Physics-based neural network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Physics-based neural network with Sine Activation\n",
    "## Motivation: \n",
    "The following sample problem will demonstrate that deep neural network can be utilized to approximate the solutions of partial differential equations (PDEs). This is a recent area of research, known as Physics Informed Neural Networks (PINNS). With this approach, a loss function is setup to penalize the fitted function’s deviation from the desired differential operator and boundary conditions. ﻿The main insight of this approach lies in the fact that the training data consists of randomly sampled points in the function’s domain. By sampling mini-batches from different parts of the domain and processing these small batches sequentially, the neural network “learns” the function without the computational bottleneck present with grid-based methods. \n",
    "\n",
    "\n",
    "Problem:\n",
    "Let us consider a non-linear Poisson equation:\n",
    "For a domain $\\Omega \\subset \\mathbb{R}^N$ with boundary $\\partial \\Omega = \\Gamma_{D} \\cup \\Gamma_{N}$, we consider the following nonlinear Poisson equation with particular boundary\n",
    "conditions reads:\n",
    "$$\n",
    "\\begin{split}- \\nabla\\cdot((1 + u^2) \\nabla u) &= f \\quad {\\rm in}\\, \\Omega,\\\\\n",
    "u &= 1  \\quad  {\\rm on}\\, \\Gamma_D,\\\\\n",
    "\\nabla u\\cdot n &= 0 \\quad  {\\rm on}\\, \\Gamma_N.\\end{split}\n",
    "$$\n",
    "Here $f$ is input data and  denotes the outward directed boundary normal. The nonlinear variational form can be written in the following canonical form: find $u \\in V$  such that\n",
    "$$\n",
    "F(u;v)=0\\quad \\forall\\,v\\in\\hat{V}\n",
    "$$\n",
    "Here $F:V\\times\\hat{V}\\rightarrow\\mathbb{R}$  is a semilinear form, linear in the argument subsequent to the semicolon, and $V$  is some suitable function space. The semilinear form is defined as follows:\n",
    "$$\n",
    "F(u;v) = \\int_\\Omega (1 + u^2)\\cdot\\nabla u \\cdot \\nabla v - f v \\,{\\rm dx} = 0.\n",
    "$$\n",
    "To solve the nonlinear system $b(U) = 0$  by Newton’s method we compute the Jacobian A = b', where $U$  is the coefficients of the linear combination in the finite element solution $u_h = \\sum_{j=1}^{N}U_j\\phi_j, \\;\n",
    "b:\\mathbb{R}^N\\rightarrow\\mathbb{R}^N$  and \n",
    "$$\n",
    "b_i(U) = F(u_h;\\hat{\\phi}_i),\\quad i = 1,2,\\dotsc,N.\n",
    "$$\n",
    "Linearizing the semilinear form $F$ around $u = u_h$, we obtain \n",
    "$$\n",
    "F'(u_h;\\delta u,v) = \\int_\\Omega [(2 \\delta u\\nabla u_h)\\cdot\\nabla v + ((1+u_h^2)\\nabla\\delta u)\\nabla v] \\,{\\rm dx}\n",
    "$$\n",
    "We note that for each fixed $u_h$,$a = F'(u_h;\\,\\cdot\\,,\\,\\cdot\\,)$  is a bilinear form and $L = F(u_h;\\,\\cdot\\,,\\,\\cdot\\,)$  is a linear form. In each Newton iteration, we thus solve a linear variational problem of the canonical form:\n",
    "find $\\delta u \\in V_{h,0}$ such that\n",
    "$$\n",
    "F'(u_h;\\delta u,v) = -F(u_h;v)\\quad\\forall\\,v\\in\\hat{V}_h.\n",
    "$$\n",
    "In this demo, we shall consider the following definitions of the input function, the domain, and the boundaries:\n",
    "\n",
    "* $\\Omega = [0,1] \\times [0,1]\\,\\,\\,$  (a unit square)\n",
    "* $\\Gamma_{D} = \\{(1, y) \\subset \\partial \\Omega\\}\\,\\,\\,$   (Dirichlet boundary)\n",
    "* $\\Gamma_{N} = \\{(x, 0) \\cup (x, 1) \\cup (0, y) \\subset \\partial \\Omega\\}\\,\\,\\,$  (Neumann boundary)\n",
    "* $f(x, y) = x\\sin(y)\\,\\,\\,$  (source term)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import clear_output\n",
    "\n",
    "try:\n",
    "    import dolfin\n",
    "except ImportError:\n",
    "    !wget \"https://fem-on-colab.github.io/releases/fenics-install.sh\" -O \"/tmp/fenics-install.sh\" && bash \"/tmp/fenics-install.sh\"\n",
    "    clear_output()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "from dolfin import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the error with reference solution on a grid of \\[200,200\\]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PDE Solver with FEniCS library\n",
    "\n",
    "How does the overall error for $u$  decreases as you increase the mesh size to \\[10,10\\], \\[20,20\\] and \\[40,40\\]? Use a reference solution on a grid of \\[200,200\\] to compute the error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DirichletBoundary(SubDomain):\n",
    "    def inside(self, x, on_boundary):\n",
