sciann_1d_curve_fitting.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "sciann_1d_curve_fitting.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOj4Nntp0Fz7gkPjnGzYOs2",
      "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/swampxx/sciann-examples/blob/main/sciann_1d_curve_fitting.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-pAhZD4gtVSs"
      },
      "source": [
        "# Install sciann\n",
        "%%capture sciann_installation\n",
        "!pip install sciann"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BiJCKvRRtdiQ",
        "outputId": "42230e6b-3bd7-416e-fe61-b3ddc5d029de"
      },
      "source": [
        "# Module imports\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import sciann as sn\n",
        "\n",
        "%matplotlib inline"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "---------------------- SCIANN 0.6.3.1 ---------------------- \n",
            "For details, check out our review paper and the documentation at: \n",
            " +  \"https://www.sciencedirect.com/science/article/pii/S0045782520307374\", \n",
            " +  \"https://arxiv.org/abs/2005.08803\", \n",
            " +  \"https://www.sciann.com\". \n",
            "\n",
            " Need support or would like to contribute, please join sciann`s slack group: \n",
            " +  \"https://join.slack.com/t/sciann/shared_invite/zt-ne1f5jlx-k_dY8RGo3ZreDXwz0f~CeA\" \n",
            " \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fyixY8xYuDLm"
      },
      "source": [
        " Consider $f(x)=sin(x)$ function over the domain $x\\rightarrow [0, 2\\pi]$. \n",
        " \n",
        " We can generate a set of discrete data by using $f$ to conduct simple experiment on SciANN."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "uE2pKMxCtwYc",
        "outputId": "5453cb01-57d2-40b6-cf85-0661668a9e9c"
      },
      "source": [
        "x_train = np.linspace(0, np.pi*2, 5000)\n",
        "y_train = np.sin(x_train)\n",
        "\n",
        "# plot the data\n",
        "plt.title('Generated Data')\n",
        "plt.xlabel('$x$')\n",
        "plt.ylabel('$y$')\n",
        "xx = [idx*np.pi/4 for idx in range(9)]\n",
        "xx_t = ['$0$', '$\\\\frac{\\\\pi}{4}$', '$\\\\frac{\\\\pi}{2}$', '$\\\\frac{3\\\\pi}{4}$', '$\\\\pi$', \n",
        "        '$\\\\frac{5\\\\pi}{4}$', '$\\\\frac{3\\\\pi}{2}$', '$\\\\frac{7\\\\pi}{4}$', '$2\\\\pi$']\n",
        "plt.xticks(xx, xx_t)\n",
        "plt.plot(x_train, y_train, label='$y = \\sin (x)$')\n",
        "plt.legend(loc=\"upper left\")\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3nXofjH1xR7h"
      },
      "source": [
        "Now, we can start to construct our model by starting.\n",
        "\n",
        "We have input $x$ and output ${f}(x)= y =\\sin(x)$. \n",
        "We use _Variable_ class to define our input layer and _Functional_ class to create the network."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7SIxcLDnvMmm"
      },
      "source": [
        "# Input\n",
        "x = sn.Variable('x')\n",
        "\n",
        "# Network\n",
        "f_hat = sn.Functional(\n",
        "    'f_hat',\n",
        "    variables=x,\n",
        "    hidden_layers=[8, 16, 8],\n",
        "    activation='tanh'\n",
        ")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WaD7l5wi1ZAu"
      },
      "source": [
        "We have created our input layer and the underlying network. Now, we need to enforce some constraints. \n",
        "\n",
        "\n",
        "First, we have data constraint. Output of the network $\\hat{f}(x)$ should match with the $\\sin(x)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lw0bVK0_1Ykn"
      },
      "source": [
        "constraint_data = sn.constraints.Data(f_hat)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iVmgr8AF590X"
      },
      "source": [
        "Second, we know that second derivative of $\\sin(x)$ is $-\\sin(x)$ and their sum is zero. Therefore, our network $\\hat{f}$ should satisy this condition as well.\n",
