Physics Informed Deep Learning - Parts I & II.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Driven Solution - Part I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.145302Z",
     "start_time": "2019-08-08T19:42:41.882816Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.13.1\n"
     ]
    }
   ],
   "source": [
    "# Tensorflow\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "from keras.layers import Input, Dense\n",
    "from keras.models import Model\n",
    "from keras import optimizers\n",
    "\n",
    "# Scientific Libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.io import loadmat\n",
    "from scipy.interpolate import BSpline\n",
    "import pandas as pd\n",
    "\n",
    "# Graphing Libraries\n",
    "import matplotlib.gridspec as gridspec\n",
    "from scipy.interpolate import griddata\n",
    "from mpl_toolkits import mplot3d\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "# For Train - Validation - Test\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# For collocation points\n",
    "from pyDOE import lhs\n",
    "print(tf.__version__)\n",
    "\n",
    "%matplotlib inline\n",
    "# %matplotlib notebook\n",
    "# Tensorboard"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.180234Z",
     "start_time": "2019-08-08T19:42:45.147483Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u shape: (25600, 1)\n",
      "x train shape: (256, 1)\n",
      "t train shape: (100, 1)\n"
     ]
    }
   ],
   "source": [
    "# Set Random Seed\n",
    "np.random.seed(101)\n",
    "tf.set_random_seed(101)\n",
    "\n",
    "data = loadmat('./burgers_shock.mat'); \n",
    "\n",
    "x = pd.Series(data['x'].flatten())[:, None]\n",
    "t = pd.Series(data['t'].flatten())[:, None]\n",
    "u_data = np.real(data['usol']).T\n",
    "usol = pd.Series(u_data.flatten())[:, None]\n",
    "\n",
    "print(f'u shape: {usol.shape}')\n",
    "print(f'x train shape: {x.shape}')\n",
    "print(f't train shape: {t.shape}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.184746Z",
     "start_time": "2019-08-08T19:42:45.182048Z"
    }
   },
   "outputs": [],
   "source": [
    "X, T = np.meshgrid(x, t); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.204568Z",
     "start_time": "2019-08-08T19:42:45.186417Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>T</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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      "text/plain": [
       "          X    T\n",
       "0 -1.000000  0.0\n",
       "1 -0.992157  0.0\n",
       "2 -0.984314  0.0\n",
       "3 -0.976471  0.0\n",
       "4 -0.968627  0.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_data = pd.DataFrame(np.hstack((X.flatten()[:, None], \n",
    "                                 T.flatten()[:, None])));\n",
    "\n",
    "X_data.columns = ['X', 'T'];\n",
    "\n",
    "X_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boundary Conditions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### At t = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.209474Z",
     "start_time": "2019-08-08T19:42:45.206235Z"
    }
   },
   "outputs": [],
   "source": [
    "x_t_at_initial_time_condition = np.hstack((X[0:1, :].T, T[0:1, :].T))\n",
    "u_at_initial_time = (u_data[0, :].T)[:, None];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### At x = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.215358Z",
     "start_time": "2019-08-08T19:42:45.211796Z"
    }
   },
   "outputs": [],
   "source": [
    "x_t_at_negative_boundary = np.hstack((X[:, 0:1], T[:, 0:1]))\n",
    "u_at_negative_boundary = u_data[:, 0:1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### At x = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.220798Z",
     "start_time": "2019-08-08T19:42:45.217401Z"
    }
   },
   "outputs": [],
   "source": [
    "x_t_at_positive_boundary = np.hstack((X[:, -1:], T[:, -1:]))\n",
    "u_at_positive_boundary = u_data[:, -1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### X_u_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.226922Z",
     "start_time": "2019-08-08T19:42:45.223879Z"
    }
   },
   "outputs": [],
   "source": [
    "X_u_train = np.vstack([x_t_at_initial_time_condition, \n",
    "                       x_t_at_negative_boundary,\n",
    "                       x_t_at_positive_boundary])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### u_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.232190Z",
     "start_time": "2019-08-08T19:42:45.229365Z"
    }
   },
   "outputs": [],
   "source": [
    "u_train = np.vstack([u_at_initial_time,\n",
    "                     u_at_negative_boundary,\n",
    "                     u_at_positive_boundary])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.242681Z",
     "start_time": "2019-08-08T19:42:45.234058Z"
    }
   },
   "outputs": [],
   "source": [
    "X_train, X_val, y_train, y_val = train_test_split(X_data, usol, \n",
    "                                                  test_size = 0.3, \n",
    "                                                  random_state = 101)\n",
    "\n",
    "X_val, X_test, y_val, y_test = train_test_split(X_val, y_val, \n",
    "                                                test_size = 0.4,\n",
    "                                                random_state = 101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.247731Z",
     "start_time": "2019-08-08T19:42:45.244327Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Data: (17920, 2)\n",
      "Validation shape: (4608, 2)\n",
      "Test shape: (3072, 2)\n",
      "Total Points: 25600\n"
     ]
    }
   ],
   "source": [
    "print(f'Training Data: {X_train.shape}')\n",
    "print(f'Validation shape: {X_val.shape}')\n",
    "print(f'Test shape: {X_test.shape}')\n",
    "print(f'Total Points: {len(X_train) + len(X_val) + len(X_test)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.255565Z",
     "start_time": "2019-08-08T19:42:45.249265Z"
    }
   },
   "outputs": [],
   "source": [
    "def init_weights(shape):\n",
    "    input_size, output_size = shape[0], shape[1]\n",
    "    std = np.sqrt(2/(input_size + output_size))\n",
    "    init_random_dist = tf.truncated_normal(shape, stddev=0.1)\n",
    "    return tf.Variable(init_random_dist, dtype = tf.float32)\n",
    "\n",
    "def init_bias(shape):\n",
    "    init_bias_vals = tf.constant(0.1, shape=shape)\n",
    "    return tf.Variable(init_bias_vals)\n",
    "\n",
    "def initial_nn(layers):\n",
    "    weights = []\n",
    "    biases = []\n",
    "    \n",
    "    for index in range(len(layers)-1):\n",
    "        shape=(layers[index], layers[index + 1])\n",
    "        W = init_weights(shape)\n",
    "        b = init_bias((1, layers[index + 1]))\n",
    "        weights.append(W)\n",
    "        biases.append(b)\n",
    "    return weights, biases\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.262085Z",
     "start_time": "2019-08-08T19:42:45.257381Z"
    }
   },
   "outputs": [],
   "source": [
    "def neural_net(x, t, weights, biases):\n",
    "    \n",
    "    X = tf.concat([t, x], 1)\n",
    "    num_layers = len(weights) + 1\n",
    "    \n",
    "    for l in range(0,num_layers-2):\n",
    "        W = weights[l]\n",
    "        b = biases[l]\n",
    "        X = tf.tanh(tf.add(tf.matmul(X, W), b))\n",
    "    W = weights[-1]\n",
    "    b = biases[-1]\n",
    "    Y = tf.add(tf.matmul(X, W), b)\n",
    "    \n",
    "    return Y\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.267446Z",
     "start_time": "2019-08-08T19:42:45.263664Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_net(x, t, weights, biases):\n",
    "    nu = 0.01/np.pi\n",
    "    u = neural_net(x, t, weights, biases)\n",
    "    u_t = tf.gradients(u, t)[0]\n",
    "    u_x = tf.gradients(u, x)[0]\n",
    "    u_xx = tf.gradients(u_x, x)[0]\n",
    "    f = u_t + u*u_x - nu*u_xx\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.272746Z",
     "start_time": "2019-08-08T19:42:45.269084Z"
    }
   },
   "outputs": [],
   "source": [
    "def stratify_sample(num_samples, X_data, num_factors = 2):\n",
    "    '''\n",
    "    Variables are sampled using a even sampling method, \n",
    "    and then randomly combined sets of those variables \n",
