Compare_BW_BW_noise1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pysindy as ps\n",
    "from scipy.integrate import odeint\n",
    "from math import pi\n",
    "from pysindy.differentiation import FiniteDifference\n",
    "fd = FiniteDifference(order=2, d=1)\n",
    "from sklearn import linear_model\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "import glob\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "np.random.seed(29)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-1.25, -1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,\n",
       "         1.  ,  1.25]),\n",
       " [Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, '')])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid(linestyle='dotted')\n",
    "t = np.linspace(0,20*pi,1000)\n",
    "x = np.sin(t)\n",
    "plt.plot(t, x)\n",
    "plt.xlabel('Time', fontsize = 20)\n",
    "plt.ylabel('Voltage', fontsize = 20)\n",
    "#plt.legend(['Actual function' , 'Learned function', 'Training Data'], prop={'size': 16})\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "#plt.savefig(\"Results/test2_input.png\", dpi = 300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f35a479b610>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "dx = fd._differentiate(x, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f35a46b1550>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "mdx = np.abs(dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f35a4638e90>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, mdx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(y, t):\n",
    "    dydt = np.cos(t) - 0.5*np.abs(np.cos(t))*y - 2*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 1)\n"
     ]
    }
   ],
   "source": [
    "y0 = 0\n",
    "y = odeint(model, y0, t)\n",
    "print(y.shape)\n",
    "# Noise level\n",
    "sigma = 0.01\n",
    "y = y*(1 + sigma*np.random.randn(1000,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f35a4665110>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f35a4555b10>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f35a44e9bd0>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dy = fd._differentiate(y, t)\n",
    "plt.plot(t, dy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "my = np.abs(y)\n",
    "my = my.reshape(-1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f35a4404050>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = y.reshape(-1,)\n",
    "dy = dy.reshape(-1,)\n",
    "t1 = dx\n",
    "t2 = mdx*y\n",
    "t3 = dx*my\n",
    "terms = t1-0.5*t2-2*t3\n",
    "plt.plot(t,terms)\n",
    "plt.plot(t, dy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.stack((y, x, dx, mdx, my), axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x0)' = 0.994 x2 + -0.504 x0 x3 + -1.974 x2 x4\n",
      "(x1)' = 1.000 x2\n",
      "(x2)' = -0.999 x1\n",
      "(x3)' = -39.797 1 + -2.128 x0 + 4.116 x1 + 2.232 x2 + 1.816 x3 + -25.462 x0^2 + 53.122 x0 x1 + 24.970 x0 x2 + -5.344 x0 x3 + 10.928 x0 x4 + 26.724 x1^2 + -13.160 x1 x2 + 1.663 x1 x3 + -12.603 x1 x4 + 17.588 x2^2 + 0.397 x2 x3 + -5.489 x2 x4 + 17.588 x3^2 + -0.937 x3 x4 + -25.462 x4^2\n",
      "(x4)' = -26.901 1 + -3.134 x0 + 2.749 x1 + 1.064 x2 + 9.270 x3 + 19.901 x4 + -5.267 x0^2 + 5.057 x0 x1 + 6.338 x0 x2 + -0.550 x0 x3 + 4.223 x0 x4 + 18.655 x1^2 + -2.605 x1 x2 + 0.077 x1 x3 + -5.518 x1 x4 + 8.581 x2^2 + 0.265 x2 x3 + -2.503 x2 x4 + 8.581 x3^2 + -19.816 x3 x4 + -5.267 x4^2\n"
     ]
    }
   ],
   "source": [
    "model = ps.SINDy()\n",
    "model.fit(X,t)\n",
    "model.print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#kkk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 0.994\n",
    "c2 = -0.504\n",
    "c3 = -1.974\n",
    "def test_model(y, t):\n",
    "    dydt = c1*np.cos(t) + c2*np.abs(np.cos(t))*y + c3*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "ytest_0 = 0\n",
    "y_test = odeint(test_model, ytest_0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid(linestyle='dotted')\n",
    "plt.plot(x, y, 'r')\n",
    "plt.plot(x, y_test, linewidth=2, linestyle=':')\n",
    "plt.xlabel('Voltage', fontsize = 20)\n",
    "plt.ylabel('Displacement', fontsize = 20)\n",
    "plt.legend(['Ground truth' , 'Learned relation'], loc='upper left', prop={'size': 12})\n",
    "plt.xticks(fontsize=20, rotation='45')\n",
    "plt.yticks(fontsize=20)\n",
    "plt.savefig(\"Pics/Slide9_1.png\", dpi = 1000, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ,\n",
