Examples/Feyn-tmp.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9333d98c",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import sys; sys.path.append('../')\n",
    "from misc import h5file\n",
    "import numpy as np\n",
    "\n",
    "import scipy.io as sio\n",
    "import sympy\n",
    "from sympy import Symbol, parse_expr, sympify, lambdify, Lambda\n",
    "\n",
    "import pandas as pd\n",
    "import subprocess\n",
    "\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "MAIN_SEED = 1234\n",
    "np.random.seed(MAIN_SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "822a3532",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = sio.loadmat('../Datasets/burgers.mat')\n",
    "u = (data['usol']).real\n",
    "x = (data['x'][0]).real\n",
    "t = (data['t'][:,0]).real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d4e9af4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.load(\"./feyn_files/coeff.npy\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b87827ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This version of feyn and the QLattice is available for academic, personal, and non-commercial use. By using the community version of this software you agree to the terms and conditions which can be found at `https://abzu.ai/eula`.\n"
     ]
    }
   ],
   "source": [
    "import feyn\n",
    "ql = feyn.QLattice()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dc1d5192",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" ?>\n",
       "<svg baseProfile=\"full\" height=\"100.0\" preserveAspectRatio=\"none\" version=\"1.1\" viewBox=\"0 0 409 100.0\" width=\"409\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:ev=\"http://www.w3.org/2001/xml-events\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><defs /><svg class=\"graph\" height=\"95.0\" width=\"409\" x=\"0\" y=\"0\"><defs /><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"12\" text-anchor=\"middle\" x=\"166.0\" y=\"69.0\">Loss: 4.34E+01</text><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"12\" text-anchor=\"start\" x=\"0\" y=\"85.0\">Epoch no. 10/10 - Tried 5416 models - Completed in 3s.</text><rect class=\"node\" fill=\"#00F082\" height=\"35\" stroke=\"#1E1E1E\" stroke-width=\"1\" width=\"90\" x=\"121\" y=\"20.0\"><title>y\n",
       "linear:\n",
       "scale=23.771692\n",
       "scale offset=0.000000\n",
       "w=-0.261467\n",
       "bias=-0.0529</title></rect><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"12\" style=\"pointer-events:none\" text-anchor=\"middle\" x=\"166.0\" y=\"41.5\">y</text><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"10\" style=\"pointer-events:none\" text-anchor=\"end\" x=\"209\" y=\"29.0\">0</text><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"10\" style=\"pointer-events:none\" text-anchor=\"start\" x=\"123\" y=\"29.0\">out</text><line stroke=\"#1E1E1E\" x1=\"91\" x2=\"121\" y1=\"37.5\" y2=\"37.5\" /><rect class=\"node\" fill=\"#00F082\" height=\"35\" stroke=\"#1E1E1E\" stroke-width=\"1\" width=\"90\" x=\"1\" y=\"20.0\"><title>x\n",
       "linear:\n",
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       "scale offset=5.000000\n",
       "w=0.159780\n",
       "bias=-0.0421</title></rect><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"12\" style=\"pointer-events:none\" text-anchor=\"middle\" x=\"46.0\" y=\"41.5\">x</text><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"10\" style=\"pointer-events:none\" text-anchor=\"end\" x=\"89\" y=\"29.0\">1</text><text fill=\"#1E1E1E\" font-family=\"monospace\" font-size=\"10\" style=\"pointer-events:none\" text-anchor=\"start\" x=\"3\" y=\"29.0\">num</text></svg></svg>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train = pd.DataFrame({'x':t.flatten(), 'y':y})\n",
    "# starting from max_complexity = 10\n",
    "models = ql.auto_run(train, output_name = 'y', max_complexity=2) # max_complexity=2, 5, 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bccb4ab4",
   "metadata": {},
   "outputs": [],
   "source": [
    "best = models[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "eff6abd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 0.198624 x - 0.00317926$"
      ],
      "text/plain": [
       "-0.198624*x - 0.00317926"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy_model = best.sympify()\n",
    "sympy_model.as_expr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f3f204aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy.abc import x as symx\n",
    "plt.plot(t, [float(sympy_model.evalf(subs={symx:tt})) for tt in t])\n",
    "plt.plot(t, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7d89237b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.003412749296613171"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = np.array([float(sympy_model.evalf(subs={symx:tt})) for tt in t])\n",
    "1-np.sqrt(((prediction-y)**2).mean())/np.sqrt(((y.mean()-y)**2).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3c01056a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ssr2llf(ssr, nobs):\n",
    "    nobs2 = nobs / 2.0\n",
    "    llf = -nobs2 * np.log(2 * np.pi) - nobs2 * np.log(ssr / nobs) - nobs2\n",
    "    return llf\n",
    "\n",
    "def log_like_value(prediction, ground):                                                                                                               \n",
    "    nobs = float(ground.shape[0])\n",
    "    ssr = np.sum(np.abs(ground - prediction)**2)\n",
    "    return ssr2llf(ssr, nobs)\n",
    "\n",
    "def BIC_AIC(prediction, ground, nparams, reg_func = lambda x: x):\n",
    "    nparams = reg_func(nparams)\n",
    "    llf = log_like_value(prediction, ground)\n",
    "    return -2*llf + np.log(ground.shape[0])*nparams, -2*llf + 2*nparams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "97f8dde9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(668.0572112915833, 668.0572112915833)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BIC_AIC(y.mean()*np.ones_like(y).reshape(-1, 1), y.reshape(-1, 1), 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "81e4be53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(676.5968979514947, 671.3666569178122)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BIC_AIC(prediction.reshape(-1, 1), y.reshape(-1, 1), \n",
    "        len(sympify(sympy_model).atoms(sympy.Number)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c727019c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BIC_AIC(y.mean()*np.ones_like(y).reshape(-1, 1), y.reshape(-1, 1), 0)[0] < \\\n",
    "BIC_AIC(prediction.reshape(-1, 1), y.reshape(-1, 1), \n",
    "        len(sympify(sympy_model).atoms(sympy.Number)))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d6ffe37",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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