Examples/Navier-Stokes with clean original data.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PDE-FIND for identifying Navier-Stokes\n",
    "\n",
    "Samuel Rudy, 2016\n",
    "\n",
    "This notebook demonstrates PDE-FIND for the vorticity equation given a simulation of fluid flowing around a cylinder.\n",
    "\\begin{align*}\n",
    "\\omega_t &= \\frac{1}{Re}\\nabla^2 \\omega - (V \\cdot \\nabla)\\omega\\\\\n",
    "V &= (v,u)\\\\\n",
    "Re &= 100\n",
    "\\end{align*}\n",
    "The x and y components of the velocity field are given as forcing terms to the PDE.  That is, they appear in $\\Theta$, but are not differentiated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (12, 6)\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import sys; sys.path.append('../')\n",
    "from PDE_FIND import *\n",
    "import scipy.io as sio\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "steps = 151\n",
    "n = 449\n",
    "m = 199\n",
    "U = np.load('../Datasets/course_timestep_cylinder/Cylinder_U.npy')\n",
    "V = np.load('../Datasets/course_timestep_cylinder/Cylinder_V.npy')\n",
    "W = np.load('../Datasets/course_timestep_cylinder/Cylinder_W.npy')\n",
    "\n",
    "dt = 0.2\n",
    "dx = 0.02\n",
    "dy = 0.02\n",
    "\n",
    "# Cut out the portion of the data before the cylinder\n",
    "cut = True\n",
    "xmin = 100\n",
    "xmax = 425\n",
    "ymin = 15\n",
    "ymax = 185\n",
    "# V2\n",
    "xmax, ymax = xmax+1, ymax+1\n",
    "\n",
    "# newcut: Cut out the portion of the data before the cylinder\n",
    "# xmin = 80\n",
    "# xmax = 450\n",
    "# ymin = 0\n",
    "# ymax = 200\n",
    "\n",
    "if cut:\n",
    "    W = W[xmin:xmax,ymin:ymax,:]\n",
    "    U = U[xmin:xmax,ymin:ymax,:]\n",
    "    V = V[xmin:xmax,ymin:ymax,:]\n",
    "\n",
    "n,m,steps = W.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = W.reshape(n*m,steps)\n",
    "U = U.reshape(n*m,steps)\n",
    "V = V.reshape(n*m,steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "uw,sigmaw,vw = svd(W, full_matrices=False); vw = vw.T\n",
    "uu,sigmau,vu = svd(U, full_matrices=False); vu = vu.T\n",
    "uv,sigmav,vv = svd(V, full_matrices=False); vv = vv.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f7fa0f9ff50>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "semilogy(sigmaw)\n",
    "semilogy(sigmau)\n",
    "semilogy(sigmav)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "Wn = W.reshape(n,m,steps)\n",
    "Un = U.reshape(n,m,steps)\n",
    "Vn = V.reshape(n,m,steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sample a collection of data points, stay away from edges so I can just use centered finite differences.\n",
    "np.random.seed(0)\n",
    "\n",
    "num_xy = 5000\n",
    "num_t = 60\n",
    "num_points = num_xy * num_t\n",
    "boundary = 5\n",
    "boundary_x = 10\n",
    "points = {}\n",
    "count = 0\n",
    "\n",
    "for p in range(num_xy):\n",
    "    x = np.random.choice(np.arange(boundary_x,n-boundary_x),1)[0]\n",
    "    y = np.random.choice(np.arange(boundary,m-boundary),1)[0]\n",
    "    for t in range(num_t):\n",
    "        points[count] = [x,y,2*t+12]\n",
    "        count = count + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Take up to second order derivatives.\n",
    "w = np.zeros((num_points,1))\n",
    "u = np.zeros((num_points,1))\n",
    "v = np.zeros((num_points,1))\n",
    "wt = np.zeros((num_points,1))\n",
    "wx = np.zeros((num_points,1))\n",
    "wy = np.zeros((num_points,1))\n",
    "wxx = np.zeros((num_points,1))\n",
    "wxy = np.zeros((num_points,1))\n",