    "    are used for one calculation of the target function.   \n",
    "    '''\n",
    "    lower_bound = X_data.min(0)\n",
    "    upper_bound = X_data.max(0)\n",
    "    bound_range = upper_bound - lower_bound\n",
    "    \n",
    "    result = lower_bound + bound_range * lhs(num_factors, num_samples)\n",
    "    return result\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.277323Z",
     "start_time": "2019-08-08T19:42:45.274347Z"
    }
   },
   "outputs": [],
   "source": [
    "def physics_nn(layers, x_u, t_u, x_f, t_f, weights, biases):    \n",
    "    u_predictions = neural_net(x_u, t_u, weights, biases)\n",
    "    f_predictions = f_net(x_f, t_f, weights, biases)\n",
    "    return u_predictions, f_predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.280957Z",
     "start_time": "2019-08-08T19:42:45.278800Z"
    }
   },
   "outputs": [],
   "source": [
    "def callback(loss):\n",
    "    print('Loss:', loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.285747Z",
     "start_time": "2019-08-08T19:42:45.282546Z"
    }
   },
   "outputs": [],
   "source": [
    "def joint_loss(u_u, u_predictions, f_predictions):\n",
    "    u_loss = tf.reduce_mean(tf.square(u_u - u_predictions))\n",
    "    f_loss = tf.reduce_mean(tf.square(f_predictions))\n",
    "    total_loss = tf.add(u_loss, f_loss)\n",
    "    return total_loss\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.289967Z",
     "start_time": "2019-08-08T19:42:45.287252Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_history(num_steps, loss_history):\n",
    "    plt.plot(range(num_steps), loss_history)\n",
    "    plt.title('Loss v. Iterations');\n",
    "    plt.ylabel('Loss');\n",
    "    plt.xlabel('Iterations');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.293651Z",
     "start_time": "2019-08-08T19:42:45.291594Z"
    }
   },
   "outputs": [],
   "source": [
    "N_f = 10000\n",
    "N_u = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.300618Z",
     "start_time": "2019-08-08T19:42:45.295152Z"
    }
   },
   "outputs": [],
   "source": [
    "lower_bound = np.array(X_data.min(0))\n",
    "upper_bound = np.array(X_data.max(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.305235Z",
     "start_time": "2019-08-08T19:42:45.302057Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.  , 0.99])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "upper_bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.316834Z",
     "start_time": "2019-08-08T19:42:45.308033Z"
    }
   },
   "outputs": [],
   "source": [
    "X_f_data = stratify_sample(N_f, X_u_train); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.321741Z",
     "start_time": "2019-08-08T19:42:45.318435Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.44956223,  0.09455335],\n",
       "       [-0.5342242 ,  0.53650042],\n",
       "       [-0.46532888,  0.08034628],\n",
       "       ...,\n",
       "       [-0.18177638,  0.13322691],\n",
       "       [ 0.12594875,  0.49823681],\n",
       "       [-0.19260854,  0.19251179]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_f_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.325997Z",
     "start_time": "2019-08-08T19:42:45.323292Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stacked/Collocated Points: (10456, 2)\n"
     ]
    }
   ],
   "source": [
    "X_f_train = np.vstack((X_f_data, X_u_train))\n",
    "print(f'Stacked/Collocated Points: {X_f_train.shape}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.329489Z",
     "start_time": "2019-08-08T19:42:45.327506Z"
    }
   },
   "outputs": [],
   "source": [
    "LAYERS = [2, 50, 50, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.334254Z",
     "start_time": "2019-08-08T19:42:45.330967Z"
    }
   },
   "outputs": [],
   "source": [
    "random_idx = np.random.choice(X_u_train.shape[0], N_u, replace = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.338641Z",
     "start_time": "2019-08-08T19:42:45.336045Z"
    }
   },
   "outputs": [],
   "source": [
    "X_u_train = X_u_train[random_idx, :]\n",
    "u_train = u_train[random_idx, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:45.367144Z",
     "start_time": "2019-08-08T19:42:45.341228Z"
    }
   },
   "outputs": [],
   "source": [
    "class PhysicsInformedNN():\n",
    "    \n",
    "    def __init__(self, X_u, u, X_f, layers, num_iter, lower_bound, upper_bound):\n",
    "        \n",
    "        self.loss_history = []  \n",
    "        self.num_iter, self.layers = num_iter, layers\n",
    "        self.u = u\n",
    "        self.lower_bound, self.upper_bound = lower_bound, upper_bound\n",
    "        self.x_u, self.t_u = X_u[:, 0][:, None], X_u[:, 1][:, None]\n",
    "        self.x_f, self.t_f = X_f[:, 0][:, None], X_f[:, 1][:, None]\n",
    "        \n",
    "        self.weights, self.biases = self.initial_nn(layers)\n",
    "        \n",
    "        self.x_u_tf, self.t_u_tf, self.u_tf, self.x_f_tf, self.t_f_tf = self.generate_placeholders()\n",
    "        \n",
    "        self.u_pred, self.f_pred = self.generate_predictions()\n",
    "        \n",
    "        self.loss = self.calc_loss()\n",
    "        \n",
    "        config = tf.ConfigProto(allow_soft_placement = True, \n",
    "                                log_device_placement = True)\n",
    "        options = {\n",
    "            'maxiter': num_iter,\n",
    "            'maxfun':  num_iter,\n",
    "            'maxcor': 50, \n",
    "            'maxls': 50,\n",
    "            'ftol' : 1.0 * np.finfo(float).eps\n",
    "        }\n",
    "        \n",
    "        self.sess = tf.Session(config = config)\n",
    "        \n",
    "        self.optimizer = tf.contrib.opt.ScipyOptimizerInterface(self.loss, \n",
    "                                                                method = 'L-BFGS-B',\n",
    "                                                                options = options)\n",
    "                                                                \n",
    "        self.sess.run(tf.global_variables_initializer())\n",
    "        \n",
    "        \n",
    "    def train(self):\n",
    "        tf_dict = {\n",
    "            self.x_u_tf: self.x_u, \n",
    "            self.t_u_tf: self.t_u, \n",
    "            self.u_tf: self.u, \n",
    "            self.x_f_tf: self.x_f, \n",
    "            self.t_f_tf: self.t_f\n",
    "        }                                                                                                                 \n",
    "        self.optimizer.minimize(self.sess, \n",
    "                                feed_dict = tf_dict, \n",
    "                                fetches = [self.loss], \n",
    "                                loss_callback = self.callback)\n",
    "    \n",
    "    def predict(self, X_data):\n",
    "        predict_dict = {\n",
    "            self.x_u_tf: X_data.iloc[:,0][:, None], \n",
    "            self.t_u_tf: X_data.iloc[:,1][:, None]\n",
    "        }\n",
    "        \n",
    "        u_predictions = self.sess.run(self.u_pred, feed_dict = predict_dict)  \n",
    "#         f_predictions = self.sess.run(self.f_pred, feed_dict = predict_dict)\n",
    "        return u_predictions\n",
    "        \n",
    "    def callback(self, loss):\n",
    "        print('Loss:', round(loss, 4))\n",
    "        self.loss_history.append(loss)\n",
    "        \n",
    "    def neural_net(self, X, weights, biases):\n",
    "        num_layers = len(weights) + 1\n",
    "        \n",
    "        h = 2.0*(X - self.lower_bound)/(self.upper_bound - self.lower_bound) - 1.0\n",
    "        for l in range(0,num_layers - 2):\n",
    "            W = weights[l]\n",
    "            b = biases[l]\n",
    "            h = tf.tanh(tf.add(tf.matmul(h, W), b))   \n",
    "        W = weights[-1]\n",
    "        b = biases[-1]\n",
    "        Y = tf.add(tf.matmul(h, W), b)\n",
    "        return Y\n",
    "    \n",
    "    def net_u(self, x, t):\n",
    "        u = self.neural_net(tf.concat([x,t], 1, name='00_concat_op'), self.weights, self.biases)\n",
    "        return u\n",
    "            \n",
    "    def net_f(self, x, t):\n",
    "        nu = 0.01 / np.pi\n",
    "        u = self.net_u(x, t)\n",
    "        u_t = tf.gradients(u, t)[0]\n",
