My_first_Crack_at_PINNs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4d3f4b90-d13b-456b-a9e6-32477609edbf",
   "metadata": {},
   "source": [
    "# Architecture of a Physics Informed Neural Network"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bbf121d-8bdd-4efb-869a-de4b1c16b081",
   "metadata": {},
   "source": [
    "The idea of neural networks as universal approximators is widely accepted now. Physics Informed Neural Networks (or PINNs) leverage domain knowledge to overcome the issue of imbalanced data & data shortage commonly encountered for a generic neural network. Let us begin with a simple ordinary differential equation (ODE) with some measured data as the initial and boundary conditions. \n",
    "\n",
    "The idea is to solve a differential equation by representing the solution through a neural network and thereby training the network so that it satisfies the conditions imposed by the differential equation.\n",
    "\n",
    "Consider a system of ODEs\n",
    "\n",
    "$$u' = f(u,t) $$\n",
    "\n",
    "Let us approximate the solution using a neural network\n",
    "\n",
    "$$u(t) \\equiv \\mathcal{N}_N (t) $$\n",
    "\n",
    "If $\\mathcal{N}_N (t)$ was the true solution, then it would hold true for $\\mathcal{N'}_N(t) = f(\\mathcal{N}_N(t), t)$ for all $t$. Thus, the associated loss function can be written as\n",
    "\n",
    "$$\\mathcal{L}(\\omega) = \\Sigma_i \\left( \\frac{d \\mathcal{N}_N(t_i)}{dt} - f(\\mathcal{N}_N(t_i), t_i) \\right)^2 $$\n",
    "\n",
    "\n",
    "When this loss function is minimized, the neural network approximately solves the differential equation.\n",
    "\n",
    "In order to handle the initial conditions, they are introduced in the loss function as\n",
    "\n",
    "$$\\mathcal{L}(\\omega) = \\Sigma_i \\left( \\frac{d \\mathcal{N}_N(t_i)}{dt} - f(\\mathcal{N}_N(t_i), t_i) \\right)^2 + \\left( \\mathcal{N}_N - u(0) \\right)^2$$\n",
    "\n",
    "$\\omega$ here represents the parameters that define the neural network. Hence the problem now reduces down to computing the weights of the neural network for minimizing the loss function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "244aef53-8bdc-46c5-83ca-c16facbb9fe0",
   "metadata": {},
   "source": [
    "### Simple ODE\n",
    "\n",
    "$$\\frac{d u}{d t} = \\cos{\\pi t}$$\n",
    "\n",
    "Initial Condition : \n",
    "\n",
    "$$u(0) = 1$$\n",
    "\n",
    "The exact solution is given as:\n",
    "\n",
    "$$u(t) = \\frac{1}{2\\pi} \\sin{2 \\pi t} + 1$$\n",
    "\n",
    "The implementation is given below:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e191a970-9168-48eb-aa8d-d21604052f91",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "06a3f68c-5adb-4a32-b372-4af17b524f0d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdacbce0-b8f8-44be-866b-533e992c73d6",
   "metadata": {},
   "source": [
    "### Construct the Neural Netwerk $\\mathcal{N}_N (t)$ and define the hyper-parameters "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fdce09c6-cb27-413a-888b-1b0616db4c3f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2023-09-17 01:32:52.524166: I metal_plugin/src/device/metal_device.cc:1154] Metal device set to: Apple M1\n",
      "2023-09-17 01:32:52.524215: I metal_plugin/src/device/metal_device.cc:296] systemMemory: 8.00 GB\n",
      "2023-09-17 01:32:52.524229: I metal_plugin/src/device/metal_device.cc:313] maxCacheSize: 2.67 GB\n",
      "2023-09-17 01:32:52.524862: I tensorflow/core/common_runtime/pluggable_device/pluggable_device_factory.cc:303] Could not identify NUMA node of platform GPU ID 0, defaulting to 0. Your kernel may not have been built with NUMA support.\n",
      "2023-09-17 01:32:52.525142: I tensorflow/core/common_runtime/pluggable_device/pluggable_device_factory.cc:269] Created TensorFlow device (/job:localhost/replica:0/task:0/device:GPU:0 with 0 MB memory) -> physical PluggableDevice (device: 0, name: METAL, pci bus id: <undefined>)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      " Layer (type)                Output Shape              Param #   \n",
      "=================================================================\n",
      " dense (Dense)               (None, 32)                64        \n",
      "                                                                 \n",
      " dense_1 (Dense)             (None, 1)                 33        \n",