    "        return abs(x[0] - 1.0) < DOLFIN_EPS and on_boundary\n",
    "\n",
    "def PDE_Solver(Nx, Ny):\n",
    "    if has_linear_algebra_backend(\"Epetra\"):\n",
    "        parameters[\"linear_algebra_backend\"] = \"Epetra\"\n",
    "\n",
    "    # Create mesh and define function space \n",
    "    mesh = UnitSquareMesh(Nx, Ny)\n",
    "    File(\"mesh.pvd\") << mesh\n",
    "\n",
    "    V = FunctionSpace(mesh, \"CG\", 1)\n",
    "\n",
    "    # Define boundary condition\n",
    "    g = Constant(1.0)\n",
    "    bc = DirichletBC(V, g, DirichletBoundary())\n",
    "\n",
    "\n",
    "    # Define variational problem \n",
    "    u = Function(V)\n",
    "    v = TestFunction(V)\n",
    "    f = Expression(\"x[0]*sin(x[1])\", degree=2)\n",
    "    F = inner((1 + u**2) * grad(u), grad(v)) * dx - f * v * dx\n",
    "\n",
    "\n",
    "    # Compute solution \n",
    "    solve(F == 0, u, bc, solver_parameters={\"newton_solver\" : {\"relative_tolerance\" : 1e-6} })\n",
    "\n",
    "    Output = u.compute_vertex_values(mesh)\n",
    "    Input = 2 * mesh.coordinates() - 1\n",
    "\n",
    "    return Input, Output, u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, _, u_10 = PDE_Solver(10, 10) # Sample1\n",
    "_, _, u_20 = PDE_Solver(20, 20) # Sample2\n",
    "_, _, u_40 = PDE_Solver(40, 40) # Sample3\n",
    "\n",
    "_, _, u_200 = PDE_Solver(200, 200) # Reference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error Norm in grad[10,10] : 0.00017628328209209516\n",
      "Error Norm in grad[20,20] : 4.4068054925008774e-05\n",
      "Error Norm in grad[40,40] : 1.0742567433924942e-05\n"
     ]
    }
   ],
   "source": [
    "Error1 = errornorm(u_10, u_200)\n",
    "Error2 = errornorm(u_20, u_200)\n",
    "Error3 = errornorm(u_40, u_200)\n",
    "\n",
    "print(\"Error Norm in grad[10,10] : {}\".format(Error1))\n",
    "print(\"Error Norm in grad[20,20] : {}\".format(Error2))\n",
    "print(\"Error Norm in grad[40,40] : {}\".format(Error3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sine Layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SineLayer(tf.keras.layers.Layer):\n",
    "    def __init__(self, in_features, units, bias=True, is_first=False, omega_0=30.):\n",
    "        super(SineLayer, self).__init__()\n",
    "        self.in_features = in_features\n",
    "        self.units = units\n",
    "        self.is_first = is_first\n",
    "        self.omega_0 = omega_0\n",
    "\n",
    "        self.dense = tf.keras.layers.Dense(self.units,\n",
    "                                           use_bias=bias,\n",
    "                                           kernel_initializer=self.init_weights(),\n",
    "                                           input_shape=(self.in_features,))\n",
    "        \n",
    "    \n",
    "    def init_weights(self):\n",
    "        if self.is_first:\n",
    "            return tf.keras.initializers.RandomUniform(minval=-1 / self.in_features,\n",
    "                                                       maxval= 1 / self.in_features)\n",
    "        else:\n",
    "            return tf.keras.initializers.RandomUniform(minval=-np.sqrt(6. / self.in_features) / self.omega_0,\n",
    "                                                       maxval= np.sqrt(6. / self.in_features) / self.omega_0)\n",
    "    \n",
    "\n",
    "    def call(self, input_tensor):\n",
    "        befor_activation = self.dense(input_tensor)\n",
    "        after_activation = tf.sin(self.omega_0 * befor_activation)\n",
    "        return after_activation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.keras.backend.clear_session() # clear keras session"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "omega_0 = 15 # Hyper Parameter\n",
    "hidden_units = 32 \n",
    "# initializers for output layer\n",
    "hidden_initializers = tf.keras.initializers.RandomUniform(minval=-np.sqrt(6/hidden_units)/omega_0,\n",
    "                                                          maxval=np.sqrt(6/hidden_units)/omega_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = tf.keras.layers.Input(shape=(2,))\n",
    "\n",
    "# Since network\n",
    "x = SineLayer(2, hidden_units, is_first=True, omega_0=omega_0)(X)\n",
    "Y = tf.keras.layers.Dense(1, kernel_initializer=hidden_initializers)(x)\n",
    "\n",
    "# Relu Network\n",
    "#x = tf.keras.layers.Dense(hidden_units, activation=\"relu\")(X)\n",
    "#Y = tf.keras.layers.Dense(1)(x)\n",
    "\n",
    "\n",