    "        u_x = tf.gradients(u, x)[0]\n",
    "        u_xx = tf.gradients(u_x, x)[0]\n",
    "        f = u_t + u*u_x - nu*u_xx\n",
    "        return f\n",
    "    \n",
    "    def calc_loss(self):\n",
    "        u_loss = tf.reduce_mean(tf.square(self.u_tf - self.u_pred)) \n",
    "        f_loss = tf.reduce_mean(tf.square(self.f_pred))  \n",
    "        return u_loss + f_loss\n",
    "               \n",
    "    def generate_predictions(self):\n",
    "        u_pred = self.net_u(self.x_u_tf, self.t_u_tf) \n",
    "        f_pred = self.net_f(self.x_f_tf, self.t_f_tf)\n",
    "        return u_pred, f_pred\n",
    "        \n",
    "    def generate_placeholders(self):\n",
    "        x_u_tf = tf.placeholder(tf.float32)\n",
    "        t_u_tf = tf.placeholder(tf.float32)        \n",
    "        \n",
    "        u_tf = tf.placeholder(tf.float32)\n",
    "        \n",
    "        x_f_tf = tf.placeholder(tf.float32)\n",
    "        t_f_tf = tf.placeholder(tf.float32)\n",
    "        \n",
    "        return x_u_tf, t_u_tf, u_tf, x_f_tf, t_f_tf\n",
    "        \n",
    "    def init_weights(self, shape):\n",
    "        input_size, output_size = shape[0], shape[1]\n",
    "        std = np.sqrt(2/(input_size + output_size))\n",
    "        init_random_dist = tf.truncated_normal(shape, stddev = std)\n",
    "        return tf.Variable(init_random_dist, dtype = tf.float32)\n",
    "\n",
    "    def init_bias(self, shape):\n",
    "        init_bias_vals = tf.constant(0.1, shape = shape)\n",
    "        return tf.Variable(init_bias_vals)\n",
    "\n",
    "    def initial_nn(self, layers):\n",
    "        weights = []\n",
    "        biases = []\n",
    "\n",
    "        for index in range(len(layers)-1):\n",
    "            shape = (layers[index], layers[index + 1])\n",
    "            W = init_weights(shape)\n",
    "            b = init_bias((1, layers[index + 1]))\n",
    "            weights.append(W)\n",
    "            biases.append(b)       \n",
    "        return weights, biases\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:42:47.256870Z",
     "start_time": "2019-08-08T19:42:45.368936Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /anaconda3/envs/pinns/lib/python3.7/site-packages/tensorflow/python/framework/op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Colocations handled automatically by placer.\n",
      "WARNING:tensorflow:From /anaconda3/envs/pinns/lib/python3.7/site-packages/tensorflow/python/ops/math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use tf.cast instead.\n",
      "\n",
      "WARNING: The TensorFlow contrib module will not be included in TensorFlow 2.0.\n",
      "For more information, please see:\n",
      "  * https://github.com/tensorflow/community/blob/master/rfcs/20180907-contrib-sunset.md\n",
      "  * https://github.com/tensorflow/addons\n",
      "If you depend on functionality not listed there, please file an issue.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "model = PhysicsInformedNN(X_u_train, u_train, X_f_train, \n",
    "                          layers = LAYERS, \n",
    "                          num_iter = 2000, \n",
    "                          lower_bound = lower_bound, upper_bound = upper_bound)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:44:36.694522Z",
     "start_time": "2019-08-08T19:42:47.258269Z"
    },
    "hide_input": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss: 0.3119\n",
      "Loss: 1.1642\n",
      "Loss: 0.2712\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss: 0.003\n",
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      "Loss: 0.0028\n",
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT'\n",
      "  Objective function value: 0.002756\n",
      "  Number of iterations: 1868\n",
      "  Number of functions evaluations: 2001\n"
     ]
    }
   ],
   "source": [
    "model.train()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:44:36.700740Z",
     "start_time": "2019-08-08T19:44:36.696629Z"
    }
   },
   "outputs": [],
   "source": [
    "def filter_cost_for_outliers(history, num_passes):\n",
    "    for i in range(num_passes):\n",
    "        idx = history.index(max(history))\n",
    "        history[idx] = np.mean([history[idx -1], history[idx + 1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:44:36.705347Z",
     "start_time": "2019-08-08T19:44:36.702954Z"
    }
   },
   "outputs": [],
   "source": [
    "# filter_cost_for_outliers(model.loss_history, num_passes = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:44:36.709828Z",
     "start_time": "2019-08-08T19:44:36.707573Z"
    }
   },
   "outputs": [],
   "source": [
    "# plt.plot(num_steps, loss);\n",
    "# plt.xlabel('Num Iterations');\n",
    "# plt.ylabel('Loss');\n",
    "# plt.title('Cost Function');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:44:36.820265Z",
     "start_time": "2019-08-08T19:44:36.712050Z"
    }
   },
   "outputs": [],
   "source": [
    "u_pred = model.predict(X_data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:44:36.847362Z",
     "start_time": "2019-08-08T19:44:36.822323Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error u: 1.557930e-01\n"
     ]
    }
   ],
   "source": [
    "error_u = np.linalg.norm(usol - u_pred,2)/np.linalg.norm(usol,2)\n",
    "print('Error u: %e' % (error_u))                     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T19:44:37.404400Z",
     "start_time": "2019-08-08T19:44:36.849286Z"
    }
   },
   "outputs": [],
   "source": [
    "U_pred = griddata(X_data, u_pred.flatten(), (X, T), method='cubic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T20:08:34.793042Z",
     "start_time": "2019-08-08T20:08:34.785552Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_subplots():\n",
    "    extent = [0, 1, -1, 1]\n",
    "    params = {\"ytick.color\" : \"w\",\n",
    "          \"xtick.color\" : \"w\",\n",
    "          \"axes.labelcolor\" : \"w\",\n",
    "          \"axes.edgecolor\" : \"w\"}\n",
    "    plt.rcParams.update(params)\n",
    "\n",
    "    fig = plt.figure(figsize = (10, 10))\n",
    "    fig.subplots_adjust(hspace = 0.5)\n",
    "    gs = fig.add_gridspec(2, 1)\n",
    "    \n",
    "    ax1 = fig.add_subplot(gs[0, :], )\n",
    "    ax1.set_title('Actual Data', color = 'white')\n",
    "    ax1.set_xlabel('time')\n",
    "    ax1.set_ylabel('x')\n",
    "    h = ax1.imshow(u_data.T, \n",
    "                   interpolation ='gaussian', cmap ='jet', \n",
    "                   extent = extent, \n",
    "                   origin ='lower', aspect ='auto')\n",
    "    plt.colorbar(h);\n",
    "\n",
    "\n",
    "    ax2 = fig.add_subplot(gs[1, :])\n",
    "    ax2.set_title('Predicted Data', color ='white')\n",
    "    ax2.set_xlabel('time')\n",
    "    ax2.set_ylabel('x')\n",
    "    h = ax2.imshow(U_pred.T, interpolation='gaussian', cmap='jet', \n",
    "                   extent = extent, \n",
    "                   origin='lower', aspect='auto')\n",
    "    plt.colorbar(h);\n",
    "   \n",
    "\n",
    "    plt.savefig('./images/burgers_partI', dpi = 1200, transparent = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T20:08:49.843114Z",
     "start_time": "2019-08-08T20:08:35.764971Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_subplots()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Driven Discovery - Part II"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-22T22:17:17.052565Z",
     "start_time": "2019-07-22T22:17:14.142459Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.13.1\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "# Tensorflow\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "from keras.layers import Input, Dense\n",
    "from keras.models import Model\n",
    "from keras import optimizers\n",
    "\n",
    "# Scientific Libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.io import loadmat\n",
    "from scipy.interpolate import BSpline\n",
    "import pandas as pd\n",
    "\n",
    "# Graphing Libraries\n",
    "import matplotlib.gridspec as gridspec\n",
    "from scipy.interpolate import griddata\n",
    "from mpl_toolkits import mplot3d\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "# For Train - Validation - Test\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# For collocation points\n",