      "                                                                 \n",
      "=================================================================\n",
      "Total params: 97 (388.00 Byte)\n",
      "Trainable params: 97 (388.00 Byte)\n",
      "Non-trainable params: 0 (0.00 Byte)\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "NN = tf.keras.models.Sequential([\n",
    "    tf.keras.layers.Input(1,),\n",
    "    tf.keras.layers.Dense(units=32, activation='tanh'),\n",
    "    tf.keras.layers.Dense(units=1)\n",
    "])\n",
    "\n",
    "NN.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5d5f9ba3-378c-43a8-8231-ba17fec26740",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "optm = tf.keras.optimizers.legacy.Adam(learning_rate=0.001)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5a1d7ea-5c65-49ad-a2d2-f972627d6d50",
   "metadata": {},
   "source": [
    "### Define ODE system and loss function\n",
    "\n",
    "* ODE loss:\n",
    "\n",
    "$$\\mathcal{L}_{ODE} = \\frac{1}{n} \\sum_{i=1}^{n} \\left(\\frac{d \\mathcal{N}_N(t_i)}{d t} - \\cos{2\\pi t_i} \\right)^2$$\n",
    "\n",
    "* I.C. loss:\n",
    "\n",
    "$$\\mathcal{L}_{IC} = \\frac{1}{n} \\sum_{i=1}^{n} \\left( \\mathcal{N}_N(0) - 1 \\right)^2$$\n",
    "\n",
    "* Total loss:\n",
    "\n",
    "$$\\mathcal{L}_{total} = \\mathcal{L}_{ODE} + \\mathcal{L}_{IC} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7dba6a5c-4577-40b0-afb1-6248e3c965fc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def ode_system(t, net):\n",
    "    t = t.reshape(-1, 1)\n",
    "    t = tf.constant(t, dtype=tf.float32)\n",
    "    t0 = tf.zeros((1,1))\n",
    "    one = tf.ones((1,1))\n",
    "    \n",
    "    with tf.GradientTape() as tape:\n",
    "        tape.watch(t)\n",
    "        \n",
    "        u = net(t)\n",
    "        u_t = tape.gradient(u,t)\n",
    "\n",
    "    ode_loss = u_t - tf.math.cos(2.0 * np.pi * t)\n",
    "    IC_loss = net(t0) - one\n",
    "    \n",
    "    squared_loss = tf.square(ode_loss) + tf.square(IC_loss)\n",
    "    total_loss = tf.reduce_mean(squared_loss)\n",
    "    \n",
    "    return total_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61e30de8-30e5-4660-b2e3-0777200040f5",
   "metadata": {},
   "source": [
    "### Training & Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "181b92c3-95cc-44fd-af25-fbd890f7d8d5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00266574\n",
      "7.2350966e-05\n",
      "6.82874e-05\n",
      "6.3841944e-05\n",
      "5.9758688e-05\n",
      "6.1674575e-05\n",
      "5.2311167e-05\n",
      "6.988044e-05\n",
      "5.05129e-05\n",
      "4.2744905e-05\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_t = (np.random.rand(30)*2).reshape(-1, 1)\n",
    "train_loss_record = []\n",
    "\n",
    "for itr in range(10000):\n",
    "    with tf.GradientTape() as tape:\n",
    "        train_loss = ode_system(train_t, NN)\n",
    "        train_loss_record.append(train_loss)\n",
    "        \n",
    "        grad_w = tape.gradient(train_loss, NN.trainable_variables)\n",
    "        optm.apply_gradients(zip(grad_w, NN.trainable_variables))\n",
    "    \n",
    "    \n",
    "    if itr % 1000 == 0:\n",
    "        print(train_loss.numpy())\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(train_loss_record)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "56c655b8-a272-43d2-ba0e-1d0cc9c44349",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4/4 [==============================] - 0s 3ms/step\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_t = np.linspace(0, 2, 100)\n",
    "\n",
    "train_u = np.sin(2.0*np.pi*train_t)/(2.0*np.pi) + 1.0\n",
    "true_u = np.sin(2.0*np.pi*test_t)/(2.0*np.pi) + 1.0\n",
    "pred_u = NN.predict(test_t).ravel()\n",
    "\n",
    "plt.figure(figsize = (10,8))\n",
    "plt.plot(train_t, train_u, 'ok', label = 'Train')\n",
    "plt.plot(test_t, true_u, '-k',label = 'True')\n",
    "plt.plot(test_t, pred_u, '--r', label = 'Prediction')\n",
    "plt.legend(fontsize = 15)\n",
    "plt.xlabel('t', fontsize = 15)\n",
    "plt.ylabel('u', fontsize = 15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6b1063e-1373-4b09-bed1-c6459bf1d176",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10 (tensorflow)",
   "language": "python",
   "name": "tensorflow"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}