    "model = tf.keras.models.Model(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"model_1\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_2 (InputLayer)         [(None, 2)]               0         \n",
      "_________________________________________________________________\n",
      "sine_layer_1 (SineLayer)     (None, 32)                96        \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 1)                 33        \n",
      "=================================================================\n",
      "Total params: 129\n",
      "Trainable params: 129\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "LR_Coordinates, LR, _ = PDE_Solver(10, 10) #Input resolution for training time\n",
    "HR_Coordinates, HR, _ = PDE_Solver(100, 100) # Resolution for test network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_dataset = tf.data.Dataset.from_tensor_slices((LR_Coordinates, LR))\n",
    "train_dataset = train_dataset.repeat(100)\n",
    "train_dataset = train_dataset.batch(128)\n",
    "\n",
    "valid_dataset = tf.data.Dataset.from_tensor_slices((HR_Coordinates, HR))\n",
    "valid_dataset = valid_dataset.batch(128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.keras.optimizers.Adam(1e-4)\n",
    "loss = tf.keras.losses.MeanSquaredError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(optimizer=optimizer, loss=loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s 6ms/step - loss: 2.8978e-07 - val_loss: 2.3696e-07\n",
      "Epoch 118/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.8318e-07 - val_loss: 2.3124e-07\n",
      "Epoch 119/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.7678e-07 - val_loss: 2.2566e-07\n",
      "Epoch 120/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.7053e-07 - val_loss: 2.2028e-07\n",
      "Epoch 121/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.6440e-07 - val_loss: 2.1510e-07\n",
      "Epoch 122/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.5839e-07 - val_loss: 2.0998e-07\n",
      "Epoch 123/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.5247e-07 - val_loss: 2.0484e-07\n",
      "Epoch 124/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.4662e-07 - val_loss: 1.9982e-07\n",
      "Epoch 125/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.4082e-07 - val_loss: 1.9507e-07\n",
      "Epoch 126/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.3507e-07 - val_loss: 1.9062e-07\n",
      "Epoch 127/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.2937e-07 - val_loss: 1.8633e-07\n",
      "Epoch 128/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 2.2374e-07 - val_loss: 1.8213e-07\n",
      "Epoch 129/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.1815e-07 - val_loss: 1.7804e-07\n",
      "Epoch 130/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.1260e-07 - val_loss: 1.7415e-07\n",
      "Epoch 131/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.0706e-07 - val_loss: 1.7048e-07\n",
      "Epoch 132/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.0156e-07 - val_loss: 1.6709e-07\n",
      "Epoch 133/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 1.9614e-07 - val_loss: 1.6394e-07\n",
      "Epoch 134/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 1.9082e-07 - val_loss: 1.6093e-07\n",
      "Epoch 135/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.8560e-07 - val_loss: 1.5801e-07\n",
      "Epoch 136/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.8047e-07 - val_loss: 1.5516e-07\n",
      "Epoch 137/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.7544e-07 - val_loss: 1.5243e-07\n",
      "Epoch 138/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.7049e-07 - val_loss: 1.4952e-07\n",
      "Epoch 139/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.6555e-07 - val_loss: 1.4593e-07\n",
      "Epoch 140/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.6060e-07 - val_loss: 1.4159e-07\n",
      "Epoch 141/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.5568e-07 - val_loss: 1.3702e-07\n",
      "Epoch 142/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.5085e-07 - val_loss: 1.3258e-07\n",
      "Epoch 143/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.4617e-07 - val_loss: 1.2854e-07\n",
      "Epoch 144/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.4166e-07 - val_loss: 1.2521e-07\n",
      "Epoch 145/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.3733e-07 - val_loss: 1.2241e-07\n",
      "Epoch 146/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.3313e-07 - val_loss: 1.1983e-07\n",
      "Epoch 147/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.2901e-07 - val_loss: 1.1726e-07\n",