    "from pyDOE import lhs\n",
    "print(tf.__version__)\n",
    "\n",
    "%matplotlib inline\n",
    "# %matplotlib notebook\n",
    "# Tensorboard"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-22T22:17:18.694445Z",
     "start_time": "2019-07-22T22:17:18.657472Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u shape: (25600, 1)\n",
      "x train shape: (256, 1)\n",
      "t train shape: (100, 1)\n"
     ]
    }
   ],
   "source": [
    "# Set Random Seed\n",
    "np.random.seed(1234)\n",
    "tf.set_random_seed(1234)\n",
    "\n",
    "data = loadmat('./burgers_shock.mat'); \n",
    "\n",
    "x = pd.Series(data['x'].flatten())[:, None]\n",
    "t = pd.Series(data['t'].flatten())[:, None]\n",
    "u_data = np.real(data['usol']).T\n",
    "usol = pd.Series(u_data.flatten())[:, None]\n",
    "\n",
    "print(f'u shape: {usol.shape}')\n",
    "print(f'x train shape: {x.shape}')\n",
    "print(f't train shape: {t.shape}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-22T22:20:33.988989Z",
     "start_time": "2019-07-22T22:20:33.982737Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.        ],\n",
       "       [-0.99215686],\n",
       "       [-0.98431373],\n",
       "       [-0.97647059],\n",
       "       [-0.96862745],\n",
       "       [-0.96078431],\n",
       "       [-0.95294118],\n",
       "       [-0.94509804],\n",
       "       [-0.9372549 ],\n",
       "       [-0.92941176],\n",
       "       [-0.92156863],\n",
       "       [-0.91372549],\n",
       "       [-0.90588235],\n",
       "       [-0.89803922],\n",
       "       [-0.89019608],\n",
       "       [-0.88235294],\n",
       "       [-0.8745098 ],\n",
       "       [-0.86666667],\n",
       "       [-0.85882353],\n",
       "       [-0.85098039],\n",
       "       [-0.84313725],\n",
       "       [-0.83529412],\n",
       "       [-0.82745098],\n",
       "       [-0.81960784],\n",
       "       [-0.81176471],\n",
       "       [-0.80392157],\n",
       "       [-0.79607843],\n",
       "       [-0.78823529],\n",
       "       [-0.78039216],\n",
       "       [-0.77254902],\n",
       "       [-0.76470588],\n",
       "       [-0.75686275],\n",
       "       [-0.74901961],\n",
       "       [-0.74117647],\n",
       "       [-0.73333333],\n",
       "       [-0.7254902 ],\n",
       "       [-0.71764706],\n",
       "       [-0.70980392],\n",
       "       [-0.70196078],\n",
       "       [-0.69411765],\n",
       "       [-0.68627451],\n",
       "       [-0.67843137],\n",
       "       [-0.67058824],\n",
       "       [-0.6627451 ],\n",
       "       [-0.65490196],\n",
       "       [-0.64705882],\n",
       "       [-0.63921569],\n",
       "       [-0.63137255],\n",
       "       [-0.62352941],\n",
       "       [-0.61568627],\n",
       "       [-0.60784314],\n",
       "       [-0.6       ],\n",
       "       [-0.59215686],\n",
       "       [-0.58431373],\n",
       "       [-0.57647059],\n",
       "       [-0.56862745],\n",
       "       [-0.56078431],\n",
       "       [-0.55294118],\n",
       "       [-0.54509804],\n",
       "       [-0.5372549 ],\n",
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       "       [-0.33333333],\n",
       "       [-0.3254902 ],\n",
       "       [-0.31764706],\n",
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       "       [-0.29411765],\n",
       "       [-0.28627451],\n",
       "       [-0.27843137],\n",
       "       [-0.27058824],\n",
       "       [-0.2627451 ],\n",
       "       [-0.25490196],\n",
       "       [-0.24705882],\n",
       "       [-0.23921569],\n",
       "       [-0.23137255],\n",
       "       [-0.22352941],\n",
       "       [-0.21568627],\n",
       "       [-0.20784314],\n",
       "       [-0.2       ],\n",
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       "       [-0.15294118],\n",
       "       [-0.14509804],\n",
       "       [-0.1372549 ],\n",
       "       [-0.12941176],\n",
       "       [-0.12156863],\n",
       "       [-0.11372549],\n",
       "       [-0.10588235],\n",
       "       [-0.09803922],\n",
       "       [-0.09019608],\n",
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       "       [-0.0745098 ],\n",
       "       [-0.06666667],\n",
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       "       [ 0.00392157],\n",
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       "       [ 0.1372549 ],\n",
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       "       [ 0.15294118],\n",
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       "       [ 0.2       ],\n",
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       "       [ 0.3254902 ],\n",
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       "       [ 0.4745098 ],\n",
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       "       [ 0.6       ],\n",
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       "       [ 0.61568627],\n",
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       "       [ 0.68627451],\n",
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       "       [ 0.7254902 ],\n",
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       "       [ 0.74901961],\n",
       "       [ 0.75686275],\n",
       "       [ 0.76470588],\n",
       "       [ 0.77254902],\n",
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       "       [ 0.8745098 ],\n",
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       "       [ 0.89803922],\n",
       "       [ 0.90588235],\n",
       "       [ 0.91372549],\n",
       "       [ 0.92156863],\n",
       "       [ 0.92941176],\n",
       "       [ 0.9372549 ],\n",
       "       [ 0.94509804],\n",
       "       [ 0.95294118],\n",
       "       [ 0.96078431],\n",
       "       [ 0.96862745],\n",
       "       [ 0.97647059],\n",
       "       [ 0.98431373],\n",
       "       [ 0.99215686],\n",
       "       [ 1.        ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.834536Z",
     "start_time": "2019-07-18T23:53:33.832143Z"
    }
   },
   "outputs": [],
   "source": [
    "X, T = np.meshgrid(x, t); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.843632Z",
     "start_time": "2019-07-18T23:53:33.835891Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>T</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.992157</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.984314</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.976471</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.968627</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X    T\n",
       "0 -1.000000  0.0\n",
       "1 -0.992157  0.0\n",
       "2 -0.984314  0.0\n",
       "3 -0.976471  0.0\n",
       "4 -0.968627  0.0"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_data = pd.DataFrame(np.hstack((X.flatten()[:, None], \n",
    "                                 T.flatten()[:, None])));\n",
    "\n",
    "X_data.columns = ['X', 'T'];\n",
    "\n",
    "X_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boundary Conditions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### At t = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.847943Z",
     "start_time": "2019-07-18T23:53:33.845007Z"
    }
   },
   "outputs": [],
   "source": [
    "x_t_at_initial_time_condition = np.hstack((X[0:1, :].T, T[0:1, :].T))\n",
    "u_at_initial_time = (u_data[0, :].T)[:, None];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### At x = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.852008Z",
     "start_time": "2019-07-18T23:53:33.849367Z"
    }
   },
   "outputs": [],
   "source": [
    "x_t_at_negative_boundary = np.hstack((X[:, 0:1], T[:, 0:1]))\n",
    "u_at_negative_boundary = u_data[:, 0:1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### At x = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.856149Z",
     "start_time": "2019-07-18T23:53:33.853401Z"
    }
   },
   "outputs": [],
   "source": [
    "x_t_at_positive_boundary = np.hstack((X[:, -1:], T[:, -1:]))\n",
    "u_at_positive_boundary = u_data[:, -1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### X_u_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.861151Z",
