
        "plt.title('Evaluation of u2(x,t)')\n",
        "plt.legend(['Real', 'Predicted'])\n",
        "plt.show()\n",
        "\n",
        "plt.plot(y_true[:, 2: 3])\n",
        "plt.plot(y_pred[:, 2: 3])\n",
        "plt.title('Evaluation of u3(x,t)')\n",
        "plt.legend(['Real', 'Predicted'])\n",
        "plt.show()\n",
        "\n",
        "ax = plt.figure().add_subplot(projection='3d')\n",
        "ax.scatter(y_pred[:, 0: 1], y_pred[:, 1: 2], y_pred[:, 2: 3])\n",
        "ax.scatter(y_true[:, 0: 1], y_true[:, 1: 2], y_true[:, 2: 3])\n",
        "ax.set_xlabel('u1(x, t)')\n",
        "ax.set_ylabel('u2(x, t')\n",
        "ax.set_zlabel('u3(x, t')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "bTNMoSn5153I",
        "outputId": "0cc55c63-5e5e-47c7-9e35-7e947b58c9d1"
      },
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}