       "         1.25]),\n",
       " [Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, '')])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = c1*t1+c2*t2+c3*t3\n",
    "plt.plot(t,dy, 'b')\n",
    "plt.plot(t,test, '--r')\n",
    "plt.grid(linestyle='dotted')\n",
    "plt.xlabel('Time', fontsize = 20)\n",
    "plt.ylabel('Time derivative of disp.', fontsize = 18)\n",
    "plt.legend(['Ground truth' , 'Learned dynamics'], prop={'size': 12})\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "#plt.savefig(\"Results/test2_Output.jpg\", dpi = 300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test SINDy:  0.01028938010868681 %\n"
     ]
    }
   ],
   "source": [
    "y = y.reshape(-1,1)\n",
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = np.mean((y_test - y)**2)/np.mean(y**2)\n",
    "print(\"Relative Error Test SINDy: \", relative_error_test*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1=t1.reshape(-1,1)\n",
    "t2=t2.reshape(-1,1)\n",
    "t3=t3.reshape(-1,1)\n",
    "Y = np.concatenate((t1, t2, t3), axis=1)\n",
    "Y.shape\n",
    "dy = dy.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(Y, dy, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.88494087 -0.57815973 -1.49995566]]\n",
      "[0.00139348]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "clf = Ridge(alpha=1.0)\n",
    "clf.fit(X_train, y_train)\n",
    "print(clf.coef_)\n",
    "print(clf.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#kkk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 0.884\n",
    "c2 = -0.578\n",
    "c3 = -1.49\n",
    "def test_model(y, t):\n",
    "    dydt = c1*np.cos(t) + c2*np.abs(np.cos(t))*y + c3*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "ytest_0 = 0\n",
    "y_test = odeint(test_model, ytest_0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test Ridge:  0.13094014721911246 %\n"
     ]
    }
   ],
   "source": [
    "y = y.reshape(-1,1)\n",
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = np.mean((y_test - y)**2)/np.mean(y**2)\n",
    "print(\"Relative Error Test Ridge: \", relative_error_test*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "linreg = LinearRegression().fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.99193534, -0.49753854, -1.96429786]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linreg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00106789])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linreg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#kkk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 0.991\n",
    "c2 = -0.49\n",
    "c3 = -1.964\n",
    "def test_model(y, t):\n",
    "    dydt = c1*np.cos(t) + c2*np.abs(np.cos(t))*y + c3*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "ytest_0 = 0\n",
    "y_test = odeint(test_model, ytest_0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test Lin reg:  0.023556723920038575 %\n"
     ]
    }
   ],
   "source": [
    "y = y.reshape(-1,1)\n",
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = np.mean((y_test - y)**2)/np.mean(y**2)\n",
    "print(\"Relative Error Test Lin reg: \", relative_error_test*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(Y, dy, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.utils\n",
    "import torch.utils.data\n",
    "from torch.utils.data import DataLoader\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Type of optimizer (ADAM or LBFGS)\n",
    "opt_type = \"LBFGS\"\n",
    "# Random Seed for dataset generation\n",
    "sampling_seed = 78\n",
    "torch.manual_seed(sampling_seed)\n",
    "\n",
    "# Number of training samples\n",
    "n_samples = 1000\n",
    "\n",
    "x = X_train\n",
    "y = y_train\n",
    "y = y.reshape(-1,1)\n",
    "\n",
    "x = x.astype(np.float32)\n",
    "y = y.astype(np.float32)\n",
    "\n",
    "x = torch.from_numpy(x)\n",
    "y = torch.from_numpy(y)\n",
    "\n",
    "batch_size = n_samples\n",
    "training_set = DataLoader(torch.utils.data.TensorDataset(x, y), batch_size=batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NeuralNet(nn.Module):\n",
    "\n",
    "    def __init__(self, input_dimension, output_dimension, n_hidden_layers, neurons):\n",
    "        super(NeuralNet, self).__init__()\n",
    "        # Number of input dimensions n\n",
    "        self.input_dimension = input_dimension\n",
    "        # Number of output dimensions m\n",