     "start_time": "2019-07-18T23:53:33.857636Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(456, 2)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_u_train = np.vstack([x_t_at_initial_time_condition, \n",
    "                       x_t_at_negative_boundary,\n",
    "                       x_t_at_positive_boundary])\n",
    "X_u_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### u_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.864811Z",
     "start_time": "2019-07-18T23:53:33.862528Z"
    }
   },
   "outputs": [],
   "source": [
    "u_train = np.vstack([u_at_initial_time,\n",
    "                     u_at_negative_boundary,\n",
    "                     u_at_positive_boundary])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train Test Split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.873486Z",
     "start_time": "2019-07-18T23:53:33.866312Z"
    }
   },
   "outputs": [],
   "source": [
    "X_train, X_val, y_train, y_val = train_test_split(X_data, usol, \n",
    "                                                  test_size = 0.3, \n",
    "                                                  random_state = 101)\n",
    "\n",
    "X_val, X_test, y_val, y_test = train_test_split(X_val, y_val, \n",
    "                                                test_size = 0.4,\n",
    "                                                random_state = 101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.878642Z",
     "start_time": "2019-07-18T23:53:33.875228Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Data: (17920, 2)\n",
      "Validation shape: (4608, 2)\n",
      "Test shape: (3072, 2)\n",
      "Total Points: 25600\n"
     ]
    }
   ],
   "source": [
    "print(f'Training Data: {X_train.shape}')\n",
    "print(f'Validation shape: {X_val.shape}')\n",
    "print(f'Test shape: {X_test.shape}')\n",
    "print(f'Total Points: {len(X_train) + len(X_val) + len(X_test)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.887256Z",
     "start_time": "2019-07-18T23:53:33.880476Z"
    }
   },
   "outputs": [],
   "source": [
    "def init_weights(shape):\n",
    "    input_size, output_size = shape[0], shape[1]\n",
    "    std = np.sqrt(2/(input_size + output_size))\n",
    "    init_random_dist = tf.truncated_normal(shape, stddev=0.1)\n",
    "    return tf.Variable(init_random_dist, dtype = tf.float32)\n",
    "\n",
    "def init_bias(shape):\n",
    "    init_bias_vals = tf.constant(0.1, shape=shape)\n",
    "    return tf.Variable(init_bias_vals)\n",
    "\n",
    "def initial_nn(layers):\n",
    "    weights = []\n",
    "    biases = []\n",
    "    \n",
    "    for index in range(len(layers)-1):\n",
    "        shape =(layers[index], layers[index + 1])\n",
    "        W = init_weights(shape)\n",
    "        b = init_bias((1, layers[index + 1]))\n",
    "        weights.append(W)\n",
    "        biases.append(b)\n",
    "    return weights, biases\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.899090Z",
     "start_time": "2019-07-18T23:53:33.894266Z"
    }
   },
   "outputs": [],
   "source": [
    "def neural_net(x, t, weights, biases):\n",
    "    \n",
    "    X = tf.concat([t, x], 1)\n",
    "    num_layers = len(weights) + 1\n",
    "    \n",
    "    for l in range(0,num_layers-2):\n",
    "        W = weights[l]\n",
    "        b = biases[l]\n",
    "        X = tf.tanh(tf.add(tf.matmul(X, W), b))\n",
    "    W = weights[-1]\n",
    "    b = biases[-1]\n",
    "    Y = tf.add(tf.matmul(X, W), b)\n",
    "    \n",
    "    return Y\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.905903Z",
     "start_time": "2019-07-18T23:53:33.901766Z"
    }
   },
   "outputs": [],
   "source": [
    "def f_net(x, t, weights, biases):\n",
    "    nu = 0.01/np.pi\n",
    "    u = neural_net(x, t, weights, biases)\n",
    "    u_t = tf.gradients(u, t)[0]\n",
    "    u_x = tf.gradients(u, x)[0]\n",
    "    u_xx = tf.gradients(u_x, x)[0]\n",
    "    f = u_t + u*u_x - nu*u_xx\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.910990Z",
     "start_time": "2019-07-18T23:53:33.907589Z"
    }
   },
   "outputs": [],
   "source": [
    "def stratify_sample(num_samples, X_data, num_factors = 2):\n",
    "    '''\n",
    "    Variables are sampled using a even sampling method, \n",
    "    and then randomly combined sets of those variables \n",
    "    are used for one calculation of the target function.   \n",
    "    '''\n",
    "    lower_bound = X_data.min(0)\n",
    "    upper_bound = X_data.max(0)\n",
    "    bound_range = upper_bound - lower_bound\n",
    "    \n",
    "    result = lower_bound + bound_range * lhs(num_factors, num_samples)\n",
    "    return result\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.915640Z",
     "start_time": "2019-07-18T23:53:33.912575Z"
    }
   },
   "outputs": [],
   "source": [
    "def physics_nn(layers, x_u, t_u, x_f, t_f, weights, biases):    \n",
    "    u_predictions = neural_net(x_u, t_u, weights, biases)\n",
    "    f_predictions = f_net(x_f, t_f, weights, biases)\n",
    "    return u_predictions, f_predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.919458Z",
     "start_time": "2019-07-18T23:53:33.917161Z"
    }
   },
   "outputs": [],
   "source": [
    "def callback(loss):\n",
    "    print('Loss:', loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.924307Z",
     "start_time": "2019-07-18T23:53:33.921039Z"
    }
   },
   "outputs": [],
   "source": [
    "def joint_loss(u_u, u_predictions, f_predictions):\n",
    "    u_loss = tf.reduce_mean(tf.square(u_u - u_predictions))\n",
    "    f_loss = tf.reduce_mean(tf.square(f_predictions))\n",
    "    total_loss = tf.add(u_loss, f_loss)\n",
    "    return total_loss\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.928930Z",
     "start_time": "2019-07-18T23:53:33.925925Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_history(num_steps, loss_history):\n",
    "    plt.plot(range(num_steps), loss_history)\n",
    "    plt.title('Loss v. Iterations');\n",
    "    plt.ylabel('Loss');\n",
    "    plt.xlabel('Iterations');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.932865Z",
     "start_time": "2019-07-18T23:53:33.930621Z"
    }
   },
   "outputs": [],
   "source": [
    "N_f = 10000\n",
    "N_u = 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.940090Z",
     "start_time": "2019-07-18T23:53:33.934546Z"
    }
   },
   "outputs": [],
   "source": [
    "lower_bound = np.array(X_data.min(0))\n",
    "upper_bound = np.array(X_data.max(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.944827Z",
     "start_time": "2019-07-18T23:53:33.941584Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.,  0.])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower_bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.955208Z",
     "start_time": "2019-07-18T23:53:33.946241Z"
    }
   },
   "outputs": [],
   "source": [
    "X_f_data = stratify_sample(N_f, X_u_train); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.959911Z",
     "start_time": "2019-07-18T23:53:33.956771Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stacked/Collocated Points: (10456, 2)\n"
     ]
    }
   ],
   "source": [
    "X_f_train = np.vstack((X_f_data, X_u_train))\n",
    "print(f'Stacked/Collocated Points: {X_f_train.shape}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.964104Z",
     "start_time": "2019-07-18T23:53:33.961585Z"
    }
   },
   "outputs": [],
   "source": [
    "LAYERS = [2, 20, 20, 20, 20, 20, 20, 20, 20, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.969244Z",
     "start_time": "2019-07-18T23:53:33.965932Z"
    }
   },
   "outputs": [],
   "source": [
    "random_idx = np.random.choice(X_data.shape[0], N_u, replace = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:33.974003Z",
     "start_time": "2019-07-18T23:53:33.970833Z"
    }
   },
   "outputs": [],
   "source": [
    "X_u_train = X_data.iloc[random_idx, :]\n",
    "u_train = usol[random_idx]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:34.004928Z",
     "start_time": "2019-07-18T23:53:33.975672Z"
    }
   },
   "outputs": [],
   "source": [
    "class PhysicsInformedNN():\n",
    "    \n",
    "    def __init__(self, X_u, u, layers, num_iter, lower_bound, upper_bound):\n",
    "        \n",
    "        self.loss_history = []  \n",
    "        self.num_iter, self.layers = num_iter, layers\n",