      "Epoch 148/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 1.2488e-07 - val_loss: 1.1417e-07\n",
      "Epoch 149/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.2076e-07 - val_loss: 1.1060e-07\n",
      "Epoch 150/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.1679e-07 - val_loss: 1.0721e-07\n",
      "Epoch 151/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.1298e-07 - val_loss: 1.0437e-07\n",
      "Epoch 152/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.0926e-07 - val_loss: 1.0205e-07\n",
      "Epoch 153/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.0563e-07 - val_loss: 9.9969e-08\n",
      "Epoch 154/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.0205e-07 - val_loss: 9.7976e-08\n",
      "Epoch 155/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 9.8537e-08 - val_loss: 9.6231e-08\n",
      "Epoch 156/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 9.5126e-08 - val_loss: 9.4461e-08\n",
      "Epoch 157/300\n",
      "95/95 [==============================] - 1s 8ms/step - loss: 9.1781e-08 - val_loss: 9.2115e-08\n",
      "Epoch 158/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 8.8477e-08 - val_loss: 8.9103e-08\n",
      "Epoch 159/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 8.5243e-08 - val_loss: 8.5550e-08\n",
      "Epoch 160/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 8.2129e-08 - val_loss: 8.1975e-08\n",
      "Epoch 161/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 7.9173e-08 - val_loss: 7.8791e-08\n",
      "Epoch 162/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 7.6366e-08 - val_loss: 7.5959e-08\n",
      "Epoch 163/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 7.3603e-08 - val_loss: 7.3339e-08\n",
      "Epoch 164/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 7.0684e-08 - val_loss: 7.1214e-08\n",
      "Epoch 165/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 6.7623e-08 - val_loss: 6.9448e-08\n",
      "Epoch 166/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 6.4717e-08 - val_loss: 6.7892e-08\n",
      "Epoch 167/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 6.2064e-08 - val_loss: 6.6680e-08\n",
      "Epoch 168/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 5.9604e-08 - val_loss: 6.5455e-08\n",
      "Epoch 169/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 5.7345e-08 - val_loss: 6.3894e-08\n",
      "Epoch 170/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 5.5290e-08 - val_loss: 6.2121e-08\n",
      "Epoch 171/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 5.3418e-08 - val_loss: 6.0203e-08\n",
      "Epoch 172/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 5.1679e-08 - val_loss: 5.8555e-08\n",
      "Epoch 173/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 5.0049e-08 - val_loss: 5.7132e-08\n",
      "Epoch 174/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 4.8489e-08 - val_loss: 5.6052e-08\n",
      "Epoch 175/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 4.6971e-08 - val_loss: 5.5610e-08\n",
      "Epoch 176/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 4.5483e-08 - val_loss: 5.5722e-08\n",
      "Epoch 177/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 4.4010e-08 - val_loss: 5.6063e-08\n",
      "Epoch 178/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 4.2511e-08 - val_loss: 5.6118e-08\n",
      "Epoch 179/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 4.0962e-08 - val_loss: 5.4917e-08\n",
      "Epoch 180/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 3.9346e-08 - val_loss: 5.1406e-08\n",
      "Epoch 181/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 3.7746e-08 - val_loss: 4.6328e-08\n",
      "Epoch 182/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 3.6151e-08 - val_loss: 4.2875e-08\n",
      "Epoch 183/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 3.4730e-08 - val_loss: 4.2434e-08\n",
      "Epoch 184/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 3.3829e-08 - val_loss: 4.2065e-08\n",
      "Epoch 185/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 3.3102e-08 - val_loss: 3.9882e-08\n",
      "Epoch 186/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 3.2610e-08 - val_loss: 3.7742e-08\n",
      "Epoch 187/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 3.2308e-08 - val_loss: 3.6440e-08\n",
      "Epoch 188/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 3.1970e-08 - val_loss: 3.5734e-08\n",
