Notebook1_ViscousBurgers.ipynb

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        "## *TensorDiffEq* Workshop Materials - Notebook 1\n",
        "### Viscous Burgers Equation\n",
        "\n",
        "In this notebook we will provide a brief overview of the interface of *TensorDiffEq* and how to implement its functionality to solve PDE systems. We will start with a basic implementation of a nonlinear PDE, the viscous Burger's Equation.\n",
        "\n",
        "Specifically we will solve the PDE system:\n",
        "\n",
        "$u_t + uu_x - (0.01/\\pi) u_{xx} = 0, \\ \\ x \\in [-1,1], t \\in [0,1]$ \\\\\n",
        "$u(0,x) = -sin(\\pi x)$ \\\\\n",
        "$u(t, -1) = u(t, 1) = 0 $\n",
        "\n",
        "First, we must install the package, which can be done via *pip*"
      ]
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        "id": "-x9DP1439xbY",
        "outputId": "ed45243d-5388-4217-a7ad-ec0e1d8259ae"
      },
      "source": [
        "!pip install tensordiffeq"
      ],
      "execution_count": 1,
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          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RHNzVSL6ShXX"
      },
      "source": [
        "Now we run some manditory import statements, including math and scipy for importing the exact solution a little later on. Notice that we dont need to import Tensorflow as tdq installs that for us"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kvjS0EYayBAO"
      },
      "source": [
        "import math\n",
        "import scipy.io\n",
        "import tensordiffeq as tdq\n",
        "from tensordiffeq.boundaries import *\n",
        "from tensordiffeq.models import CollocationSolverND"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BoKpRn1hSzAl"
      },
      "source": [
        "The first step of any forward or inverse problem is defining the domain on which the solution lies"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "84PY7jJdyeSU"
      },
      "source": [
        "Domain = DomainND([\"x\", \"t\"], time_var='t')\n",
        "\n",
        "Domain.add(\"x\", [-1.0, 1.0], 256)\n",
        "Domain.add(\"t\", [0.0, 1.0], 100)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UtEJqgUJTNsj"
      },
      "source": [
        "Next, we need to generate collocation points inside the domain for training"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IYgdkZ0cyeGk"
      },
      "source": [
        "N_f = 10000\n",
        "Domain.generate_collocation_points(N_f)"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QtbsWm7yTX2v"
      },
      "source": [
        "Define the initial condition function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KMH-_aAWydwy"
      },
      "source": [
        "def func_ic(x):\n",
        "    return -np.sin(x * math.pi)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wQci9QGQTkHK"
      },
      "source": [
        "Define the actual initial condition method, and the subsequent upper and lower dirichlect BCs. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "anMC_NDxydmI"
      },
      "source": [
        "init = IC(Domain, [func_ic], var=[['x']])\n",
        "upper_x = dirichletBC(Domain, val=0.0, var='x', target=\"upper\")\n",
        "lower_x = dirichletBC(Domain, val=0.0, var='x', target=\"lower\")\n"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_y1QI-LPTiZG"
      },
      "source": [
        "tdq takes in initial conditions and boundary conditions as a list"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LMtkNiz7ydMo"
      },
      "source": [
        "BCs = [init, upper_x, lower_x]"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jdttAnGLWDcd"
      },
      "source": [
        "Define the strong-form PDE in terms of tf.gradients where derivatives are required. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qXiB1Wi9yc8g"
      },
      "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",
        "    f_u = u_t + u * u_x - (0.01 / tf.constant(math.pi)) * u_xx\n",
        "    return f_u"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ukT28x7VWvSX"
      },
      "source": [
        "Define layer sizes as a list of hidden layer widths"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wk9lj4vhybaI"
      },
      "source": [
        "layer_sizes = [2, 20, 20, 20, 20, 20, 1]"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xnxtzWtyW5mY"
      },
      "source": [
        "Define the model, compile the model using the defined layer sizes, PDE model, and domain/BCs, and call model.fit"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676,
          "referenced_widgets": [
            "3cf287d87060456fa74f8b5abe17d283",
            "38b0a7fb312e45bc9c873db7d9c5289b",
            "5c53020c3caa4aeea7c4ef19400f0abb",
            "5960d3b93bde4c50a7e2f101d0027be1",
            "2f050e3610f142b5948e994f4719eda9",
            "17547468e4a14aab9098ffbe7ca1ffcb",
            "b9967c16a5e4444fafc70d9f0d1193d6",
            "1f266519be0e437d990293737a7f3f39",
            "6f131abc78bb46df99b2a323246d7d1e",
            "c5a36d653a9e4f819eb1b7a5c375b065",
            "90424a4e89e543c59adf063e1ca17c97",
            "7424e183bd77411da72bf1e295ce22e7",
