Notebook2_Allen_Cahn.ipynb

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        "<a href=\"https://colab.research.google.com/github/levimcclenny/notebooks/blob/main/Notebook2_Allen_Cahn.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Allen-Cahn using the SA-PINN\n",
        "\n",
        "In this example we will explore a few more advanced features of TensorDiffEq, such as self-adaptive solving, in order to solve harder systems of PDEs. In this example, we will solve the Allen-Cahn equation, taking the form:\n",
        "\n",
        "$u_t -0.0001u_{xx} + 5u^3 -5u = 0\\,, \\ \\  x \\in [-1,1], \\ t \\in [0,1]\\,, $ \\\\\n",
        "$ u(x, 0) = x^2cos(\\pi x)\\,$ \\\\\n",
        "$ u(t, -1) = u(t,1)\\, $ \\\\\n",
        "$ u_x(t,-1) = u_x(t,1)\\ $\n",
        "\n",
        "Similar to last time, we first must install the *TensorDiffEq* package"
      ]
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        },
        "outputId": "14979cad-3261-45fd-b3a2-766124edd109"
      },
      "source": [
        "!pip install tensordiffeq"
      ],
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            "Building wheels for collected packages: pyDOE2\n",
            "  Building wheel for pyDOE2 (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pyDOE2: filename=pyDOE2-1.3.0-cp37-none-any.whl size=25519 sha256=988aacc17533e4dbd0f96773418db68da6440f8bb4571608d0c646832ca23d7d\n",
            "  Stored in directory: /root/.cache/pip/wheels/60/88/1d/b334ee00dd83e82d111ec56c3be91573d335c93870698037f1\n",
            "Successfully built pyDOE2\n",
            "Installing collected packages: pyDOE2, pyfiglet, tensordiffeq\n",
            "Successfully installed pyDOE2-1.3.0 pyfiglet-0.8.post1 tensordiffeq-0.1.8\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GuAX6VZatmAN"
      },
      "source": [
        "First, necessary imports. Then we define the domain - a simple 1D w/time domain, and generate collocation points in that domain,"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oGvQfBXn58B6"
      },
      "source": [
        "import math\n",
        "import scipy.io\n",
        "import tensordiffeq as tdq\n",
        "from tensordiffeq.boundaries import *\n",
        "from tensordiffeq.models import CollocationSolverND\n",
        "\n",
        "Domain = DomainND([\"x\", \"t\"], time_var='t')\n",
        "\n",
        "Domain.add(\"x\", [-1.0, 1.0], 512)\n",
        "Domain.add(\"t\", [0.0, 1.0], 201)\n",
        "\n",
        "N_f = 10000\n",
        "Domain.generate_collocation_points(N_f)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iDJDvXsJtxWX"
      },
      "source": [
        "Next, we define the IC function, the derivative model which is implemented at the boundaries of the periodic BC (i.e. first order, second order, etc). Then we define the IC/BC classes and stack them into a list to feed into the solver."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sbi0WnKls1_V"
      },
      "source": [
        "def func_ic(x):\n",
        "    return x ** 2 * np.cos(math.pi * x)\n",
        "\n",
        "\n",
        "# Conditions to be considered at the boundaries for the periodic BC\n",
        "def deriv_model(u_model, x, t):\n",
        "    u = u_model(tf.concat([x, t], 1))\n",
        "    u_x = tf.gradients(u, x)[0]\n",
        "    return u, u_x\n",
        "\n",
        "\n",
        "init = IC(Domain, [func_ic], var=[['x']])\n",
        "x_periodic = periodicBC(Domain, ['x'], [deriv_model])\n",
        "\n",
        "BCs = [init, x_periodic]"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A8MaDliWuNLD"
      },
      "source": [
        "Now we define our strong-form PDE using the tf.gradients syntax"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pkuYZ9G_s828"
      },
      "source": [
        "def f_model(u_model, x, t):\n",
        "    u = u_model(tf.concat([x, t], 1))\n",
        "    u_x = tf.gradients(u, x)\n",
        "    u_xx = tf.gradients(u_x, x)\n",
        "    u_t = tf.gradients(u, t)\n",
        "    c1 = tdq.utils.constant(.0001)\n",
        "    c2 = tdq.utils.constant(5.0)\n",
        "    f_u = u_t - c1 * u_xx + c2 * u * u * u - c2 * u\n",
        "    return f_u"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0H-_FrAluV10"
      },
