Poisson_Dirichlet_1d.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Building feed-forward neural network...\n",
      "'build' took 0.032996 s\n",
      "\n",
      "Compiling model...\n",
      "'compile' took 0.421212 s\n",
      "\n",
      "Initializing variables...\n",
      "Training model...\n",
      "\n",
      "Step      Train loss              Test loss               Test metric   \n",
      "0         [4.91e+01, 5.68e-02]    [5.26e+01, 0.00e+00]    [1.20e+00]    \n",
      "Epoch 1: train loss improved from inf to 4.91e+01, saving model to ./model/model.ckpt-1 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-1 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "1000      [1.17e+01, 4.13e+00]    [1.22e+01, 0.00e+00]    [1.34e+00]    \n",
      "Epoch 1000: train loss improved from 4.91e+01 to 1.58e+01, saving model to ./model/model.ckpt-1000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-1000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "2000      [5.26e+00, 6.53e+00]    [5.25e+00, 0.00e+00]    [1.91e+00]    \n",
      "Epoch 2000: train loss improved from 1.58e+01 to 1.18e+01, saving model to ./model/model.ckpt-2000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-2000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "3000      [3.30e+00, 6.98e+00]    [3.15e+00, 0.00e+00]    [2.02e+00]    \n",
      "Epoch 3000: train loss improved from 1.18e+01 to 1.03e+01, saving model to ./model/model.ckpt-3000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-3000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "4000      [3.63e+00, 6.38e+00]    [3.48e+00, 0.00e+00]    [1.92e+00]    \n",
      "Epoch 4000: train loss improved from 1.03e+01 to 1.00e+01, saving model to ./model/model.ckpt-4000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-4000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "5000      [3.70e+00, 6.27e+00]    [3.55e+00, 0.00e+00]    [1.90e+00]    \n",
      "Epoch 5000: train loss improved from 1.00e+01 to 9.97e+00, saving model to ./model/model.ckpt-5000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-5000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "6000      [3.69e+00, 6.25e+00]    [3.54e+00, 0.00e+00]    [1.90e+00]    \n",
      "Epoch 6000: train loss improved from 9.97e+00 to 9.94e+00, saving model to ./model/model.ckpt-6000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-6000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "7000      [3.69e+00, 6.23e+00]    [3.55e+00, 0.00e+00]    [1.90e+00]    \n",
      "Epoch 7000: train loss improved from 9.94e+00 to 9.92e+00, saving model to ./model/model.ckpt-7000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-7000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "8000      [3.70e+00, 6.22e+00]    [3.55e+00, 0.00e+00]    [1.90e+00]    \n",
      "Epoch 8000: train loss improved from 9.92e+00 to 9.92e+00, saving model to ./model/model.ckpt-8000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-8000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "9000      [3.70e+00, 6.22e+00]    [3.56e+00, 0.00e+00]    [1.90e+00]    \n",
      "Epoch 9000: train loss improved from 9.92e+00 to 9.92e+00, saving model to ./model/model.ckpt-9000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-9000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "10000     [3.70e+00, 6.22e+00]    [3.56e+00, 0.00e+00]    [1.90e+00]    \n",
      "Epoch 10000: train loss improved from 9.92e+00 to 9.92e+00, saving model to ./model/model.ckpt-10000 ...\n",
      "\n",
      "INFO:tensorflow:./model/model.ckpt-10000 is not in all_model_checkpoint_paths. Manually adding it.\n",
      "\n",
      "Saving the movie of function to model/movie_x.txt, model/movie_y.txt, model/movie_y.gif...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter imagemagick unavailable; trying to use <class 'matplotlib.animation.PillowWriter'> instead.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving the movie of spectrum to model/movie_spectrum.txt, model/movie_spectrum.gif...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter imagemagick unavailable; trying to use <class 'matplotlib.animation.PillowWriter'> instead.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Best model at step 10000:\n",
      "  train loss: 9.92e+00\n",
      "  test loss: 3.56e+00\n",
      "  test metric: [1.90e+00]\n",
      "\n",
      "'train' took 36.136420 s\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving loss history to loss.dat ...\n",
      "Saving training data to train.dat ...\n",
      "Saving test data to test.dat ...\n",
      "Predicting...\n",
      "'predict' took 0.491637 s\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "\n",
    "import deepxde as dde\n",
    "\n",
    "def pde(x, y):\n",
    "    dy_x = tf.gradients(y, x)[0]\n",
    "    dy_xx = tf.gradients(dy_x, x)[0]\n",
    "    return -dy_xx - np.pi ** 2 * tf.sin(np.pi * x)\n",
    "\n",
    "def boundary(x, on_boundary):\n",
    "    return on_boundary\n",
    "\n",
    "def func(x):\n",
    "    return np.sin(np.pi * x)\n",
    "\n",
    "def plot_loss_history(losshistory,filename=\"losshistory.jpeg\"):\n",
    "    loss_train = np.sum(\n",
    "        np.array(losshistory.loss_train) * losshistory.loss_weights, axis=1\n",
    "    )\n",
    "    loss_test = np.sum(\n",
    "        np.array(losshistory.loss_test) * losshistory.loss_weights, axis=1\n",