        "\n",
        "We can enforce this by using PDE constraint."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1HkmOI61ynG0"
      },
      "source": [
        "# diff(f, x, order=2) + y should be zero, \n",
        "#     while training zero labels will be used.\n",
        "constraint_pde = sn.constraints.PDE(sn.utils.diff(f_hat, x, order=2) + f_hat)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dcj-DgGs8Uwv"
      },
      "source": [
        "SciModel is ready to be constructed!\n",
        "\n",
        "Mean Squared Error is used for loss function.\n",
        "\n",
        "ADAM with default values is used for optimizer. (lr=0.001, beta=(0.9, 0.999))\n",
        "\n",
        "_Limitation: We can not employ weighting for the constraints. It is not supported!_"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tgqUNBTxyoye",
        "outputId": "4f2df840-cf70-4c8f-e354-15d349f55991"
      },
      "source": [
        "model = sn.SciModel(x, [constraint_data, constraint_pde],\n",
        "                    loss_func='mse',\n",
        "                    optimizer='adam',\n",
        "                    plot_to_file='network.png')\n",
        "\n",
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"model\"\n",
            "__________________________________________________________________________________________________\n",
            "Layer (type)                    Output Shape         Param #     Connected to                     \n",
            "==================================================================================================\n",
            "x (InputLayer)                  [(None, 1)]          0                                            \n",
            "__________________________________________________________________________________________________\n",
            "D8b (Dense)                     (None, 8)            16          x[0][0]                          \n",
            "__________________________________________________________________________________________________\n",
            "sci_activation (SciActivation)  (None, 8)            0           D8b[0][0]                        \n",
            "__________________________________________________________________________________________________\n",
            "D16b (Dense)                    (None, 16)           144         sci_activation[0][0]             \n",
            "__________________________________________________________________________________________________\n",
            "sci_activation_1 (SciActivation (None, 16)           0           D16b[0][0]                       \n",
            "__________________________________________________________________________________________________\n",
            "D8b_2 (Dense)                   (None, 8)            136         sci_activation_1[0][0]           \n",
            "__________________________________________________________________________________________________\n",
            "sci_activation_2 (SciActivation (None, 8)            0           D8b_2[0][0]                      \n",
            "__________________________________________________________________________________________________\n",
            "f_hat (Field)                   (None, 1)            9           sci_activation_2[0][0]           \n",
            "__________________________________________________________________________________________________\n",
            "Grad2_f_hat_x/ (Lambda)         (None, 1)            0           f_hat[0][0]                      \n",
            "__________________________________________________________________________________________________\n",
            "add (Lambda)                    (None, 1)            0           Grad2_f_hat_x/[0][0]             \n",
            "                                                                 f_hat[0][0]                      \n",