            "7c0e3c89e4fd44ce99f949ef7b8684db",
            "27635965c6574b40bf4ef2027b3ae12d",
            "2896c9d09d064cb0988bdd2a07627df4",
            "2b6dbc3874a64de49e7d9975b2057de6"
          ]
        },
        "id": "JcSIX8NuCzSK",
        "outputId": "0d09530d-d33f-42c6-d113-93e9f349b047"
      },
      "source": [
        "model = CollocationSolverND()\n",
        "model.compile(layer_sizes, f_model, Domain, BCs)\n",
        "# to reproduce results from Raissi and the SA-PINNs paper, train for 10k newton and 10k adam\n",
        "model.fit(tf_iter=2000, newton_iter = 2000)"
      ],
      "execution_count": 13,
      "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_6 (Dense)              (None, 20)                60        \n",
            "_________________________________________________________________\n",
            "dense_7 (Dense)              (None, 20)                420       \n",
            "_________________________________________________________________\n",
            "dense_8 (Dense)              (None, 20)                420       \n",
            "_________________________________________________________________\n",
            "dense_9 (Dense)              (None, 20)                420       \n",
            "_________________________________________________________________\n",
            "dense_10 (Dense)             (None, 20)                420       \n",
            "_________________________________________________________________\n",
            "dense_11 (Dense)             (None, 1)                 21        \n",
            "=================================================================\n",
            "Total params: 1,761\n",
            "Trainable params: 1,761\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": "3cf287d87060456fa74f8b5abe17d283",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=2000.0), 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": "6f131abc78bb46df99b2a323246d7d1e",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=2000.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QCFwMS8QXLAV"
      },
      "source": [
        "Download high-fidelity solution data for comparison and L2 error calculations"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dd8vHE8FCzdZ",
        "outputId": "a336ff5b-3d1c-4559-e760-707b7a22ff8b"
      },
      "source": [
        "!wget --no-check-certificate https://github.com/tensordiffeq/TensorDiffEq/blob/main/examples/burgers_shock.mat?raw=true \\\n",
        "    -O burgers_shock.mat"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2021-05-06 02:03:09--  https://github.com/tensordiffeq/TensorDiffEq/blob/main/examples/burgers_shock.mat?raw=true\n",
            "Resolving github.com (github.com)... 192.30.255.113\n",
            "Connecting to github.com (github.com)|192.30.255.113|:443... connected.\n",
            "HTTP request sent, awaiting response... 302 Found\n",
            "Location: https://github.com/tensordiffeq/TensorDiffEq/raw/main/examples/burgers_shock.mat [following]\n",
            "--2021-05-06 02:03:10--  https://github.com/tensordiffeq/TensorDiffEq/raw/main/examples/burgers_shock.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/burgers_shock.mat [following]\n",
            "--2021-05-06 02:03:10--  https://raw.githubusercontent.com/tensordiffeq/TensorDiffEq/main/examples/burgers_shock.mat\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.111.133, 185.199.110.133, 185.199.108.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.111.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 207944 (203K) [application/octet-stream]\n",
            "Saving to: ‘burgers_shock.mat’\n",
            "\n",
            "burgers_shock.mat   100%[===================>] 203.07K  --.-KB/s    in 0.02s   \n",
            "\n",
            "2021-05-06 02:03:10 (10.7 MB/s) - ‘burgers_shock.mat’ saved [207944/207944]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5OmNXFu7XZN8"
      },
      "source": [
        "Import the high-fidelity solution, calculate the L2 error, and plot the solution domain "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 372
        },
        "id": "gNI_NW1ECzrd",
        "outputId": "75e177c3-1b39-4f45-d0d2-acc5f2e0be09"
      },
      "source": [
        "data = scipy.io.loadmat('burgers_shock.mat')\n",
        "\n",
        "Exact = data['usol']\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",
        "X, T = np.meshgrid(x, t)\n",
        "\n",
        "# print(np.shape((X,T))) #2, 100, 256\n",
        "X_star = np.hstack((X.flatten()[:, None], T.flatten()[:, None]))\n",
        "u_star = Exact_u.T.flatten()[:, None]\n",
        "\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": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Error u: 4.793710e-03\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": "mokOhZHdCz0Q"
      },
      "source": [
        ""
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6iLJQSsiC1FD"
      },
      "source": [
        ""
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pMwPS5ugC1GL"
      },
      "source": [
        ""
      ],
      "execution_count": 12,
      "outputs": []
    }
  ]
}