      "Epoch 189/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 3.1427e-08 - val_loss: 3.5176e-08\n",
      "Epoch 190/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 3.0764e-08 - val_loss: 3.4729e-08\n",
      "Epoch 191/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 3.0081e-08 - val_loss: 3.4375e-08\n",
      "Epoch 192/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.9422e-08 - val_loss: 3.4054e-08\n",
      "Epoch 193/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.8759e-08 - val_loss: 3.3773e-08\n",
      "Epoch 194/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.8066e-08 - val_loss: 3.3523e-08\n",
      "Epoch 195/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.7299e-08 - val_loss: 3.3524e-08\n",
      "Epoch 196/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.6379e-08 - val_loss: 3.4165e-08\n",
      "Epoch 197/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.5177e-08 - val_loss: 3.5124e-08\n",
      "Epoch 198/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.3911e-08 - val_loss: 3.5942e-08\n",
      "Epoch 199/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.3216e-08 - val_loss: 3.5953e-08\n",
      "Epoch 200/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.3313e-08 - val_loss: 4.0464e-08\n",
      "Epoch 201/300\n",
      "95/95 [==============================] - 1s 8ms/step - loss: 2.4263e-08 - val_loss: 4.7247e-08\n",
      "Epoch 202/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.4427e-08 - val_loss: 4.7641e-08\n",
      "Epoch 203/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.4061e-08 - val_loss: 4.7441e-08\n",
      "Epoch 204/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 2.3675e-08 - val_loss: 4.7123e-08\n",
      "Epoch 205/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 2.3280e-08 - val_loss: 4.7044e-08\n",
      "Epoch 206/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.2914e-08 - val_loss: 4.7027e-08\n",
      "Epoch 207/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.2579e-08 - val_loss: 4.7001e-08\n",
      "Epoch 208/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.2256e-08 - val_loss: 4.6558e-08\n",
      "Epoch 209/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 2.1903e-08 - val_loss: 4.6317e-08\n",
      "Epoch 210/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.1612e-08 - val_loss: 4.5994e-08\n",
      "Epoch 211/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 2.1305e-08 - val_loss: 4.5931e-08\n",
      "Epoch 212/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.1027e-08 - val_loss: 4.5936e-08\n",
      "Epoch 213/300\n",
      "95/95 [==============================] - 1s 7ms/step - loss: 2.0753e-08 - val_loss: 4.5732e-08\n",
      "Epoch 214/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 2.0470e-08 - val_loss: 4.5783e-08\n",
      "Epoch 215/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 2.0215e-08 - val_loss: 4.5680e-08\n",
      "Epoch 216/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.9957e-08 - val_loss: 4.5524e-08\n",
      "Epoch 217/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.9677e-08 - val_loss: 4.4969e-08\n",
      "Epoch 218/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.9313e-08 - val_loss: 4.3058e-08\n",
      "Epoch 219/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.8684e-08 - val_loss: 3.6132e-08\n",
      "Epoch 220/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.7430e-08 - val_loss: 2.2136e-08\n",
      "Epoch 221/300\n",
      "95/95 [==============================] - 1s 8ms/step - loss: 1.7881e-08 - val_loss: 2.1143e-08\n",
      "Epoch 222/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.7261e-08 - val_loss: 2.1812e-08\n",
      "Epoch 223/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.7264e-08 - val_loss: 2.4669e-08\n",
      "Epoch 224/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.7577e-08 - val_loss: 2.3838e-08\n",
      "Epoch 225/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.7215e-08 - val_loss: 2.4684e-08\n",
      "Epoch 226/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.7220e-08 - val_loss: 2.5223e-08\n",
      "Epoch 227/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.6964e-08 - val_loss: 2.5829e-08\n",
      "Epoch 228/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.6953e-08 - val_loss: 2.6478e-08\n",
      "Epoch 229/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.6756e-08 - val_loss: 2.6598e-08\n",
      "Epoch 230/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.6644e-08 - val_loss: 2.7157e-08\n",