      "source": [
        "In order to implement the self-adaptive solvers we must define tf.Variable vectors of length corresponding to the number of points in the domain, in this case N_f is the number of collocation points and 512 is the number of initial boundary points (from the Domain cell)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TfaEPnVHs__L"
      },
      "source": [
        "col_weights = tf.Variable(tf.random.uniform([N_f, 1]), trainable=True, dtype=tf.float32)\n",
        "u_weights = tf.Variable(100 * tf.random.uniform([512, 1]), trainable=True, dtype=tf.float32)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "90BO9ITAut6C"
      },
      "source": [
        "Define the network layer sizes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "djqEMcX-_CUq",
        "outputId": "3a981328-71a7-49cb-974d-cd7135cb42cd"
      },
      "source": [
        "layer_sizes = [2] \n",
        "layer_sizes.extend([128]*4)\n",
        "layer_sizes.extend([1])\n",
        "print(layer_sizes)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2, 128, 128, 128, 128, 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N7M68XuWu1lX"
      },
      "source": [
        "Initialize the collocation model and solve using the SA-PINN"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 642,
          "referenced_widgets": [
            "25728485533a44d580be4503dcdcb147",
            "8117df14331b41cb8b023675d6ccd70e",
            "121e16ea1fab4b8ba7a1a41de817ec0f",
            "70008091e4444776a4add4c520ae8936",
            "5f8f73c6e455489da7ecbd7306a47bf0",
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            "7f88fa371162428c813d1864e600d4a5",
            "255b663b1d4b4e728bc33fe24f5073b6",
            "74ee5d6a5d084cd0988e678a7f754fa9",
            "bf753eef8d094eb6af76e738476f5e13",
            "7a2c5fd953ab4bd6adae87fd5b14e147",
            "c164931b5d854bed80e30ead00383687",
            "5d9e14e89d8b46a3826fb5215860bb37",
            "fa0222dcf784458fb394d091d8ab8991",
            "732c44b16dbc4c24a1d7311b78a60072",
            "3bcf497c7624493c8b80bc689fefe111"
          ]
        },
        "id": "HOvWWg00sdUF",
        "outputId": "40f67aca-fa19-4d4e-8f9e-acb1184a87b9"
      },
      "source": [
        "model = CollocationSolverND()\n",
        "model.compile(layer_sizes, f_model, Domain, BCs, isAdaptive=True, col_weights=col_weights, u_weights=u_weights)\n",
        "model.fit(tf_iter=10000, newton_iter=1000)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "  ______                           ____  _ ______________     \n",
            " /_  __/__  ____  _________  _____/ __ \\(_) __/ __/ ____/___ _\n",
            "  / / / _ \\/ __ \\/ ___/ __ \\/ ___/ / / / / /_/ /_/ __/ / __ `/\n",
            " / / /  __/ / / (__  ) /_/ / /  / /_/ / / __/ __/ /___/ /_/ / \n",
            "/_/  \\___/_/ /_/____/\\____/_/  /_____/_/_/ /_/ /_____/\\__, /  \n",
            "                                                        /_/   \n",
            "\n",
            "Neural Network Model Summary\n",
            "\n",
            "Model: \"sequential_1\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "dense_5 (Dense)              (None, 128)               384       \n",
            "_________________________________________________________________\n",
            "dense_6 (Dense)              (None, 128)               16512     \n",
            "_________________________________________________________________\n",
            "dense_7 (Dense)              (None, 128)               16512     \n",
            "_________________________________________________________________\n",
            "dense_8 (Dense)              (None, 128)               16512     \n",
            "_________________________________________________________________\n",
            "dense_9 (Dense)              (None, 1)                 129       \n",
            "=================================================================\n",
            "Total params: 50,049\n",
            "Trainable params: 50,049\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n",
            "None\n",
            "starting Adam training\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "25728485533a44d580be4503dcdcb147",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=10000.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Starting L-BFGS training\n",