    "        self.u = u\n",
    "        self.lower_bound, self.upper_bound = lower_bound, upper_bound\n",
    "        self.x_u, self.t_u = X_u.iloc[:, 0:1], X_u.iloc[:, 1:2]\n",
    "#         self.x_f, self.t_f = X_f[:, 0][:, None], X_f[:, 1][:, None]\n",
    "        \n",
    "        self.weights, self.biases = self.initial_nn(layers)\n",
    "         \n",
    "            # Initialize parameters\n",
    "            \n",
    "        self.lambda1 = tf.Variable([0.0], dtype = tf.float32)\n",
    "        self.lambda2 = tf.Variable([-6.0], dtype = tf.float32)\n",
    "        \n",
    "        self.x_u_tf, self.t_u_tf, self.u_tf = self.generate_placeholders()\n",
    "        \n",
    "        self.u_pred, self.f_pred = self.generate_predictions()\n",
    "        \n",
    "        self.loss = self.calc_loss()\n",
    "        \n",
    "       \n",
    "        config = tf.ConfigProto(allow_soft_placement = True, \n",
    "                                log_device_placement = True)\n",
    "        options = {\n",
    "            'maxiter': num_iter,\n",
    "            'maxfun':  num_iter,\n",
    "            'maxcor': 50, \n",
    "            'maxls': 50,\n",
    "            'ftol' : 1.0 * np.finfo(float).eps\n",
    "        }\n",
    "        \n",
    "        self.sess = tf.Session(config = config)\n",
    "        \n",
    "        # For DiffEq?\n",
    "        self.optimizer = tf.contrib.opt.ScipyOptimizerInterface(self.loss, \n",
    "                                                                method = 'L-BFGS-B',\n",
    "                                                                options = options)\n",
    "        # For Adam?\n",
    "        self.optimizer_Adam = tf.train.AdamOptimizer()\n",
    "        self.train_op_Adam = self.optimizer_Adam.minimize(self.loss)\n",
    "                                                                \n",
    "        self.sess.run(tf.global_variables_initializer())\n",
    "        \n",
    "        \n",
    "    def train(self, num_iterations):\n",
    "        tf_dict = {\n",
    "            self.x_u_tf: self.x_u, \n",
    "            self.t_u_tf: self.t_u, \n",
    "            self.u_tf: self.u, \n",
    "#             self.x_f_tf: self.x_f, \n",
    "#             self.t_f_tf: self.t_f\n",
    "        }\n",
    "        start_time = time.time()\n",
    "        for i in range(num_iterations):\n",
    "            self.sess.run(self.train_op_Adam, tf_dict)\n",
    "    \n",
    "            self.print_stats(i, start_time, tf_dict)\n",
    "        \n",
    "        self.optimizer.minimize(self.sess,\n",
    "                                feed_dict = tf_dict,\n",
    "                                fetches = [self.loss, self.lambda1, self.lambda2], \n",
    "                                loss_callback = self.callback)\n",
    "    \n",
    "    def print_stats(self, i, start_time, tf_dict):\n",
    "        if i % 10 == 0:\n",
    "            elapsed = time.time() - start_time\n",
    "            loss_value = self.sess.run(self.loss, tf_dict)\n",
    "            lambda1_value = self.sess.run(self.lambda1)\n",
    "            lambda2_value = np.exp(self.sess.run(self.lambda2))\n",
    "            print('It: %d, Loss: %.3e, Lambda_1: %.3f, Lambda_2: %.6f, Time: %.2f' % \n",
    "                  (i, loss_value, lambda1_value, lambda2_value, elapsed))\n",
    "            start_time = time.time()\n",
    "    \n",
    "    def predict(self, X_data):\n",
    "        predict_dict = {\n",
    "            self.x_u_tf: X_data.iloc[:,0][:, None], \n",
    "            self.t_u_tf: X_data.iloc[:,1][:, None]\n",
    "        }\n",
    "        \n",
    "        u_predictions = self.sess.run(self.u_pred, feed_dict = predict_dict)  \n",
    "#         f_predictions = self.sess.run(self.f_pred, feed_dict = predict_dict)\n",
    "        return u_predictions\n",
    "\n",
    "    def callback(self, loss, lambda1, lambda2):\n",
    "        print('Loss: %e, l1: %.5f, l2: %.5f' % (loss, lambda1, np.exp(lambda2)))\n",
    "        self.loss_history.append(loss)\n",
    "    \n",
    "        \n",
    "    def neural_net(self, X, weights, biases):\n",
    "        num_layers = len(weights) + 1\n",
    "        \n",
    "        h = 2.0*(X - self.lower_bound)/(self.upper_bound - self.lower_bound) - 1.0\n",
    "        for l in range(0,num_layers - 2):\n",
    "            W = weights[l]\n",
    "            b = biases[l]\n",
    "            h = tf.tanh(tf.add(tf.matmul(h, W), b))   \n",
    "        W = weights[-1]\n",
    "        b = biases[-1]\n",
    "        Y = tf.add(tf.matmul(h, W), b)\n",
    "        return Y\n",
    "    \n",
    "    def net_u(self, x, t):\n",
    "        u = self.neural_net(tf.concat([x,t], 1, name='00_concat_op'), self.weights, self.biases)\n",
    "        return u\n",
    "            \n",
    "    def net_f(self, x, t):\n",
    "#         nu = 0.01 / np.pi\n",
    "        lambda1 = self.lambda1       \n",
    "        lambda2 = tf.exp(self.lambda2)\n",
    "        u = self.net_u(x, t)\n",
    "        u_t = tf.gradients(u, t)[0]\n",
    "        u_x = tf.gradients(u, x)[0]\n",
    "        u_xx = tf.gradients(u_x, x)[0]\n",
    "        f = u_t + (lambda1) * u*u_x - (lambda2) *u_xx\n",
    "        return f\n",
    "    \n",
    "    def calc_loss(self):\n",
    "        u_loss = tf.reduce_mean(tf.square(self.u_tf - self.u_pred)) \n",
    "        f_loss = tf.reduce_mean(tf.square(self.f_pred))\n",
    "        return u_loss + f_loss\n",
    "               \n",
    "    def generate_predictions(self):\n",
    "        u_pred = self.net_u(self.x_u_tf, self.t_u_tf) \n",
    "        f_pred = self.net_f(self.x_u_tf, self.t_u_tf)\n",
    "        return u_pred, f_pred\n",
    "        \n",
    "    def generate_placeholders(self):\n",
    "        x_u_tf = tf.placeholder(tf.float32)\n",
    "        t_u_tf = tf.placeholder(tf.float32)        \n",
    "        \n",
    "        u_tf = tf.placeholder(tf.float32)\n",
    "        \n",
    "#         x_f_tf = tf.placeholder(tf.float32)\n",
    "#         t_f_tf = tf.placeholder(tf.float32)\n",
    "        \n",
    "        return x_u_tf, t_u_tf, u_tf\n",
    "        \n",
    "    def init_weights(self, shape):\n",
    "        input_size, output_size = shape[0], shape[1]\n",
    "        std = np.sqrt(2/(input_size + output_size))\n",
    "        init_random_dist = tf.truncated_normal(shape, stddev = std)\n",
    "        return tf.Variable(init_random_dist, dtype = tf.float32)\n",
    "\n",
    "    def init_bias(self, shape):\n",
    "        init_bias_vals = tf.constant(0.1, shape = shape)\n",
    "        return tf.Variable(init_bias_vals)\n",
    "\n",
    "    def initial_nn(self, layers):\n",
    "        weights = []\n",
    "        biases = []\n",
    "\n",
    "        for index in range(len(layers)-1):\n",
    "            shape = (layers[index], layers[index + 1])\n",
    "            W = init_weights(shape)\n",
    "            b = init_bias((1, layers[index + 1]))\n",
    "            weights.append(W)\n",
    "            biases.append(b)       \n",
    "        return weights, biases\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:34.009623Z",
     "start_time": "2019-07-18T23:53:34.006516Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 20, 20, 20, 20, 20, 20, 20, 20, 1]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LAYERS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:53:38.714758Z",
     "start_time": "2019-07-18T23:53:34.011042Z"
    }
   },
   "outputs": [],
   "source": [
    "model = PhysicsInformedNN(X_u_train, u_train,\n",
    "                          layers = LAYERS, \n",
    "                          num_iter = 1500, \n",
    "                          lower_bound = lower_bound, upper_bound = upper_bound)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:57.796770Z",
     "start_time": "2019-07-18T23:53:38.716080Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It: 0, Loss: 3.826e-01, Lambda_1: 0.000, Lambda_2: 0.002479, Time: 3.79\n",