      "Epoch 231/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.6528e-08 - val_loss: 2.7005e-08\n",
      "Epoch 232/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.6372e-08 - val_loss: 2.7197e-08\n",
      "Epoch 233/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.6261e-08 - val_loss: 2.7328e-08\n",
      "Epoch 234/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.6116e-08 - val_loss: 2.7154e-08\n",
      "Epoch 235/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.5987e-08 - val_loss: 2.7464e-08\n",
      "Epoch 236/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.5865e-08 - val_loss: 2.7222e-08\n",
      "Epoch 237/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.5759e-08 - val_loss: 2.7316e-08\n",
      "Epoch 238/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.5625e-08 - val_loss: 2.6568e-08\n",
      "Epoch 239/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.5484e-08 - val_loss: 2.7396e-08\n",
      "Epoch 240/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.5408e-08 - val_loss: 2.6499e-08\n",
      "Epoch 241/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.5259e-08 - val_loss: 2.6927e-08\n",
      "Epoch 242/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.5153e-08 - val_loss: 2.6629e-08\n",
      "Epoch 243/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.5046e-08 - val_loss: 2.6839e-08\n",
      "Epoch 244/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.4938e-08 - val_loss: 2.6665e-08\n",
      "Epoch 245/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4864e-08 - val_loss: 2.6756e-08\n",
      "Epoch 246/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4723e-08 - val_loss: 2.5796e-08\n",
      "Epoch 247/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4628e-08 - val_loss: 2.7127e-08\n",
      "Epoch 248/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4532e-08 - val_loss: 2.5682e-08\n",
      "Epoch 249/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4453e-08 - val_loss: 2.7480e-08\n",
      "Epoch 250/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4343e-08 - val_loss: 2.5263e-08\n",
      "Epoch 251/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4207e-08 - val_loss: 2.7862e-08\n",
      "Epoch 252/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.4219e-08 - val_loss: 2.6195e-08\n",
      "Epoch 253/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.4064e-08 - val_loss: 2.6940e-08\n",
      "Epoch 254/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.4020e-08 - val_loss: 2.6559e-08\n",
      "Epoch 255/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.3883e-08 - val_loss: 2.6814e-08\n",
      "Epoch 256/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.3743e-08 - val_loss: 2.7417e-08\n",
      "Epoch 257/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.3442e-08 - val_loss: 2.6588e-08\n",
      "Epoch 258/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.2994e-08 - val_loss: 5.4430e-08\n",
      "Epoch 259/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 2.0345e-08 - val_loss: 2.2935e-08\n",
      "Epoch 260/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.1838e-08 - val_loss: 1.8582e-08\n",
      "Epoch 261/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.2070e-08 - val_loss: 1.6231e-08\n",
      "Epoch 262/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1719e-08 - val_loss: 2.4269e-08\n",
      "Epoch 263/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.2867e-08 - val_loss: 3.9014e-08\n",
      "Epoch 264/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.8457e-08 - val_loss: 2.2712e-08\n",
      "Epoch 265/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1383e-08 - val_loss: 1.4484e-08\n",
      "Epoch 266/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1471e-08 - val_loss: 1.8570e-08\n",
      "Epoch 267/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1852e-08 - val_loss: 2.0444e-08\n",
      "Epoch 268/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.2906e-08 - val_loss: 2.0112e-08\n",
      "Epoch 269/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.2798e-08 - val_loss: 3.5049e-08\n",
      "Epoch 270/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.6908e-08 - val_loss: 1.8583e-08\n",
      "Epoch 271/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1190e-08 - val_loss: 1.5785e-08\n",
      "Epoch 272/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1146e-08 - val_loss: 2.3371e-08\n",
      "Epoch 273/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.2172e-08 - val_loss: 3.7696e-08\n",