            "==================================================================================================\n",
            "Total params: 305\n",
            "Trainable params: 305\n",
            "Non-trainable params: 0\n",
            "__________________________________________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7vaepfva9YnU"
      },
      "source": [
        "SciModel is constructed and it should be trained with the data we created in the beginning and the PDE constraint on network $f$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zbqUBLaA85C9",
        "outputId": "08e797a6-c658-4e98-87a2-7fa0b6124f64"
      },
      "source": [
        "training_history = model.train(x_train,             # input x\n",
        "                               [y_train, 'zeros'],  # y_train for data constraint, zeros for PDE constraint\n",
        "                               batch_size = 32,\n",
        "                               epochs=100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Total samples: 5000 \n",
            "Batch size: 32 \n",
            "Total batches: 157 \n",
            "\n",
            "Epoch 1/100\n",
            "157/157 [==============================] - 1s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.3204 - f_hat_loss: 0.2708 - add_loss: 0.0496 - lr: 0.0010 - time: 1.2460\n",
            "Epoch 2/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.2052 - f_hat_loss: 0.1318 - add_loss: 0.0733 - lr: 0.0010 - time: 0.4122\n",
            "Epoch 3/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.1714 - f_hat_loss: 0.0964 - add_loss: 0.0750 - lr: 0.0010 - time: 0.4234\n",
            "Epoch 4/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.1598 - f_hat_loss: 0.0841 - add_loss: 0.0758 - lr: 0.0010 - time: 0.4317\n",
            "Epoch 5/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.1488 - f_hat_loss: 0.0763 - add_loss: 0.0725 - lr: 0.0010 - time: 0.4100\n",
            "Epoch 6/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.1348 - f_hat_loss: 0.0674 - add_loss: 0.0674 - lr: 0.0010 - time: 0.4190\n",
            "Epoch 7/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.1117 - f_hat_loss: 0.0530 - add_loss: 0.0587 - lr: 0.0010 - time: 0.4323\n",
            "Epoch 8/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0755 - f_hat_loss: 0.0332 - add_loss: 0.0423 - lr: 0.0010 - time: 0.4251\n",
            "Epoch 9/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0305 - f_hat_loss: 0.0132 - add_loss: 0.0173 - lr: 0.0010 - time: 0.4181\n",
            "Epoch 10/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0145 - f_hat_loss: 0.0053 - add_loss: 0.0092 - lr: 0.0010 - time: 0.4593\n",
            "Epoch 11/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0086 - f_hat_loss: 0.0024 - add_loss: 0.0062 - lr: 0.0010 - time: 0.4545\n",
            "Epoch 12/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0056 - f_hat_loss: 0.0012 - add_loss: 0.0043 - lr: 0.0010 - time: 0.4150\n",
            "Epoch 13/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0037 - f_hat_loss: 6.4455e-04 - add_loss: 0.0030 - lr: 0.0010 - time: 0.4281\n",
            "Epoch 14/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0026 - f_hat_loss: 3.7759e-04 - add_loss: 0.0022 - lr: 0.0010 - time: 0.4349\n",
            "Epoch 15/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0018 - f_hat_loss: 2.0237e-04 - add_loss: 0.0016 - lr: 0.0010 - time: 0.4366\n",
            "Epoch 16/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 0.0013 - f_hat_loss: 1.4388e-04 - add_loss: 0.0012 - lr: 0.0010 - time: 0.4253\n",
            "Epoch 17/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 9.5612e-04 - f_hat_loss: 8.6518e-05 - add_loss: 8.6959e-04 - lr: 0.0010 - time: 0.3979\n",
            "Epoch 18/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 7.1674e-04 - f_hat_loss: 5.9451e-05 - add_loss: 6.5728e-04 - lr: 0.0010 - time: 0.4095\n",