    "    )\n",
    "\n",
    "    plt.figure()\n",
    "    plt.semilogy(losshistory.steps, loss_train, label=\"Train loss\")\n",
    "    plt.semilogy(losshistory.steps, loss_test, label=\"Test loss\")\n",
    "    for i in range(len(losshistory.metrics_test[0])):\n",
    "        plt.semilogy(\n",
    "            losshistory.steps,\n",
    "            np.array(losshistory.metrics_test)[:, i],\n",
    "            label=\"Test metric\",\n",
    "        )\n",
    "    plt.xlabel(\"# Steps\")\n",
    "    plt.legend()\n",
    "    if filename:\n",
    "        plt.savefig(filename)\n",
    "\n",
    "def plot_best_state(train_state,solution_filename=\"pdesolution.jpeg\",residual_filename=\"pderesidual.jpeg\"):\n",
    "    X_train, y_train, X_test, y_test, best_y, best_ystd = train_state.packed_data()\n",
    "\n",
    "    y_dim = y_train.shape[1]\n",
    "\n",
    "    # Regression plot\n",
    "    plt.figure()\n",
    "    idx = np.argsort(X_test[:, 0])\n",
    "    X = X_test[idx, 0]\n",
    "    for i in range(y_dim):\n",
    "        plt.plot(X_train[:, 0], y_train[:, i], \"ok\", label=\"Train\")\n",
    "        plt.plot(X, y_test[idx, i], \"-k\", label=\"True\")\n",
    "        plt.plot(X, best_y[idx, i], \"--r\", label=\"Prediction\")\n",
    "        if best_ystd is not None:\n",
    "            plt.plot(X, best_y[idx, i] + 2 * best_ystd[idx, i], \"-b\", label=\"95% CI\")\n",
    "            plt.plot(X, best_y[idx, i] - 2 * best_ystd[idx, i], \"-b\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.legend()\n",
    "    if solution_filename:\n",
    "        plt.savefig(solution_filename)\n",
    "\n",
    "    # Residual plot\n",
    "    plt.figure()\n",
    "    residual = y_test[:, 0] - best_y[:, 0]\n",
    "    plt.plot(best_y[:, 0], residual, \"o\", zorder=1)\n",
    "    plt.hlines(0, plt.xlim()[0], plt.xlim()[1], linestyles=\"dashed\", zorder=2)\n",
    "    plt.xlabel(\"Predicted\")\n",
    "    plt.ylabel(\"Residual = Observed - Predicted\")\n",
    "    plt.tight_layout()\n",
    "\n",
    "    if best_ystd is not None:\n",
    "        plt.figure()\n",
    "        for i in range(y_dim):\n",
    "            plt.plot(X_test[:, 0], best_ystd[:, i], \"-b\")\n",
    "            plt.plot(\n",
    "                X_train[:, 0],\n",
    "                np.interp(X_train[:, 0], X_test[:, 0], best_ystd[:, i]),\n",
    "                \"ok\",\n",
    "            )\n",
    "        plt.xlabel(\"x\")\n",
    "        plt.ylabel(\"std(y)\")\n",
    "\n",
    "    if residual_filename:\n",
    "        plt.savefig(residual_filename)\n",
    "\n",
    "geom = dde.geometry.Interval(-1, 1)\n",
    "bc = dde.DirichletBC(geom, func, boundary)\n",
    "data = dde.data.PDE(geom, 1, pde, bc, 16, 2, func=func, num_test=100)\n",
    "\n",
    "layer_size = [1] + [2] * 1 + [1]\n",
    "activation = \"tanh\"\n",
    "initializer = \"Glorot uniform\"\n",
    "net = dde.maps.FNN(layer_size, activation, initializer)\n",
    "\n",
    "model = dde.Model(data, net)\n",
    "model.compile(\"adam\", lr=0.001, metrics=[\"l2 relative error\"])\n",
    "\n",
    "checkpointer = dde.callbacks.ModelCheckpoint(\n",
    "    \"./model/model.ckpt\", verbose=1, save_better_only=True\n",
    ")\n",
    "movie = dde.callbacks.MovieDumper(\n",
    "    \"model/movie\", [-1], [1], period=100, save_spectrum=True, y_reference=func\n",
    ")\n",
    "losshistory, train_state = model.train(\n",
    "    epochs=10000, callbacks=[checkpointer, movie]\n",
    ")\n",
    "\n",
    "dd = dde.saveplot(losshistory, train_state, issave=True, isplot=True)\n",
    "\n",
    "plot_loss_history(losshistory)\n",
    "plot_best_state(train_state)\n",
    "\n",
    "# Plot PDE residue\n",
    "x = geom.uniform_points(1000, True)\n",
    "y = model.predict(x, operator=pde)\n",
    "plt.figure()\n",
    "plt.plot(x, y)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"PDE residue\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mlflow\n",
    "from  mlflow.tracking import MlflowClient\n",
    "mlflow_params  = {}\n",
    "mlflow_metrics = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "tracking_uri = \"https://j1002148222.babyrocket.net/mlflow\"\n",
    "client = MlflowClient(tracking_uri=tracking_uri)\n",
    "mlflow.set_tracking_uri(tracking_uri)\n",
    "experiments = client.list_experiments()\n",
    "experiment_names = []\n",
    "for exp in experiments:\n",
    "    experiment_names.append(exp.name)\n",
    "experiment_name = \"sciml_demo\"\n",
    "if experiment_name not in experiment_names:\n",
    "    mlflow.create_experiment(experiment_name)\n",
    "mlflow.set_experiment(experiment_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8957987"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "losshistory.metrics_test[-1][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "mlflow_params[\"layers\"] = layer_size\n",
    "mlflow_metrics[\"accuracy\"] = losshistory.metrics_test[-1][0]\n",
    "mlflow_params[\"steps\"] = losshistory.steps[-1]\n",
    "with mlflow.start_run():\n",
    "    mlflow.log_params(mlflow_params)\n",
    "    mlflow.log_metrics(mlflow_metrics)\n",
    "    mlflow.log_artifact(\"losshistory.jpeg\")\n",
    "    mlflow.log_artifact(\"pderesidual.jpeg\")\n",
    "    mlflow.log_artifact(\"pdesolution.jpeg\")"
   ]
  }
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