    "        self.output_dimension = output_dimension\n",
    "        # Number of neurons per layer \n",
    "        self.neurons = neurons\n",
    "        # Number of hidden layers \n",
    "        self.n_hidden_layers = n_hidden_layers\n",
    "        # Activation function \n",
    "        self.activation = nn.Tanh()\n",
    "        \n",
    "        self.input_layer = nn.Linear(self.input_dimension, self.neurons)\n",
    "        self.hidden_layers = nn.ModuleList([nn.Linear(self.neurons, self.neurons) for _ in range(n_hidden_layers)])\n",
    "        self.output_layer = nn.Linear(self.neurons, self.output_dimension)\n",
    "\n",
    "    def forward(self, x):\n",
    "        # The forward function performs the set of affine and non-linear transformations defining the network \n",
    "        # (see equation above)\n",
    "        x = self.activation(self.input_layer(x))\n",
    "        for k, l in enumerate(self.hidden_layers):\n",
    "            x = self.activation(l(x))\n",
    "        return self.output_layer(x)\n",
    "\n",
    "def NeuralNet_Seq(input_dimension, output_dimension, n_hidden_layers, neurons):\n",
    "    modules = list()\n",
    "    modules.append(nn.Linear(input_dimension, neurons))\n",
    "    modules.append(nn.Tanh())\n",
    "    for _ in range(n_hidden_layers):\n",
    "        modules.append(nn.Linear(neurons, neurons))\n",
    "        modules.append(nn.Tanh())\n",
    "    modules.append(nn.Linear(neurons, output_dimension))\n",
    "    model =  nn.Sequential(*modules)\n",
    "    return model\n",
    "\n",
    "  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Model definition\n",
    "my_network = NeuralNet(input_dimension=x.shape[1], output_dimension=y.shape[1], n_hidden_layers=4, neurons=20)\n",
    "# my_network = NeuralNet_Seq(input_dimension=x.shape[1], output_dimension=y.shape[1], n_hidden_layers=4, neurons=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "        [ 0.8119],\n",
      "        [ 0.5961],\n",
      "        [ 0.4559],\n",
      "        [-0.6549]], grad_fn=<AddmmBackward0>)\n"
     ]
    }
   ],
   "source": [
    "def init_xavier(model, retrain_seed):\n",
    "    torch.manual_seed(retrain_seed)\n",
    "    def init_weights(m):\n",
    "        if type(m) == nn.Linear and m.weight.requires_grad and m.bias.requires_grad:\n",
    "            g = nn.init.calculate_gain('tanh')\n",
    "            torch.nn.init.xavier_uniform_(m.weight, gain=g)\n",
    "            #torch.nn.init.xavier_normal_(m.weight, gain=g)\n",
    "            m.bias.data.fill_(0)\n",
    "    model.apply(init_weights)\n",
    "\n",
    "# Random Seed for weight initialization\n",
    "retrain = 128\n",
    "# Xavier weight initialization\n",
    "init_xavier(my_network, retrain)\n",
    "# Model definition\n",
    "\n",
    "# Predict network value of x\n",
    "print(my_network(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "if opt_type == \"ADAM\":\n",
    "    optimizer_ = optim.Adam(my_network.parameters(), lr=0.001)\n",
    "elif opt_type == \"LBFGS\":\n",
    "    optimizer_ = optim.LBFGS(my_network.parameters(), lr=0.1, max_iter=1, max_eval=50000, tolerance_change=1.0 * np.finfo(float).eps)\n",
    "else:\n",
    "    raise ValueError(\"Optimizer not recognized\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit(model, training_set, num_epochs, optimizer, p, verbose=True):\n",
    "    history = list()\n",
    "    \n",
    "    # Loop over epochs\n",
    "    for epoch in range(num_epochs):\n",
    "        if verbose: print(\"################################ \", epoch, \" ################################\")\n",
    "\n",
    "        running_loss = list([0])\n",
    "        \n",
    "        # Loop over batches\n",
    "        for j, (x_train_, u_train_) in enumerate(training_set):\n",
    "            \n",
    "            def closure():\n",
    "                # zero the parameter gradients\n",
    "                optimizer.zero_grad()\n",
    "                # forward + backward + optimize\n",
    "                u_pred_ = model(x_train_)\n",
    "                # Item 1. below\n",
    "                loss = torch.mean((u_pred_.reshape(-1, ) - u_train_.reshape(-1, ))**p)\n",
    "                # Item 2. below\n",
    "                loss.backward()\n",
    "                # Compute average training loss over batches for the current epoch\n",
    "                running_loss[0] += loss.item()\n",