    "wyy = np.zeros((num_points,1))\n",
    "\n",
    "N = 2*boundary-1  # odd number of points to use in fitting\n",
    "Nx = 2*boundary_x-1  # odd number of points to use in fitting\n",
    "deg = 5 # degree of polynomial to use\n",
    "\n",
    "for p in points.keys():\n",
    "    \n",
    "    [x,y,t] = points[p]\n",
    "    w[p] = Wn[x,y,t]\n",
    "    u[p] = Un[x,y,t]\n",
    "    v[p] = Vn[x,y,t]\n",
    "    \n",
    "    wt[p] = PolyDiffPoint(Wn[x,y,t-(N-1)//2:t+(N+1)//2], np.arange(N)*dt, deg, 1)[0]\n",
    "    \n",
    "    x_diff = PolyDiffPoint(Wn[x-(Nx-1)//2:x+(Nx+1)//2,y,t], np.arange(Nx)*dx, deg, 2)\n",
    "    y_diff = PolyDiffPoint(Wn[x,y-(N-1)//2:y+(N+1)//2,t], np.arange(N)*dy, deg, 2)\n",
    "    wx[p] = x_diff[0]\n",
    "    wy[p] = y_diff[0]\n",
    "    \n",
    "    x_diff_yp = PolyDiffPoint(Wn[x-(Nx-1)//2:x+(Nx+1)//2,y+1,t], np.arange(Nx)*dx, deg, 2)\n",
    "    x_diff_ym = PolyDiffPoint(Wn[x-(Nx-1)//2:x+(Nx+1)//2,y-1,t], np.arange(Nx)*dx, deg, 2)\n",
    "    \n",
    "    wxx[p] = x_diff[1]\n",
    "    wxy[p] = (x_diff_yp[0]-x_diff_ym[0])/(2*dy)\n",
    "    wyy[p] = y_diff[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Form Theta using up to quadratic polynomials in all variables.\n",
    "X_data = np.hstack([w,u,v])\n",
    "X_ders = np.hstack([np.ones((num_points,1)), wx, wy, wxx, wxy, wyy])\n",
    "X_ders_descr = ['','w_{x}', 'w_{y}','w_{xx}','w_{xy}','w_{yy}']\n",
    "X, description = build_Theta(X_data, X_ders, X_ders_descr, 2, data_description = ['w','u','v'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l0_penalty: 1.7380138324983672\n",
      "w_t = (0.009949 +0.000000i)w_{xx}\n",
      "    + (0.009886 +0.000000i)w_{yy}\n",
      "    + (-0.990411 +0.000000i)uw_{x}\n",
      "    + (-0.986631 +0.000000i)vw_{y}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "lam = 10**-5\n",
    "d_tol = 5\n",
    "c = TrainSTRidge(X,wt,lam,d_tol)\n",
    "print_pde(c, description, ut = 'w_t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 1.00000000e+00+0.j,  8.81757412e-02+0.j,  5.65069341e-02+0.j,\n",
       "         ...,  8.46601790e-04+0.j,  1.79712928e-03+0.j,\n",
       "          2.59191747e-05+0.j],\n",
       "        [ 1.00000000e+00+0.j, -2.45448910e-02+0.j,  2.33524103e-02+0.j,\n",
       "         ...,  1.66713216e-04+0.j,  3.53510462e-04+0.j,\n",
       "          2.09737709e-06+0.j],\n",
       "        [ 1.00000000e+00+0.j, -1.62559789e-01+0.j,  1.15086379e-01+0.j,\n",
       "         ...,  4.02485719e-03+0.j,  8.56657047e-03+0.j,\n",
       "          2.32904611e-04+0.j],\n",
       "        ...,\n",
       "        [ 1.00000000e+00+0.j,  3.75538025e-02+0.j,  3.18186427e-01+0.j,\n",
       "         ..., -1.34457438e-03+0.j,  1.09964423e-01+0.j,\n",
       "         -2.33653188e-03+0.j],\n",
       "        [ 1.00000000e+00+0.j, -1.24006655e-02+0.j,  7.55306680e-01+0.j,\n",
       "         ...,  3.54990736e-02+0.j,  5.80462873e-01+0.j,\n",
       "         -3.23828310e-02+0.j],\n",
       "        [ 1.00000000e+00+0.j, -1.89506738e-01+0.j,  1.06737891e+00+0.j,\n",
       "         ...,  1.27387360e-01+0.j,  1.04095244e+00+0.j,\n",
       "         -9.36734602e-02+0.j]]),\n",
       " array([[-0.11582833],\n",
       "        [ 0.02125791],\n",
       "        [ 0.10790165],\n",
       "        ...,\n",
       "        [-0.0758372 ],\n",
       "        [-0.11161393],\n",
       "        [-0.03039266]]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from misc import h5file\n",
    "h5file('../Datasets/nv_originalV2_clean.h5', {'X':X, 'wt':wt}, mode='w')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (12, 8)\n",