            "Epoch 19/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.4710e-04 - f_hat_loss: 4.0599e-05 - add_loss: 5.0650e-04 - lr: 0.0010 - time: 0.4323\n",
            "Epoch 20/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.3296e-04 - f_hat_loss: 3.0869e-05 - add_loss: 4.0209e-04 - lr: 0.0010 - time: 0.4168\n",
            "Epoch 21/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.4154e-04 - f_hat_loss: 2.5910e-05 - add_loss: 3.1562e-04 - lr: 0.0010 - time: 0.4249\n",
            "Epoch 22/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.8457e-04 - f_hat_loss: 2.0651e-05 - add_loss: 2.6392e-04 - lr: 0.0010 - time: 0.4520\n",
            "Epoch 23/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.3014e-04 - f_hat_loss: 1.7938e-05 - add_loss: 2.1222e-04 - lr: 0.0010 - time: 0.4186\n",
            "Epoch 24/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.9195e-04 - f_hat_loss: 1.3978e-05 - add_loss: 1.7797e-04 - lr: 0.0010 - time: 0.4280\n",
            "Epoch 25/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.6307e-04 - f_hat_loss: 1.2929e-05 - add_loss: 1.5014e-04 - lr: 0.0010 - time: 0.4238\n",
            "Epoch 26/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.6099e-04 - f_hat_loss: 2.2940e-05 - add_loss: 1.3805e-04 - lr: 0.0010 - time: 0.4173\n",
            "Epoch 27/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.3053e-04 - f_hat_loss: 1.4384e-05 - add_loss: 1.1614e-04 - lr: 0.0010 - time: 0.4325\n",
            "Epoch 28/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.0961e-04 - f_hat_loss: 9.7816e-06 - add_loss: 9.9826e-05 - lr: 0.0010 - time: 0.4196\n",
            "Epoch 29/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 9.4175e-05 - f_hat_loss: 7.1078e-06 - add_loss: 8.7068e-05 - lr: 0.0010 - time: 0.4390\n",
            "Epoch 30/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 8.7443e-05 - f_hat_loss: 8.6115e-06 - add_loss: 7.8831e-05 - lr: 0.0010 - time: 0.4325\n",
            "Epoch 31/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.1304e-04 - f_hat_loss: 2.8575e-05 - add_loss: 8.4467e-05 - lr: 0.0010 - time: 0.4171\n",
            "Epoch 32/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.9966e-05 - f_hat_loss: 6.9842e-06 - add_loss: 6.2981e-05 - lr: 0.0010 - time: 0.4204\n",
            "Epoch 33/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.8654e-05 - f_hat_loss: 1.0166e-05 - add_loss: 5.8488e-05 - lr: 0.0010 - time: 0.4197\n",
            "Epoch 34/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.7413e-05 - f_hat_loss: 6.2096e-06 - add_loss: 5.1203e-05 - lr: 0.0010 - time: 0.4333\n",
            "Epoch 35/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.4942e-05 - f_hat_loss: 6.9601e-06 - add_loss: 4.7983e-05 - lr: 0.0010 - time: 0.4311\n",
            "Epoch 36/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.9172e-05 - f_hat_loss: 5.8663e-06 - add_loss: 4.3306e-05 - lr: 0.0010 - time: 0.4468\n",
            "Epoch 37/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.8911e-05 - f_hat_loss: 1.2978e-05 - add_loss: 4.5933e-05 - lr: 0.0010 - time: 0.3997\n",
            "Epoch 38/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.5368e-05 - f_hat_loss: 1.3361e-05 - add_loss: 4.2007e-05 - lr: 0.0010 - time: 0.4283\n",
            "Epoch 39/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.1192e-05 - f_hat_loss: 1.1341e-05 - add_loss: 3.9849e-05 - lr: 0.0010 - time: 0.4199\n",
            "Epoch 40/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.9318e-05 - f_hat_loss: 6.8089e-06 - add_loss: 3.2509e-05 - lr: 0.0010 - time: 0.4268\n",
            "Epoch 41/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.6064e-05 - f_hat_loss: 6.9499e-06 - add_loss: 2.9115e-05 - lr: 0.0010 - time: 0.4455\n",
            "Epoch 42/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.5674e-05 - f_hat_loss: 5.9380e-06 - add_loss: 2.9736e-05 - lr: 0.0010 - time: 0.4088\n",