    "                return loss\n",
    "            \n",
    "            # Item 3. below\n",
    "            optimizer.step(closure=closure)\n",
    "            \n",
    "        print('Loss: ', (running_loss[0] / len(training_set)))\n",
    "        history.append(running_loss[0])\n",
    "\n",
    "    return history\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "################################  0  ################################\n",
      "Loss:  0.9658915996551514\n",
      "################################  1  ################################\n",
      "Loss:  0.9194313883781433\n",
      "################################  2  ################################\n",
      "Loss:  0.7390236854553223\n",
      "################################  3  ################################\n",
      "Loss:  0.5687392950057983\n",
      "################################  4  ################################\n",
      "Loss:  0.45325732231140137\n",
      "################################  5  ################################\n",
      "Loss:  0.38344189524650574\n",
      "################################  6  ################################\n",
      "Loss:  0.3367900848388672\n",
      "################################  7  ################################\n",
      "Loss:  0.30229100584983826\n",
      "################################  8  ################################\n",
      "Loss:  0.27517959475517273\n",
      "################################  9  ################################\n",
      "Loss:  0.25299203395843506\n",
      "################################  10  ################################\n",
      "Loss:  0.23424991965293884\n",
      "################################  11  ################################\n",
      "Loss:  0.21798019111156464\n",
      "################################  12  ################################\n",
      "Loss:  0.20349924266338348\n",
      "################################  13  ################################\n",
      "Loss:  0.1903005838394165\n",
      "################################  14  ################################\n",
      "Loss:  0.1779906004667282\n",
      "################################  15  ################################\n",
      "Loss:  0.16624949872493744\n",
      "################################  16  ################################\n",
      "Loss:  0.1548061966896057\n",
      "################################  17  ################################\n",
      "Loss:  0.1434236615896225\n",
      "################################  18  ################################\n",
      "Loss:  0.13189709186553955\n",
      "################################  19  ################################\n",
      "Loss:  0.12007533758878708\n",
      "################################  20  ################################\n",
      "Loss:  0.10792125761508942\n",
      "################################  21  ################################\n",
      "Loss:  0.09552711993455887\n",
      "################################  22  ################################\n",
      "Loss:  0.08276201039552689\n",
      "################################  23  ################################\n",
      "Loss:  0.0706227496266365\n",
      "################################  24  ################################\n",
      "Loss:  0.06080298498272896\n",
      "################################  25  ################################\n",
      "Loss:  0.053122323006391525\n",
      "################################  26  ################################\n",
      "Loss:  0.045341573655605316\n",
      "################################  27  ################################\n",
      "Loss:  0.0408787876367569\n",
      "################################  28  ################################\n",
      "Loss:  0.036891479045152664\n",
      "################################  29  ################################\n",
      "Loss:  0.03287205845117569\n",
      "################################  30  ################################\n",
      "Loss:  0.02853737398982048\n",
      "################################  31  ################################\n",
      "Loss:  0.02407439611852169\n",
      "################################  32  ################################\n",
      "Loss:  0.019662348553538322\n",
      "################################  33  ################################\n",
      "Loss:  0.015665384009480476\n",