    "import warnings; warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from sympy import symbols\n",
    "\n",
    "import sys; sys.path.append('../')\n",
    "from PDE_FIND import *\n",
    "\n",
    "import sys; sys.path.append('../../parametric-discovery/')\n",
    "from best_subset import *\n",
    "from frols import frols\n",
    "from p_linear_regression import PLinearRegression\n",
    "from r_pca import R_pca\n",
    "from pde_diff_new import RPCA\n",
    "from RobustPCA.rpca import RobustPCA\n",
    "\n",
    "import scipy.io as sio\n",
    "from scipy.signal import savgol_filter\n",
    "import itertools\n",
    "\n",
    "from sklearn.preprocessing import normalize\n",
    "from sklearn.linear_model import Ridge, BayesianRidge, LinearRegression as SkLinearRegression\n",
    "from sklearn.base import BaseEstimator\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from abess.linear import LinearRegression\n",
    "from bess import PdasLm\n",
    "import pysindy as ps\n",
    "\n",
    "from tqdm import trange\n",
    "from os.path import join as join_path\n",
    "FIGURE_EXPORT_PATH = \"./\"\n",
    "\n",
    "from misc import h5file\n",
    "import pickle\n",
    "with open(\"../Datasets/nv_desc.pkl\", \"rb\") as desc_fp:\n",
    "    description = pickle.load(desc_fp)\n",
    "ground_indices = (3, 5, 16, 24)\n",
    "ground_coeffs = np.array([0.01, 0.01, -1, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['X', 'wt']\n"
     ]
    }
   ],
   "source": [
    "Xr, wtr = h5file(\"../Datasets/nv_clean.h5\")\n",
    "# Xr, wtr = h5file(\"../Datasets/nv_newcut_original_clean.h5\")\n",
    "Xr = Xr.real[:, 1:]\n",
    "wtr = wtr.real\n",
    "description = description[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "combine = False\n",
    "if not combine:\n",
    "    newXr = Xr\n",
    "else:\n",
    "    # Combine features\n",
    "    newXr = np.hstack((Xr, Xr[:, 2:3]+Xr[:, 4:5], Xr[:, 15:16]+Xr[:, 23:24]))\n",
    "    description.append(f\"{description[2]}+{description[4]}\")\n",
    "    description.append(f\"{description[15]}+{description[23]}\")\n",
    "    newXr = np.delete(newXr, [2, 4, 15, 23], axis=1)\n",
    "    print(description.pop(2))\n",
    "    print(description.pop(4-1))\n",
    "    print(description.pop(15-2))\n",
    "    print(description.pop(23-3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l0_penalty: 0.8419563843488794\n",
      "w_t = (0.011051 +0.000000i)w_{xy}\n",
      "    + (0.012470 +0.000000i)v\n",
      "    + (-1.017017 +0.000000i)ww_{x}\n",
      "    + (-1.006237 +0.000000i)uw_{y}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "lam = 10**-5\n",
    "d_tol = 5\n",
    "c = TrainSTRidge(newXr,wtr,lam,d_tol)\n",
    "print_pde(c, description, ut = 'w_t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "if not combine:\n",
    "    errs = np.abs(c[nonz(c), :].real.ravel()-ground_coeffs)/np.abs(ground_coeffs)\n",
    "    errs.mean(), errs.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0,)\n",
      "-796427.2205235633\n",
      "(0, 23)\n",
      "-836586.6055949634\n",
      "(4, 15, 23)\n",
      "-1841687.5792230521\n",
      "(2, 4, 15, 23)\n",
      "-2029540.5710186984\n",
      "(2, 4, 15, 23, 38)\n",
      "-2054764.859675489\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "-2074301.666054327\n",
      "(2, 4, 15, 23, 38, 40, 45)\n",
      "-2081515.1463659473\n",
      "(2, 4, 5, 15, 23, 38, 40, 45)\n",
      "-2088373.1216945727\n",
      "(2, 4, 5, 15, 23, 37, 38, 40, 45)\n",
