ODE 2 example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import autograd.numpy as np\n",
    "from autograd import grad \n",
    "import autograd.numpy.random as npr\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nx = 10\n",
    "dx = 1. / nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x, psy, dpsy):\n",
    "    '''\n",
    "        d2(psy)/dx2 = f(x, dpsy/dx, psy)\n",
    "        This is f() function on the right\n",
    "    '''\n",
    "    return -1./5. * np.exp(-x/5.) * np.cos(x) - 1./5. * dpsy - psy\n",
    "\n",
    "\n",
    "def psy_analytic(x):\n",
    "    '''\n",
    "        Analytical solution of current problem\n",
    "    '''\n",
    "    return np.exp(-x/5.) * np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_space = np.linspace(0, 2, nx)    \n",
    "y_space = psy_analytic(x_space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.204183983972\n"
     ]
    }
   ],
   "source": [
    "def sigmoid(x):\n",
    "    return 1. / (1. + np.exp(-x))\n",
    "\n",
    "def neural_network(W, x):\n",
    "    a1 = sigmoid(np.dot(x, W[0]))\n",
    "    return np.dot(a1, W[1])\n",
    "\n",
    "def neural_network_x(x):\n",
    "    a1 = sigmoid(np.dot(x, W[0]))\n",
    "    return np.dot(a1, W[1])\n",
    "\n",
    "def psy_trial(xi, net_out):\n",
    "    return xi + xi**2 * net_out\n",
    "\n",
    "psy_grad = grad(psy_trial)\n",
    "psy_grad2 = grad(psy_grad)\n",
    "\n",
    "def loss_function(W, x):\n",
    "    loss_sum = 0.\n",
    "    \n",
    "    for xi in x:\n",
    "        net_out = neural_network(W, xi)[0][0]\n",
    "\n",
    "        net_out_d = grad(neural_network_x)(xi)\n",
    "        net_out_dd = grad(grad(neural_network_x))(xi)\n",
    "        \n",
    "        psy_t = psy_trial(xi, net_out)\n",
    "        \n",
    "        gradient_of_trial = psy_grad(xi, net_out)\n",
    "        second_gradient_of_trial = psy_grad2(xi, net_out)\n",
    "        \n",
    "        func = f(xi, psy_t, gradient_of_trial) # right part function\n",
    "        \n",
    "        err_sqr = (second_gradient_of_trial - func)**2\n",
    "        loss_sum += err_sqr\n",
    "        \n",
    "    return loss_sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "W = [npr.randn(1, 10), npr.randn(10, 1)]\n",
    "lmb = 0.001\n",
    "\n",
    "for i in range(50):\n",
    "    loss_grad =  grad(loss_function)(W, x_space)\n",
    "\n",
    "    W[0] = W[0] - lmb * loss_grad[0]\n",
    "    W[1] = W[1] - lmb * loss_grad[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.07399913899\n"
     ]
    },
    {
     "data": {
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hqy+gHHAWmBrTokXk/iz+azFFRhSh0YxGFMhUgF/a/sKIKiPIkiaKGxvch507nU+NTz/t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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcd96f3c910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print loss_function(W, x_space)\n",
    "res = [psy_trial(xi, neural_network(W, xi)[0][0]) for xi in x_space] \n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x_space, y_space) \n",
    "plt.plot(x_space, res)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}