      "Epoch 274/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.8175e-08 - val_loss: 2.0280e-08\n",
      "Epoch 275/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0632e-08 - val_loss: 1.3991e-08\n",
      "Epoch 276/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0864e-08 - val_loss: 1.7822e-08\n",
      "Epoch 277/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1213e-08 - val_loss: 1.9319e-08\n",
      "Epoch 278/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.3415e-08 - val_loss: 2.5481e-08\n",
      "Epoch 279/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1392e-08 - val_loss: 1.9384e-08\n",
      "Epoch 280/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1954e-08 - val_loss: 3.9622e-08\n",
      "Epoch 281/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.8070e-08 - val_loss: 2.0429e-08\n",
      "Epoch 282/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0214e-08 - val_loss: 1.3790e-08\n",
      "Epoch 283/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0471e-08 - val_loss: 1.7695e-08\n",
      "Epoch 284/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0992e-08 - val_loss: 1.8278e-08\n",
      "Epoch 285/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1663e-08 - val_loss: 3.6929e-08\n",
      "Epoch 286/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.7657e-08 - val_loss: 1.9589e-08\n",
      "Epoch 287/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 9.9168e-09 - val_loss: 1.3533e-08\n",
      "Epoch 288/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0164e-08 - val_loss: 2.0329e-08\n",
      "Epoch 289/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1677e-08 - val_loss: 2.3552e-08\n",
      "Epoch 290/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0787e-08 - val_loss: 3.1086e-08\n",
      "Epoch 291/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.5208e-08 - val_loss: 1.5491e-08\n",
      "Epoch 292/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.0109e-08 - val_loss: 1.5609e-08\n",
      "Epoch 293/300\n",
      "95/95 [==============================] - 1s 5ms/step - loss: 1.0129e-08 - val_loss: 1.8654e-08\n",
      "Epoch 294/300\n",
      "95/95 [==============================] - 1s 6ms/step - loss: 1.4554e-08 - val_loss: 1.3612e-08\n",
      "Epoch 295/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0110e-08 - val_loss: 1.5929e-08\n",
      "Epoch 296/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.0025e-08 - val_loss: 2.0024e-08\n",
      "Epoch 297/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.1190e-08 - val_loss: 3.7680e-08\n",
      "Epoch 298/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 1.7214e-08 - val_loss: 1.8223e-08\n",
      "Epoch 299/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 9.3183e-09 - val_loss: 1.3286e-08\n",
      "Epoch 300/300\n",
      "95/95 [==============================] - 0s 5ms/step - loss: 9.5717e-09 - val_loss: 2.0752e-08\n"
     ]
    }
   ],
   "source": [
    "Epoch = 300\n",
    "history = model.fit(train_dataset,\n",
    "                    epochs=Epoch,\n",
    "                    validation_data=valid_dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "predicted = model(HR_Coordinates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "319/319 [==============================] - 1s 3ms/step - loss: 2.0752e-08\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2.0752212392949332e-08"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.evaluate(HR_Coordinates, HR) # Test Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f11200d5510>]"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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       "\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 36.465625 224.64 \n",
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       "L 371.265625 224.64 \n",
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       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 36.465625 7.2 \n",
       "L 371.265625 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p985880f024\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"36.465625\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(predicted) # Predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f10cc5c0890>]"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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   "source": [
    "plt.plot(HR) # Original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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