      "-2092559.2794152587\n"
     ]
    }
   ],
   "source": [
    "lrs = []\n",
    "ebics = []\n",
    "eff_indices = []\n",
    "max_complexity = 10\n",
    "for s in range(1, max_complexity):\n",
    "    lr = LinearRegression(support_size=s, ic_type='bic', always_select=None)\n",
    "    lr.fit(newXr, wtr)\n",
    "    lrs.append(lr)\n",
    "    eff_indices.append(nonz(lr.coef_))\n",
    "    ebics.append(lr.ic_)\n",
    "    print(nonz(lr.coef_))\n",
    "    print(lr.ic_)\n",
    "abess_feature_hierarchy = set(eff_indices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([i for i in range(1, max_complexity)], ebics)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0,),\n",
       " (0, 2, 4, 5, 15, 20, 23, 33, 38, 45),\n",
       " (0, 2, 4, 15, 20, 23),\n",
       " (0, 2, 4, 15, 20, 23, 33, 38, 45),\n",
       " (0, 2, 4, 15, 20, 23, 38),\n",
       " (0, 2, 4, 15, 20, 23, 38, 45),\n",
       " (0, 4, 15, 20, 23),\n",
       " (0, 15, 20),\n",
       " (0, 15, 20, 23),\n",
       " (0, 20)}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nor_axis = 0\n",
    "if nor_axis is not None: Xfrols = normalize(newXr, axis=nor_axis)\n",
    "else: Xfrols = newXr.copy()\n",
    "frols_coeffs,selected_inds_list,_,_,_ = frols(wtr, Xfrols, max_nonzeros=max_complexity)\n",
    "selected_inds_list = set(selected_inds_list)\n",
    "selected_inds_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_hierarchy = abess_feature_hierarchy.union(selected_inds_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RFE_PLinearRegression\n",
      "(0, 15, 20)\n",
      "(0, 20)\n",
      "(0,)\n",
      "--------------------------------------------------\n",
      "(2, 4, 5, 15, 23, 38, 40, 45)\n",
      "(2, 4, 15, 23, 38, 40, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "(2, 4, 15, 23, 38)\n",
      "(2, 4, 15, 23)\n",
      "(4, 15, 23)\n",
      "(15, 23)\n",
      "(15,)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 4, 15, 20, 23)\n",
      "(0, 4, 15, 23)\n",
      "(4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 20)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23)\n",
      "(0, 2, 4, 15, 23)\n",
      "(2, 4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23, 33, 38, 45)\n",
      "(0, 2, 4, 15, 23, 33, 38, 45)\n",
      "(2, 4, 15, 23, 33, 38, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23, 38)\n",
      "--------------------------------------------------\n",
      "(2, 4, 5, 15, 23, 37, 38, 40, 45)\n",
      "(2, 4, 5, 15, 23, 38, 40, 45)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23, 38, 45)\n",
      "(0, 2, 4, 15, 23, 38, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n",
      "(4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 23)\n",
      "(0,)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23, 38)\n",
      "(2, 4, 15, 20, 23, 38)\n",
      "(2, 4, 15, 23, 38)\n",
      "--------------------------------------------------\n",
      "(0, 15, 20, 23)\n",
      "(15, 20, 23)\n",
      "(15, 23)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23, 38, 40, 45)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 5, 15, 20, 23, 33, 38, 45)\n",
      "(0, 2, 4, 5, 15, 23, 33, 38, 45)\n",
      "(2, 4, 5, 15, 23, 33, 38, 45)\n",
      "(2, 4, 5, 15, 23, 38, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n",
      "SelectKBest\n",
      "(0, 15, 20)\n",
      "(0, 20)\n",
      "(0,)\n",
      "--------------------------------------------------\n",
      "(2, 4, 5, 15, 23, 38, 40, 45)\n",
      "(2, 4, 15, 23, 38, 40, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "(2, 4, 15, 23, 38)\n",