            "Epoch 43/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.9607e-05 - f_hat_loss: 4.2662e-06 - add_loss: 2.5342e-05 - lr: 0.0010 - time: 0.4201\n",
            "Epoch 44/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.4709e-05 - f_hat_loss: 8.8334e-06 - add_loss: 2.5876e-05 - lr: 0.0010 - time: 0.4542\n",
            "Epoch 45/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.5765e-05 - f_hat_loss: 8.6431e-06 - add_loss: 2.7122e-05 - lr: 0.0010 - time: 0.4094\n",
            "Epoch 46/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.4855e-05 - f_hat_loss: 8.3403e-06 - add_loss: 2.6514e-05 - lr: 0.0010 - time: 0.4608\n",
            "Epoch 47/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.6176e-05 - f_hat_loss: 1.7571e-05 - add_loss: 2.8604e-05 - lr: 0.0010 - time: 0.4195\n",
            "Epoch 48/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.7531e-05 - f_hat_loss: 6.1186e-06 - add_loss: 2.1412e-05 - lr: 0.0010 - time: 0.4253\n",
            "Epoch 49/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.5214e-05 - f_hat_loss: 5.7314e-06 - add_loss: 1.9483e-05 - lr: 0.0010 - time: 0.4214\n",
            "Epoch 50/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.6129e-05 - f_hat_loss: 7.2803e-06 - add_loss: 1.8849e-05 - lr: 0.0010 - time: 0.4410\n",
            "Epoch 51/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.0463e-05 - f_hat_loss: 4.2985e-06 - add_loss: 1.6164e-05 - lr: 0.0010 - time: 0.4008\n",
            "Epoch 52/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.9054e-05 - f_hat_loss: 8.5602e-06 - add_loss: 2.0494e-05 - lr: 0.0010 - time: 0.4199\n",
            "Epoch 53/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.1941e-05 - f_hat_loss: 5.8059e-06 - add_loss: 1.6134e-05 - lr: 0.0010 - time: 0.4403\n",
            "Epoch 54/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.0094e-05 - f_hat_loss: 5.6837e-06 - add_loss: 1.4410e-05 - lr: 0.0010 - time: 0.4179\n",
            "Epoch 55/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 7.5848e-05 - f_hat_loss: 3.6286e-05 - add_loss: 3.9565e-05 - lr: 0.0010 - time: 0.4211\n",
            "Epoch 56/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.5701e-05 - f_hat_loss: 3.2152e-06 - add_loss: 1.2485e-05 - lr: 0.0010 - time: 0.4351\n",
            "Epoch 57/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.5357e-05 - f_hat_loss: 3.3485e-06 - add_loss: 1.2009e-05 - lr: 0.0010 - time: 0.4244\n",
            "Epoch 58/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 7.6472e-05 - f_hat_loss: 3.9508e-05 - add_loss: 3.6962e-05 - lr: 0.0010 - time: 0.4367\n",
            "Epoch 59/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.2117e-05 - f_hat_loss: 7.7007e-06 - add_loss: 1.4416e-05 - lr: 0.0010 - time: 0.4573\n",
            "Epoch 60/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.7703e-05 - f_hat_loss: 5.2307e-06 - add_loss: 1.2472e-05 - lr: 0.0010 - time: 0.4564\n",
            "Epoch 61/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.4540e-05 - f_hat_loss: 3.5916e-06 - add_loss: 1.0948e-05 - lr: 0.0010 - time: 0.4365\n",
            "Epoch 62/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.9426e-05 - f_hat_loss: 6.5181e-06 - add_loss: 1.2907e-05 - lr: 0.0010 - time: 0.4159\n",
            "Epoch 63/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.3991e-05 - f_hat_loss: 3.7612e-06 - add_loss: 1.0230e-05 - lr: 0.0010 - time: 0.4233\n",
            "Epoch 64/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.0886e-05 - f_hat_loss: 7.5581e-06 - add_loss: 1.3328e-05 - lr: 0.0010 - time: 0.4182\n",
            "Epoch 65/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.2391e-05 - f_hat_loss: 3.0425e-06 - add_loss: 9.3487e-06 - lr: 0.0010 - time: 0.4142\n",
            "Epoch 66/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.1078e-05 - f_hat_loss: 8.4640e-06 - add_loss: 1.2614e-05 - lr: 0.0010 - time: 0.4433\n",