      "################################  34  ################################\n",
      "Loss:  0.012305444106459618\n",
      "################################  35  ################################\n",
      "Loss:  0.009837914258241653\n",
      "################################  36  ################################\n",
      "Loss:  0.007912525907158852\n",
      "################################  37  ################################\n",
      "Loss:  0.00668422831222415\n",
      "################################  38  ################################\n",
      "Loss:  0.005730506032705307\n",
      "################################  39  ################################\n",
      "Loss:  0.004869685973972082\n",
      "################################  40  ################################\n",
      "Loss:  0.0042584300972521305\n",
      "################################  41  ################################\n",
      "Loss:  0.003796579083427787\n",
      "################################  42  ################################\n",
      "Loss:  0.0034147135447710752\n",
      "################################  43  ################################\n",
      "Loss:  0.003143907291814685\n",
      "################################  44  ################################\n",
      "Loss:  0.0029138599056750536\n",
      "################################  45  ################################\n",
      "Loss:  0.0027062350418418646\n",
      "################################  46  ################################\n",
      "Loss:  0.0025429604575037956\n",
      "################################  47  ################################\n",
      "Loss:  0.0024100826121866703\n",
      "################################  48  ################################\n",
      "Loss:  0.0022995928302407265\n",
      "################################  49  ################################\n",
      "Loss:  0.0022067727986723185\n",
      "################################  50  ################################\n",
      "Loss:  0.002126803155988455\n",
      "################################  51  ################################\n",
      "Loss:  0.0020568398758769035\n",
      "################################  52  ################################\n",
      "Loss:  0.0019943267107009888\n",
      "################################  53  ################################\n",
      "Loss:  0.0019375404808670282\n",
      "################################  54  ################################\n",
      "Loss:  0.0018844259902834892\n",
      "################################  55  ################################\n",
      "Loss:  0.0018335144268348813\n",
      "################################  56  ################################\n",
      "Loss:  0.0017917768564075232\n",
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     "name": "stdout",
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    {
     "name": "stdout",
     "output_type": "stream",
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      "################################  999  ################################\n",
      "Loss:  0.0012409535702317953\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 1000\n",
    "history = fit(my_network, training_set, n_epochs, optimizer_, p=2, verbose=True )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f35980cc210>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid(True, which=\"both\", ls=\":\")\n",
    "plt.plot(np.arange(1,n_epochs+1), np.log10(history), label=\"Train Loss\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test = X_test.astype(np.float32)\n",
    "X_test = torch.from_numpy(X_test)\n",
    "\n",
    "y_test = y_test.astype(np.float32)\n",
    "y_test = torch.from_numpy(y_test)\n",
    "\n",
    "y_test_pred = my_network(X_test).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test = y_test.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test DNN:  1.216082088649273 %\n"
     ]
    }
   ],
   "source": [
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = torch.mean((y_test_pred - y_test)**2)/torch.mean(y_test**2)\n",
    "print(\"Relative Error Test DNN: \", relative_error_test.detach().numpy()*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([250, 1])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([250, 1])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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