      "(2, 4, 15, 23)\n",
      "(4, 15, 23)\n",
      "(15, 23)\n",
      "(15,)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 4, 15, 20, 23)\n",
      "(0, 4, 15, 23)\n",
      "(4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 20)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23)\n",
      "(0, 2, 4, 15, 23)\n",
      "(2, 4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23, 33, 38, 45)\n",
      "(0, 2, 4, 15, 23, 33, 38, 45)\n",
      "(2, 4, 15, 23, 33, 38, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23, 38)\n",
      "--------------------------------------------------\n",
      "(2, 4, 5, 15, 23, 37, 38, 40, 45)\n",
      "(2, 4, 5, 15, 23, 38, 40, 45)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23, 38, 45)\n",
      "(0, 2, 4, 15, 23, 38, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n",
      "(4, 15, 23)\n",
      "--------------------------------------------------\n",
      "(0, 23)\n",
      "(0,)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 15, 20, 23, 38)\n",
      "(2, 4, 15, 20, 23, 38)\n",
      "(2, 4, 15, 23, 38)\n",
      "--------------------------------------------------\n",
      "(0, 15, 20, 23)\n",
      "(15, 20, 23)\n",
      "(15, 23)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23, 38, 40, 45)\n",
      "--------------------------------------------------\n",
      "(0, 2, 4, 5, 15, 20, 23, 33, 38, 45)\n",
      "(0, 2, 4, 5, 15, 23, 33, 38, 45)\n",
      "(2, 4, 5, 15, 23, 33, 38, 45)\n",
      "(2, 4, 5, 15, 23, 38, 45)\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n",
      "(2, 4, 15, 23, 38, 45)\n",
      "--------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{1: ((0,), 262887.0079276183), 2: ((15, 23), -352605.01745888294), 3: ((4, 15, 23), -782379.578216547), 4: ((2, 4, 15, 23), -970233.2767355026), 5: ((2, 4, 15, 23, 38), -995457.4147197137), 6: ((2, 4, 15, 23, 38, 45), -1014994.0684590864), 7: ((2, 4, 15, 23, 38, 40, 45), -1022207.7118246884), 8: ((2, 4, 5, 15, 23, 38, 40, 45), -1029065.7028349556), 9: ((2, 4, 5, 15, 23, 37, 38, 40, 45), -1033251.9540299956), 10: ((0, 2, 4, 5, 15, 20, 23, 33, 38, 45), -1034490.1484523542)}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "br1 = backward_refinement(feature_hierarchy, (newXr, wtr), mode='rfe', ic_type='bic', verbose=True)\n",
    "br2 = backward_refinement(feature_hierarchy, (newXr, wtr), mode='k best', ic_type='bic', verbose=True)\n",
    "br_u=br1+br2; br_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ploting less than max_complexity\n"
     ]
    }
   ],
   "source": [
    "print(\"Ploting less than max_complexity\")\n",
    "for c in range(max_complexity+1, max(list(br_u.track.keys()))+1):\n",
    "    del_c = br_u.delete(c)\n",
    "    if del_c is not None: print(f\"Delete {c} complexity\")\n",
    "    else: print(f\"{c} not exist\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0,) 262887.0079276183\n",
      "(15, 23) -352605.01745888294\n",
      "(4, 15, 23) -782379.578216547\n",
      "(2, 4, 15, 23) -970233.2767355026\n",
      "(2, 4, 15, 23, 38) -995457.4147197137\n",
      "(2, 4, 15, 23, 38, 45) -1014994.0684590864\n",
      "(2, 4, 15, 23, 38, 40, 45) -1022207.7118246884\n",
      "(2, 4, 5, 15, 23, 38, 40, 45) -1029065.7028349556\n",
      "(2, 4, 5, 15, 23, 37, 38, 40, 45) -1033251.9540299956\n",
      "(0, 2, 4, 5, 15, 20, 23, 33, 38, 45) -1034490.1484523542\n"
     ]
    }
   ],
   "source": [
    "complexities = np.array(sorted(list(br_u.track.keys())))\n",
    "bic_scores = []\n",
    "eff_feature_names = []\n",