            "Epoch 67/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.1704e-05 - f_hat_loss: 8.1237e-06 - add_loss: 1.3580e-05 - lr: 0.0010 - time: 0.4457\n",
            "Epoch 68/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.3934e-05 - f_hat_loss: 9.6131e-06 - add_loss: 1.4322e-05 - lr: 0.0010 - time: 0.4232\n",
            "Epoch 69/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 2.2495e-05 - f_hat_loss: 8.8845e-06 - add_loss: 1.3610e-05 - lr: 0.0010 - time: 0.4377\n",
            "Epoch 70/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.6241e-05 - f_hat_loss: 6.0223e-06 - add_loss: 1.0219e-05 - lr: 0.0010 - time: 0.4278\n",
            "Epoch 71/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.9151e-05 - f_hat_loss: 7.3435e-06 - add_loss: 1.1807e-05 - lr: 0.0010 - time: 0.4080\n",
            "Epoch 72/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.4860e-05 - f_hat_loss: 5.1352e-06 - add_loss: 9.7242e-06 - lr: 0.0010 - time: 0.4117\n",
            "Epoch 73/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.7945e-05 - f_hat_loss: 6.6266e-06 - add_loss: 1.1318e-05 - lr: 0.0010 - time: 0.4096\n",
            "Epoch 74/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.9245e-05 - f_hat_loss: 7.8259e-06 - add_loss: 1.1419e-05 - lr: 0.0010 - time: 0.4253\n",
            "Epoch 75/100\n",
            "156/157 [============================>.] - ETA: 0s - batch: 77.5000 - size: 31.8462 - loss: 3.2964e-05 - f_hat_loss: 1.5723e-05 - add_loss: 1.7241e-05\n",
            "Epoch 00075: ReduceLROnPlateau reducing learning rate to 0.0005000000237487257.\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 3.2895e-05 - f_hat_loss: 1.5639e-05 - add_loss: 1.7255e-05 - lr: 0.0010 - time: 0.4523\n",
            "Epoch 76/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 7.0807e-06 - f_hat_loss: 1.3109e-06 - add_loss: 5.7703e-06 - lr: 5.0000e-04 - time: 0.4232\n",
            "Epoch 77/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.8373e-06 - f_hat_loss: 1.1291e-06 - add_loss: 5.7082e-06 - lr: 5.0000e-04 - time: 0.4197\n",
            "Epoch 78/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.6645e-06 - f_hat_loss: 1.0768e-06 - add_loss: 5.5877e-06 - lr: 5.0000e-04 - time: 0.4148\n",
            "Epoch 79/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.8576e-06 - f_hat_loss: 7.4804e-07 - add_loss: 5.1095e-06 - lr: 5.0000e-04 - time: 0.4243\n",
            "Epoch 80/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 7.6043e-06 - f_hat_loss: 1.6200e-06 - add_loss: 5.9847e-06 - lr: 5.0000e-04 - time: 0.4233\n",
            "Epoch 81/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.4313e-06 - f_hat_loss: 1.0357e-06 - add_loss: 5.3956e-06 - lr: 5.0000e-04 - time: 0.4416\n",
            "Epoch 82/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 7.3524e-06 - f_hat_loss: 1.7214e-06 - add_loss: 5.6308e-06 - lr: 5.0000e-04 - time: 0.4500\n",
            "Epoch 83/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 9.3043e-06 - f_hat_loss: 2.8213e-06 - add_loss: 6.4829e-06 - lr: 5.0000e-04 - time: 0.4488\n",
            "Epoch 84/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.1683e-06 - f_hat_loss: 1.1724e-06 - add_loss: 4.9958e-06 - lr: 5.0000e-04 - time: 0.3987\n",
            "Epoch 85/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.8905e-06 - f_hat_loss: 1.4699e-06 - add_loss: 5.4207e-06 - lr: 5.0000e-04 - time: 0.4108\n",
            "Epoch 86/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 6.2784e-06 - f_hat_loss: 1.2441e-06 - add_loss: 5.0342e-06 - lr: 5.0000e-04 - time: 0.4028\n",
            "Epoch 87/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 8.1813e-06 - f_hat_loss: 2.3766e-06 - add_loss: 5.8046e-06 - lr: 5.0000e-04 - time: 0.4516\n",
            "Epoch 88/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 7.5848e-06 - f_hat_loss: 2.0598e-06 - add_loss: 5.5249e-06 - lr: 5.0000e-04 - time: 0.4268\n",
            "Epoch 89/100\n",