      "Loss: 3.794845e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 1.588665e+00, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.793010e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.793007e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.792990e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.792893e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.792465e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786064e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.127458e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 7.119427e+02, l1: 0.00000, l2: 0.00248\n",
      "Loss: 5.094491e+00, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.109967e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.088827e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.088827e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 4.593479e+01, l1: 0.00001, l2: 0.00248\n",
      "Loss: 9.511972e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.088806e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 2.812231e-01, l1: -0.00042, l2: 0.00248\n",
      "Loss: 2.616490e-01, l1: -0.00150, l2: 0.00248\n",
      "Loss: 2.552404e-01, l1: -0.00207, l2: 0.00248\n",
      "Loss: 2.493403e-01, l1: -0.00642, l2: 0.00248\n",
      "Loss: 2.479253e-01, l1: -0.00865, l2: 0.00248\n",
      "Loss: 2.470224e-01, l1: -0.01097, l2: 0.00248\n",
      "Loss: 2.438253e-01, l1: -0.02004, l2: 0.00248\n",
      "Loss: 2.399856e-01, l1: -0.03337, l2: 0.00248\n",
      "Loss: 2.342827e-01, l1: -0.05769, l2: 0.00248\n",
      "Loss: 2.312063e-01, l1: -0.07436, l2: 0.00248\n",
      "Loss: 2.248391e-01, l1: -0.08687, l2: 0.00248\n",
      "Loss: 1.978018e-01, l1: -0.11420, l2: 0.00248\n",
      "Loss: 2.169839e+00, l1: -0.14153, l2: 0.00247\n",
      "Loss: 1.965547e-01, l1: -0.11471, l2: 0.00248\n",
      "Loss: 1.817247e-01, l1: -0.08990, l2: 0.00248\n",
      "Loss: 1.593364e-01, l1: -0.08701, l2: 0.00248\n",
      "Loss: 1.480367e-01, l1: -0.07672, l2: 0.00248\n",
      "Loss: 1.376345e-01, l1: -0.08645, l2: 0.00247\n",
      "Loss: 1.301182e-01, l1: -0.08339, l2: 0.00247\n",
      "Loss: 1.195346e-01, l1: -0.08680, l2: 0.00247\n",
      "Loss: 1.102293e-01, l1: -0.08073, l2: 0.00247\n",
      "Loss: 1.020400e-01, l1: -0.03676, l2: 0.00245\n",
      "Loss: 9.518284e-02, l1: 0.04061, l2: 0.00242\n",
      "Loss: 9.368320e-02, l1: 0.23216, l2: 0.00235\n",
      "Loss: 9.034200e-02, l1: 0.11046, l2: 0.00240\n",
      "Loss: 1.093404e-01, l1: 0.30437, l2: 0.00233\n",
      "Loss: 8.664402e-02, l1: 0.17361, l2: 0.00238\n",
      "Loss: 8.524499e-02, l1: 0.23532, l2: 0.00235\n",
      "Loss: 8.025681e-02, l1: 0.20473, l2: 0.00236\n",
      "Loss: 8.050588e-02, l1: 0.18688, l2: 0.00237\n",
      "Loss: 7.955595e-02, l1: 0.19655, l2: 0.00237\n",
      "Loss: 7.910451e-02, l1: 0.19332, l2: 0.00237\n",
      "Loss: 7.879986e-02, l1: 0.20286, l2: 0.00236\n",
      "Loss: 7.664453e-02, l1: 0.18367, l2: 0.00236\n",
      "Loss: 7.072906e-02, l1: 0.10694, l2: 0.00235\n",
      "Loss: 3.059530e-01, l1: -0.26577, l2: 0.00228\n",
      "Loss: 6.910848e-02, l1: 0.09140, l2: 0.00234\n",
      "Loss: 6.520112e-02, l1: 0.00912, l2: 0.00233\n",
      "Loss: 5.851492e-02, l1: 0.01696, l2: 0.00231\n",
      "Loss: 5.937717e-02, l1: 0.04219, l2: 0.00229\n",
      "Loss: 5.380689e-02, l1: 0.02901, l2: 0.00230\n",
      "Loss: 4.735585e-02, l1: 0.02953, l2: 0.00227\n",
      "Loss: 8.686759e-02, l1: 0.09478, l2: 0.00224\n",
      "Loss: 4.540886e-02, l1: 0.04242, l2: 0.00227\n",
      "Loss: 4.529191e-02, l1: 0.02108, l2: 0.00224\n",
      "Loss: 4.381189e-02, l1: 0.03332, l2: 0.00225\n",
      "Loss: 4.360737e-02, l1: 0.02738, l2: 0.00225\n",
      "Loss: 4.354686e-02, l1: 0.02782, l2: 0.00224\n",
      "Loss: 4.350289e-02, l1: 0.02813, l2: 0.00224\n",
      "Loss: 4.348211e-02, l1: 0.02787, l2: 0.00224\n",
      "Loss: 4.339112e-02, l1: 0.02745, l2: 0.00223\n",
      "Loss: 4.314415e-02, l1: 0.02740, l2: 0.00222\n",
      "Loss: 4.269302e-02, l1: 0.02742, l2: 0.00219\n",
      "Loss: 4.244594e-02, l1: 0.03335, l2: 0.00216\n",
      "Loss: 4.202317e-02, l1: 0.03159, l2: 0.00215\n",
      "Loss: 4.171667e-02, l1: 0.03002, l2: 0.00216\n",
      "Loss: 4.148634e-02, l1: 0.03299, l2: 0.00216\n",
      "Loss: 4.141634e-02, l1: 0.03356, l2: 0.00215\n",
      "Loss: 4.137862e-02, l1: 0.03375, l2: 0.00214\n",
      "Loss: 4.134726e-02, l1: 0.03485, l2: 0.00214\n",
      "Loss: 4.125508e-02, l1: 0.03601, l2: 0.00212\n",
      "Loss: 4.097440e-02, l1: 0.03892, l2: 0.00208\n",
      "Loss: 4.042126e-02, l1: 0.04406, l2: 0.00198\n",
      "Loss: 3.986393e-02, l1: 0.04420, l2: 0.00192\n",
      "Loss: 3.929549e-02, l1: 0.03819, l2: 0.00189\n",
      "Loss: 3.900298e-02, l1: 0.04162, l2: 0.00188\n",
      "Loss: 3.894587e-02, l1: 0.04903, l2: 0.00192\n",
      "Loss: 3.859062e-02, l1: 0.05057, l2: 0.00188\n",
      "Loss: 3.847441e-02, l1: 0.04640, l2: 0.00187\n",
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     ]
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    {
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     "output_type": "stream",
     "text": [
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    {
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     "output_type": "stream",
     "text": [
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
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     "text": [
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      "Loss: 4.347730e-04, l1: 0.96574, l2: 0.00395\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss: 4.333833e-04, l1: 0.96615, l2: 0.00395\n",
      "Loss: 4.326307e-04, l1: 0.96663, l2: 0.00395\n",
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      "Loss: 4.255134e-04, l1: 0.96731, l2: 0.00396\n",
      "Loss: 4.238805e-04, l1: 0.96792, l2: 0.00396\n",
      "Loss: 4.213888e-04, l1: 0.96877, l2: 0.00395\n",
      "Loss: 4.199844e-04, l1: 0.96957, l2: 0.00396\n",
      "Loss: 4.207404e-04, l1: 0.96966, l2: 0.00395\n",
      "Loss: 4.189107e-04, l1: 0.96961, l2: 0.00396\n",
      "Loss: 4.177170e-04, l1: 0.96933, l2: 0.00396\n",
      "Loss: 4.142737e-04, l1: 0.96864, l2: 0.00397\n",
      "Loss: 4.127144e-04, l1: 0.96866, l2: 0.00397\n",
      "Loss: 4.110727e-04, l1: 0.96879, l2: 0.00397\n",
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT'\n",
      "  Objective function value: 0.000411\n",
      "  Number of iterations: 1382\n",
      "  Number of functions evaluations: 1501\n"
     ]
    }
   ],
   "source": [
    "model.train(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:58.057162Z",
     "start_time": "2019-07-18T23:54:57.798068Z"
    }
   },
   "outputs": [],
   "source": [
    "u_pred = model.predict(X_data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:58.064051Z",
     "start_time": "2019-07-18T23:54:58.059122Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error u: 2.247617e-02\n"
     ]
    }
   ],
   "source": [
    "error_u = np.linalg.norm(usol - u_pred,2)/np.linalg.norm(usol,2)\n",
    "print('Error u: %e' % (error_u))                     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:58.627302Z",
     "start_time": "2019-07-18T23:54:58.066226Z"
    }
   },
   "outputs": [],
   "source": [
    "U_pred = griddata(X_data, u_pred.flatten(), (X, T), method='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:58.634000Z",
     "start_time": "2019-07-18T23:54:58.628668Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error u: 2.247617e-02\n",
      "Error l1: 3.121%\n",
      "Error l2: 24.784%\n"
     ]
    }
   ],
   "source": [
    "nu = 0.01/np.pi\n",
    "\n",
    "lambda_1_value = model.sess.run(model.lambda1)\n",
    "lambda_2_value = model.sess.run(model.lambda2)\n",
    "lambda_2_value = np.exp(lambda_2_value)\n",
    "\n",
    "error_lambda_1 = np.abs(lambda_1_value - 1.0) * 100\n",
    "error_lambda_2 = np.abs(lambda_2_value - nu)/nu * 100\n",
    "\n",
    "print('Error u: %e' % (error_u))    \n",
    "print('Error l1: %.3f%%' % (error_lambda_1))                             \n",
    "print('Error l2: %.3f%%' % (error_lambda_2))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:58.641569Z",
     "start_time": "2019-07-18T23:54:58.635571Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_subplots():\n",
    "    extent = [0, 1, -1, 1]\n",
    "\n",
    "    fig = plt.figure(figsize = (10, 10))\n",
    "    fig.subplots_adjust(hspace = 0.5)\n",
    "    gs = fig.add_gridspec(2, 1)\n",
    "    \n",