    "for com in complexities:\n",
    "    indices, bic = br_u.track[com]\n",
    "    bic_scores.append(bic)\n",
    "    print(indices, bic)\n",
    "bic_scores = np.array(bic_scores)\n",
    "min_bic_score = np.min(bic_scores)\n",
    "div_scale = 1e3\n",
    "rel_bic_scores = (bic_scores-min_bic_score)/div_scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with plt.style.context('science'):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(complexities, rel_bic_scores, color='black', linewidth=2.5//2)\n",
    "    ax.scatter(complexities, rel_bic_scores, marker='o', c='black', s=25)\n",
    "    plt.xlim(min(complexities)-0.3,max(complexities)+0.3)\n",
    "    plt.ylabel(r\"Relative BIC ($\\times 10^{3}$)\")\n",
    "    plt.xlabel(\"Complexity\")\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 improves 1\n",
      "Percent improve: 2.3412797393014078\n",
      "3 improves 2\n",
      "Percent improve: 1.2188554883731337 0.6982617857441533\n",
      "4 improves 3\n",
      "Percent improve: 0.24010557502941554 0.4370982270048325\n",
      "5 does not improve 4\n",
      "Percent improve: 0.025998013662324113\n",
      "2 improves 1\n",
      "Percent improve: 2.3412797393014078\n",
      "3 improves 2\n",
      "Percent improve: 1.2188554883731337 0.6982617857441533\n",
      "4 improves 3\n",
      "Percent improve: 0.24010557502941554 0.4370982270048325\n",
      "5 does not improve 4\n",
      "Percent improve: 0.025998013662324113\n",
      "2 improves 1\n",
      "Percent improve: 2.3412797393014078\n",
      "3 improves 2\n",
      "Percent improve: 1.2188554883731337 0.6982617857441533\n",
      "4 improves 3\n",
      "Percent improve: 0.24010557502941554 0.4370982270048325\n",
      "5 does not improve 4\n",
      "Percent improve: 0.025998013662324113\n",
      "2 improves 1\n",
      "Percent improve: 2.3412797393014078\n",
      "3 improves 2\n",
      "Percent improve: 1.2188554883731337\n",
      "4 improves 3\n",
      "Percent improve: 0.24010557502941554\n",
      "5 does not improve 4\n",
      "Percent improve: 0.025998013662324113\n"
     ]
    }
   ],
   "source": [
    "d_bic_scores, d_coms, _ = get_decreasing_vals(bic_scores, complexities)\n",
    "find_transition_V2(d_bic_scores, d_coms, 0.099)\n",
    "find_transition_V3(d_bic_scores, d_coms, 0.099)\n",
    "find_transition_V4(d_bic_scores, d_coms, 0.099)\n",
    "# bc = find_transition_V5(d_bic_scores, d_coms, 0.095)\n",
    "bc = find_transition_V5(d_bic_scores, d_coms, 0.09, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0023061953597677334"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((wtr-newXr[:, br_u.track[bc][0]]@np.linalg.lstsq(newXr[:, br_u.track[bc][0]], wtr, rcond=None)[0])**2).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.042223785677891, 0.22734982406002108)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errs = 100*np.abs(np.linalg.lstsq(newXr[:, br_u.track[bc][0]], wtr, rcond=None)[0].flatten()-ground_coeffs)/np.abs(ground_coeffs)\n",
    "errs.mean(), errs.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  262887.00792762,  -352605.01745888,  -782379.57821655,\n",
       "         -970233.2767355 ,  -995457.41471971, -1014994.06845909,\n",
       "        -1022207.71182469, -1029065.70283496, -1033251.95403   ,\n",
       "        -1034490.14845235]),\n",
       " array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10]))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bic_scores, complexities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_t = (0.009927 +0.000000i)w_{xx}\n",