            "Executing eager-mode L-BFGS\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "74ee5d6a5d084cd0988e678a7f754fa9",
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              "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dO2azQ7hscqP"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eZG_8gJK_8Vj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "90cf7a63-ad8e-476c-b21f-0ab395830cea"
      },
      "source": [
        "# Get AC data from repo, requires the ?raw=true so wget doesnt download the webpage instead of the data!\n",
        "!wget --no-check-certificate https://github.com/tensordiffeq/TensorDiffEq/blob/main/examples/AC.mat?raw=true \\\n",
        "    -O AC.mat"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2021-05-06 04:05:56--  https://github.com/tensordiffeq/TensorDiffEq/blob/main/examples/AC.mat?raw=true\n",
            "Resolving github.com (github.com)... 140.82.114.4\n",
            "Connecting to github.com (github.com)|140.82.114.4|:443... connected.\n",
            "HTTP request sent, awaiting response... 302 Found\n",
            "Location: https://github.com/tensordiffeq/TensorDiffEq/raw/main/examples/AC.mat [following]\n",
            "--2021-05-06 04:05:56--  https://github.com/tensordiffeq/TensorDiffEq/raw/main/examples/AC.mat\n",
            "Reusing existing connection to github.com:443.\n",
            "HTTP request sent, awaiting response... 302 Found\n",
            "Location: https://raw.githubusercontent.com/tensordiffeq/TensorDiffEq/main/examples/AC.mat [following]\n",
            "--2021-05-06 04:05:56--  https://raw.githubusercontent.com/tensordiffeq/TensorDiffEq/main/examples/AC.mat\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.108.133, 185.199.109.133, 185.199.110.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.108.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 559196 (546K) [application/octet-stream]\n",
            "Saving to: ‘AC.mat’\n",
            "\n",
            "AC.mat              100%[===================>] 546.09K  --.-KB/s    in 0.01s   \n",
            "\n",
            "2021-05-06 04:05:56 (38.7 MB/s) - ‘AC.mat’ saved [559196/559196]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 389
        },
        "id": "j6PoDGZM58LI",
        "outputId": "b634ff70-9898-4bfc-e000-a4af0ca61bc2"
      },
      "source": [
        "\n",
        "save_model = model.u_model\n",
        "print(\"training pass 1 completed\")\n",
        "\n",
        "# Load high-fidelity data for error calculation\n",
        "data = scipy.io.loadmat('AC.mat')\n",
        "\n",
        "Exact = data['uu']\n",
        "Exact_u = np.real(Exact)\n",
        "\n",
        "# t = data['tt'].flatten()[:,None]\n",
        "# x = data['x'].flatten()[:,None]\n",
        "\n",
        "x = Domain.domaindict[0]['xlinspace']\n",
        "t = Domain.domaindict[1][\"tlinspace\"]\n",
        "\n",
        "# create mesh for plotting\n",
        "\n",
        "X, T = np.meshgrid(x, t)\n",
        "\n",
        "X_star = np.hstack((X.flatten()[:, None], T.flatten()[:, None]))\n",
        "u_star = Exact_u.T.flatten()[:, None]\n",
        "\n",
        "# forward pass through model\n",
        "u_pred, f_u_pred = model.predict(X_star)\n",
        "\n",
        "error_u = tdq.helpers.find_L2_error(u_pred, u_star)\n",
        "print('Error u: %e' % (error_u))\n",
        "\n",
        "U_pred = tdq.plotting.get_griddata(X_star, u_pred.flatten(), (X, T))\n",
        "FU_pred = tdq.plotting.get_griddata(X_star, f_u_pred.flatten(), (X, T))\n",
        "\n",
        "lb = np.array([-1.0, 0.0])\n",
        "ub = np.array([1.0, 1])\n",
        "\n",
        "tdq.plotting.plot_solution_domain1D(model, [x, t], ub=ub, lb=lb, Exact_u=Exact_u)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "training pass 1 completed\n",
            "Error u: 6.747827e-02\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "No handles with labels found to put in legend.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 505.106x312.173 with 5 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VK5mubeF6VF4"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}