sciann_burgers_equation.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "sciann_burgers_equation.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyM7OwvAu2Fqc5j3bySxyGKE",
      "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_burgers_equation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CGD-ihQ5ELZv"
      },
      "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": "yBncc3uWRP5m",
        "outputId": "3eefb89a-a350-4653-a2c8-a4243a534b83"
      },
      "source": [
        "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": "5LOhU_gKREGK"
      },
      "source": [
        "We reproduce the Burgers Equation example which is illustraded in the SciANN paper.\n",
        "\n",
        "Burgers Equation:\n",
        "\n",
        "$u_{,t} + u u_{,x} - (0.01/\\pi)u_{,xx} = 0, t \\in [0,1], x \\in [-1,1]$\n",
        "\n",
        "initial and boundary conditions $u(t=0, x)=-\\sin (\\pi x)$ and $u(t, x= \\pm 1) = 0$, respectively. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cflo-SAnRao8"
      },
      "source": [
        "# In this cell, we define the input variables (x, t)\n",
        "# and the solution variable u\n",
        "\n",
        "x = sn.Variable('x')\n",
        "t = sn.Variable('t')\n",
        "u = sn.Functional('u', [t, x], 8*[20], 'tanh')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O2scCAfLRbUT"
      },
      "source": [
        "# the governing equation\n",
        "L1 = sn.diff(u, t) + u * sn.diff(u, x) - (0.01 / np.pi) * sn.diff(u, x, order=2)\n",
        "\n",
        "# initial and boundary conditions should be defined as continuous fucntions\n",
        "TOL = 0.001  # tolerance value\n",
        "\n",
        "# note that C1 is zero at all sampling points except t < 0\n",
        "# if the result of the solution variable u is not zero,\n",
        "# we penalize it with the loss term\n",
        "\n",
        "C1 = (1-sn.sign(t - TOL)) * (u + sn.sin(np.pi*x))\n",
        "C2 = (1-sn.sign(x - (-1+TOL))) * (u)\n",
        "C3 = (1+sn.sign(x - ( 1-TOL))) * (u)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dI3ELjxnSpsI"
      },
      "source": [
        "# define SciANN model\n",
        "m = sn.SciModel([x, t], [L1, C1, C2, C3])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ByNYdnkoSwjp"
      },
      "source": [
        "# generate input data\n",
        "x_data, t_data = np.meshgrid(\n",
        "    np.linspace(-1, 1, 100), \n",
        "    np.linspace(0, 1, 100)\n",
        ")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F4GhoMnqSy2V"
      },
      "source": [
        "# training...\n",
        "h = m.train([x_data, t_data], 4*['zero'], batch_size=256, epochs=10000, verbose=2)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zgr8UFY-S0mg"
      },
      "source": [
        "# test data\n",
        "x_test, t_test = np.meshgrid(\n",
        "    np.linspace(-1, 1, 200), \n",
        "    np.linspace(0, 1, 200)\n",
        ")\n",
        "\n",
        "# generate predictions for the test data\n",
        "u_pred = u.eval(m, [x_test, t_test])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a5RlDL8TS3KS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3935c527-a2bc-45ad-be39-0d20431c58bf"
      },
      "source": [
        "# visualization\n",
        "\n",
        "fig = plt.figure(figsize=(3, 4))\n",
        "plt.pcolor(x_test, t_test, u_pred, cmap='seismic')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('t')\n",
        "plt.colorbar()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.colorbar.Colorbar at 0x7f99b9804510>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 216x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}