    "    ax1 = fig.add_subplot(gs[0, :], )\n",
    "    ax1.set_title('Actual Data')\n",
    "    ax1.set_xlabel('time')\n",
    "    ax1.set_ylabel('x')\n",
    "    h = ax1.imshow(u_data.T, \n",
    "                   interpolation ='gaussian', cmap ='jet', \n",
    "                   extent = extent, \n",
    "                   origin ='lower', aspect ='auto')\n",
    "    plt.colorbar(h);\n",
    "\n",
    "\n",
    "    ax2 = fig.add_subplot(gs[1, :])\n",
    "    ax2.set_title('Predicted Data')\n",
    "    ax2.set_xlabel('time')\n",
    "    ax2.set_ylabel('x')\n",
    "    h = ax2.imshow(U_pred.T, interpolation='gaussian', cmap='jet', \n",
    "                   extent = extent, \n",
    "                   origin='lower', aspect='auto')\n",
    "    plt.colorbar(h);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T20:48:02.344015Z",
     "start_time": "2019-08-08T20:48:02.336135Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_actual_vs_predicted(time_intervals):\n",
    "    params = {\"ytick.color\" : \"w\",\n",
    "          \"xtick.color\" : \"w\",\n",
    "          \"axes.labelcolor\" : \"w\",\n",
    "          \"axes.edgecolor\" : \"w\"}\n",
    "    plt.rcParams.update(params)\n",
    "    fig = plt.figure(figsize = (15, 15))\n",
    "    fig.subplots_adjust(hspace = 0.75)\n",
    "    gs = fig.add_gridspec(1 , len(time_intervals))\n",
    "    \n",
    "    for index, time in enumerate(time_intervals):\n",
    "        ax = fig.add_subplot(gs[:, index], )\n",
    "        ax.plot(x, u_data[time,:], 'b-', linewidth = 2, label = 'Exact')       \n",
    "        ax.plot(x, U_pred[time,:], 'r--', linewidth = 2, label = 'Prediction')\n",
    "        \n",
    "        ax.set_xlabel('$x$')\n",
    "        ax.set_ylabel('$u(t,x)$')    \n",
    "        ax.set_title(f'$t = 0.{time}$', fontsize = 10, color ='white')\n",
    "        ax.axis('square')\n",
    "        ax.set_xlim([-1.1, 1.1])\n",
    "        ax.set_ylim([-1.1, 1.1])\n",
    "    legend = ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.35), ncol=5, frameon=False)\n",
    "    plt.setp(legend.get_texts(), color='w')\n",
    "    plt.savefig('./images/burgers_actualvspredicted', dpi = 1200, transparent = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:58.656723Z",
     "start_time": "2019-07-18T23:54:58.652308Z"
    }
   },
   "outputs": [],
   "source": [
    "def display_PDEs(l1, l2, l1_noise = None, l2_noise = None,  noise = False):\n",
    "    print('Correct PDE:')\n",
    "    correct = 'u_t + u u_x - 0.0031831 u_{xx} = 0'\n",
    "    print(correct)\n",
    "    print('---------------------------------')\n",
    "    print('Identified PDE (clean data)')\n",
    "    identified = 'u_t + %.3f u u_x - %.3f u_{xx} = 0' % (l1, l2)\n",
    "    print(identified)\n",
    "    \n",
    "    if noise:\n",
    "        print('---------------------------------')\n",
    "        print('Identified PDE (noisy data)')\n",
    "        identified_noise = 'u_t + %.3f u u_x - %.3f u_{xx} = 0' % (l1_noise, l2_noise)\n",
    "        print(identified_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:58.661762Z",
     "start_time": "2019-07-18T23:54:58.658617Z"
    },
    "hide_input": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct PDE:\n",
      "u_t + u u_x - 0.0031831 u_{xx} = 0\n",
      "---------------------------------\n",
      "Identified PDE (clean data)\n",
      "u_t + 0.969 u u_x - 0.004 u_{xx} = 0\n"
     ]
    }
   ],
   "source": [
    "display_PDEs(lambda_1_value, lambda_2_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-08T20:48:16.821141Z",
     "start_time": "2019-08-08T20:48:05.194641Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_actual_vs_predicted([25, 50, 75])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:59.868798Z",
     "start_time": "2019-07-18T23:54:59.301863Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_subplots()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add Noise to Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:54:59.872699Z",
     "start_time": "2019-07-18T23:54:59.869824Z"
    }
   },
   "outputs": [],
   "source": [
    "noise = 0.10       \n",
    "u_train = u_train + noise*np.std(u_train)*np.random.randn(u_train.shape[0], u_train.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:55:11.679816Z",
     "start_time": "2019-07-18T23:54:59.873874Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss: 3.951706e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 1.647504e+00, l1: -0.00000, l2: 0.00248\n",
      "Loss: 3.827433e-01, l1: -0.00000, l2: 0.00248\n",
      "Loss: 3.827427e-01, l1: -0.00000, l2: 0.00248\n",
      "Loss: 3.827427e-01, l1: -0.00000, l2: 0.00248\n",
      "Loss: 3.827423e-01, l1: -0.00000, l2: 0.00248\n",
      "Loss: 3.827413e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.827369e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.827282e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.827118e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.826911e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.826771e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.826741e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.826724e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.826666e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.826558e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.825758e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.809080e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 6.108615e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.787388e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 4.329305e+03, l1: 0.00002, l2: 0.00248\n",
      "Loss: 3.786097e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "Loss: 3.786096e-01, l1: 0.00000, l2: 0.00248\n",
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
      "  Objective function value: 0.378610\n",
      "  Number of iterations: 15\n",
      "  Number of functions evaluations: 39\n"
     ]
    }
   ],
   "source": [
    "model = PhysicsInformedNN(X_u_train, u_train,\n",
    "                          layers = LAYERS, \n",
    "                          num_iter = 500, \n",
    "                          lower_bound = lower_bound, upper_bound = upper_bound)\n",
    "model.train(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:55:12.832004Z",
     "start_time": "2019-07-18T23:55:11.682021Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error lambda_1: 99.999985%\n",
      "Error lambda_2: 22.127703%\n"
     ]
    }
   ],
   "source": [
    "u_pred = model.predict(X_data)\n",
    "U_pred = griddata(X_data, u_pred.flatten(), (X, T), method='cubic')\n",
    "\n",
    "lambda_1_value_noisy = model.sess.run(model.lambda1)\n",
    "lambda_2_value_noisy = model.sess.run(model.lambda2)\n",
    "lambda_2_value_noisy = np.exp(lambda_2_value_noisy)\n",
    "\n",
    "error_lambda_1_noisy = np.abs(lambda_1_value_noisy - 1.0)*100\n",
    "error_lambda_2_noisy = np.abs(lambda_2_value_noisy - nu)/nu * 100\n",
    "\n",
    "print('Error lambda_1: %f%%' % (error_lambda_1_noisy))\n",
    "print('Error lambda_2: %f%%' % (error_lambda_2_noisy))                            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:55:12.837877Z",
     "start_time": "2019-07-18T23:55:12.833680Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correct PDE:\n",
      "u_t + u u_x - 0.0031831 u_{xx} = 0\n",
      "---------------------------------\n",
      "Identified PDE (clean data)\n",
      "u_t + 0.969 u u_x - 0.004 u_{xx} = 0\n",
      "---------------------------------\n",
      "Identified PDE (noisy data)\n",
      "u_t + 0.000 u u_x - 0.002 u_{xx} = 0\n"
     ]
    }
   ],
   "source": [
    "display_PDEs(lambda_1_value, lambda_2_value, \n",
    "             lambda_1_value_noisy, lambda_2_value_noisy,\n",
    "             noise = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:55:13.378015Z",
     "start_time": "2019-07-18T23:55:12.839495Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_actual_vs_predicted([25, 50, 75])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-18T23:55:13.917737Z",
     "start_time": "2019-07-18T23:55:13.379597Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_subplots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}