            "140/157 [=========================>....] - ETA: 0s - batch: 69.5000 - size: 31.8286 - loss: 1.2655e-05 - f_hat_loss: 5.0387e-06 - add_loss: 7.6164e-06\n",
            "Epoch 00089: ReduceLROnPlateau reducing learning rate to 0.0002500000118743628.\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 1.3184e-05 - f_hat_loss: 5.3900e-06 - add_loss: 7.7937e-06 - lr: 5.0000e-04 - time: 0.4267\n",
            "Epoch 90/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.6097e-06 - f_hat_loss: 5.6821e-07 - add_loss: 4.0416e-06 - lr: 2.5000e-04 - time: 0.4189\n",
            "Epoch 91/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.0050e-06 - f_hat_loss: 6.9916e-07 - add_loss: 4.3058e-06 - lr: 2.5000e-04 - time: 0.4240\n",
            "Epoch 92/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.5967e-06 - f_hat_loss: 5.8340e-07 - add_loss: 4.0133e-06 - lr: 2.5000e-04 - time: 0.4232\n",
            "Epoch 93/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.8948e-06 - f_hat_loss: 7.7483e-07 - add_loss: 4.1199e-06 - lr: 2.5000e-04 - time: 0.4426\n",
            "Epoch 94/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.8855e-06 - f_hat_loss: 7.1674e-07 - add_loss: 4.1688e-06 - lr: 2.5000e-04 - time: 0.4590\n",
            "Epoch 95/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.4553e-06 - f_hat_loss: 5.1091e-07 - add_loss: 3.9444e-06 - lr: 2.5000e-04 - time: 0.4420\n",
            "Epoch 96/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.5228e-06 - f_hat_loss: 1.0434e-06 - add_loss: 4.4794e-06 - lr: 2.5000e-04 - time: 0.4095\n",
            "Epoch 97/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.3585e-06 - f_hat_loss: 5.4404e-07 - add_loss: 3.8144e-06 - lr: 2.5000e-04 - time: 0.4422\n",
            "Epoch 98/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.5327e-06 - f_hat_loss: 5.7721e-07 - add_loss: 3.9555e-06 - lr: 2.5000e-04 - time: 0.4548\n",
            "Epoch 99/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 4.8530e-06 - f_hat_loss: 8.9533e-07 - add_loss: 3.9578e-06 - lr: 2.5000e-04 - time: 0.4099\n",
            "Epoch 100/100\n",
            "157/157 [==============================] - 0s 2ms/step - batch: 78.0000 - size: 31.8471 - loss: 5.2671e-06 - f_hat_loss: 1.1259e-06 - add_loss: 4.1412e-06 - lr: 2.5000e-04 - time: 0.4370\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wUI0kw84ImoG"
      },
      "source": [
        "We have trained our SciModel with Data and PDE constraints. In this section, we plot Loss vs. Epoch values to make some observations about the training procedure.\n",
        "\n",
        "Please note that, all of the Keras functionalities are inherited. We can replace or customize our loss functions and optimizers by using Keras backend."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "Vf57bBqCCIK6",
        "outputId": "2810d7a9-8eff-45ff-ff7d-feb627f360e0"
      },
      "source": [
        "plt.plot(training_history.history['loss'])\n",
        "plt.plot(training_history.history['f_hat_loss'])\n",
        "plt.title('Epoch vs. Loss')\n",
        "plt.ylabel('Loss')\n",
        "plt.xlabel('Epoch')\n",
        "plt.legend(['Data Constraint Loss', 'PDE Constraint Loss'], loc='upper left')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "Yvk0ovAa-2E-",
        "outputId": "f9cf4bc2-eb42-44f0-e416-62da6b7bd927"
      },
      "source": [
        "y_pred = f_hat.eval(model, x_train)\n",
        "\n",
        "# plot the data\n",
        "plt.title('Predicted Data')\n",
        "plt.xlabel('$x$')\n",
        "plt.ylabel('$y$')\n",
        "xx = [idx*np.pi/4 for idx in range(9)]\n",
        "xx_t = ['$0$', '$\\\\frac{\\\\pi}{4}$', '$\\\\frac{\\\\pi}{2}$', '$\\\\frac{3\\\\pi}{4}$', '$\\\\pi$', \n",
        "        '$\\\\frac{5\\\\pi}{4}$', '$\\\\frac{3\\\\pi}{2}$', '$\\\\frac{7\\\\pi}{4}$', '$2\\\\pi$']\n",
        "plt.xticks(xx, xx_t)\n",
        "plt.plot(x_train, y_pred, label='$y=\\hat{f}(x)$')\n",
        "plt.legend(loc=\"upper left\")\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}