      "    + (0.009886 +0.000000i)w_{yy}\n",
      "    + (-0.990430 +0.000000i)uw_{x}\n",
      "    + (-0.986591 +0.000000i)vw_{y}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "pred = np.linalg.lstsq(newXr[:, br_u.track[bc][0]], wtr, rcond=None)[0]\n",
    "print_pde(pred, \n",
    "          np.array(description)[list(br_u.track[bc][0])], ut = 'w_t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00992737],\n",
       "       [ 0.00988553],\n",
       "       [-0.99043016],\n",
       "       [-0.98659113]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'raw_bic_scores': array([  262887.00792762,  -352605.01745888,  -782379.57821655,\n",
       "         -970233.2767355 ,  -995457.41471971, -1014994.06845909,\n",
       "        -1022207.71182469, -1029065.70283496, -1033251.95403   ,\n",
       "        -1034490.14845235]),\n",
       " 'rel_bic_scores': array([1.29737716e+03, 6.81885131e+02, 2.52110570e+02, 6.42568717e+01,\n",
       "        3.90327337e+01, 1.94960800e+01, 1.22824366e+01, 5.42444562e+00,\n",
       "        1.23819442e+00, 0.00000000e+00]),\n",
       " 'complexities': array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10]),\n",
       " 'min_bic_score': -1034490.1484523542,\n",
       " 'found_coeff': array([[ 0.00992737],\n",
       "        [ 0.00988553],\n",
       "        [-0.99043016],\n",
       "        [-0.98659113]]),\n",
       " 'percent_coefficient_error_mean': 1.042223785677891,\n",
       " 'percent_coefficient_error_std': 0.22734982406002108}"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metric_dict = {'raw_bic_scores': bic_scores, \n",
    "               'rel_bic_scores': rel_bic_scores, \n",
    "               'complexities': complexities, \n",
    "               'min_bic_score': min_bic_score, \n",
    "               'found_coeff': pred, \n",
    "               'percent_coefficient_error_mean': errs.mean(), \n",
    "               'percent_coefficient_error_std': errs.std()}\n",
    "metric_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "./Visualization/nv_originalV2_clean.mat\n"
     ]
    }
   ],
   "source": [
    "file_name = f\"./Visualization/nv_originalV2_clean.mat\"\n",
    "print(file_name)\n",
    "sio.savemat(file_name, metric_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# com: [1, 2, ..., 10]\n",
    "\n",
    "# newcut, combine\n",
    "# array([ -332355.44607765, -1035795.14538756, -1057091.36427579,\n",
    "#        -1076639.62239269, -1082597.22430468, -1089590.5449716 ,\n",
    "#        -1094282.40806104, -1096878.65510116, -1102794.45455926,\n",
    "#        -1106311.92289121])\n",
    "# newcut, uncombine\n",
    "# array([  251110.64932581,  -333165.27467149,  -840972.20873175,\n",
    "#        -1036207.88784906, -1059438.7461814 , -1077859.72577538,\n",
    "#        -1083532.20071458, -1090186.68146309, -1094490.81171453,\n",
    "#        -1088245.56928538])\n",
    "\n",
    "# oldcut, combine\n",
    "# array([ -349374.66981932,  -968971.59168413,  -992041.15314337,\n",
    "#        -1013371.88401361, -1020348.44091455, -1027434.38564214,\n",
    "#        -1032635.90280207, -1036111.54192447, -1038606.42694382,\n",
    "#        -1043402.45129067])\n",
    "# oldcut, uncombine\n",
    "# array([  265432.17776937,  -350773.84091166,  -781272.27172945,\n",
    "#         -969542.42013941,  -994869.46058713, -1014440.47018371,\n",
    "#        -1021723.14013316, -1028539.3848122 , -1032692.26442869,\n",
    "#        -1033833.82629057])"
   ]
  }
 ],
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