Examples/Navier-Stokes with noise nPIML.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PDE-FIND for identifying Navier-Stokes with added noise\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 with artificial noise added to the solution.\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": 18,
   "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, 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": "markdown",
   "metadata": {},
   "source": [
    "First load the data.  Plotted below is a single timepoint with red outlining the area in which points have been samples for use in the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "steps = 151\n",
    "n = 66\n",
    "m = 35\n",
    "data = sio.loadmat('../Datasets/nv.mat')\n",
    "U = data['u']\n",
    "V = data['v']\n",
    "W = data['w']\n",
    "\n",
    "dt = data['t'][0][1]-data['t'][0][0]\n",
    "dx = data['x'][0][1]-data['x'][0][0]\n",
    "dy = data['y'][0][1]-data['y'][0][0]\n",
    "\n",
    "# plot the data\n",
    "xx, yy = meshgrid(np.arange(n)*dx, np.arange(m)*dy)\n",
    "\n",
    "n,m,steps = W.shape\n",
    "\n",
    "# Add in noise with magnitude equal to 1% of std dev of data\n",
    "numpy.random.seed(0)\n",
    "Wn = W + 0.01*np.std(W)*np.random.randn(n,m,steps)\n",
    "Un = U + 0.01*np.std(U)*np.random.randn(n,m,steps)\n",
    "Vn = V + 0.01*np.std(V)*np.random.randn(n,m,steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Denoising using the SVD\n",
    "\n",
    "Now denoise using the SVD.  Each snapshot in time is arranged into a column and the resulting matrix is projected onto a low dimensional subspace given by it's most dominant singular vectors.  The dimension used is determined visually from looking for a Pareto front on the singular values, which is easy to see in their plot.  Notice that compared to the clean data, the noisy data's singular values do not fall below a certain value.  We consider those lying on this flat line to correspond to the artificial noise, and throw them away."
   ]
  },
  {
   "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)\n",
    "\n",
    "Wn = Wn.reshape(n*m,steps)\n",
    "Un = Un.reshape(n*m,steps)\n",
    "Vn = Vn.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\n",
    "\n",
    "uwn,sigmawn,vwn = svd(Wn, full_matrices=False); vwn = vwn.T\n",
    "uun,sigmaun,vun = svd(Un, full_matrices=False); vun = vun.T\n",
    "uvn,sigmavn,vvn = svd(Vn, full_matrices=False); vvn = vvn.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Singular Values from Proper Orthogonal Decomposition\\n (Dashed with noise)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# singular values of clean data\n",
    "semilogy(np.arange(151),sigmaw, 'r', label = r'$\\omega$')\n",
    "semilogy(np.arange(151),sigmau, 'g', label = r'$u$')\n",
    "semilogy(np.arange(151),sigmav, 'b', label = r'$v$')\n",
    "\n",
    "# singular values of noisy data\n",
    "semilogy(np.arange(151),sigmawn, '--',color ='r')\n",
    "semilogy(np.arange(151),sigmaun, '--',color ='g')\n",
    "semilogy(np.arange(151),sigmavn, '--',color ='b')\n",
    "\n",
    "legend(loc = 'upper right', fontsize = 20)\n",
    "xticks(fontsize = 16)\n",
    "yticks(fontsize = 16)\n",
    "\n",
    "title('Singular Values from Proper Orthogonal Decomposition\\n (Dashed with noise)', fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "dim_w = 26\n",
    "dim_u = 20\n",
    "dim_v = 20\n",
    "\n",
    "Wn = uwn[:,0:dim_w].dot(np.diag(sigmawn[0:dim_w]).dot(vwn[:,0:dim_w].T)).reshape(n,m,steps)\n",
    "Un = uun[:,0:dim_u].dot(np.diag(sigmaun[0:dim_u]).dot(vun[:,0:dim_u].T)).reshape(n,m,steps)\n",
    "Vn = uvn[:,0:dim_v].dot(np.diag(sigmavn[0:dim_v]).dot(vvn[:,0:dim_v].T)).reshape(n,m,steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample data points\n",
    "\n",
    "Now collect a sample of points to use for PDE-FIND.  Here we take 5000 spatial points and 60 time points at each."
   ]
  },
  {
   "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",
    "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": "markdown",
   "metadata": {},
   "source": [
    "## Construct $\\Theta (U)$ and compute $U_t$\n",
    "\n",
    "Take derivatives and assemble into $\\Theta(\\omega, u ,v)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Take derivatives of vorticity at each point.  Not the most elegant way of doing this...\n",
    "#PolyDiffPoint(array of fcn vals, domain vals, degree, derivatives to take): -> array of derivatives  \n",
    "\n",
    "# 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": "markdown",
   "metadata": {},
   "source": [
    "These are all the cadidate functions which we are selecting from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['',\n",
       " 'w_{x}',\n",
       " 'w_{y}',\n",
       " 'w_{xx}',\n",
       " 'w_{xy}',\n",
       " 'w_{yy}',\n",
       " 'v',\n",
       " 'u',\n",
       " 'w',\n",
       " 'v^2',\n",
       " 'uv',\n",
       " 'u^2',\n",
       " 'wv',\n",
       " 'wu',\n",
       " 'w^2',\n",
       " 'vw_{x}',\n",
       " 'uw_{x}',\n",
       " 'ww_{x}',\n",
       " 'v^2w_{x}',\n",
       " 'uvw_{x}',\n",
       " 'u^2w_{x}',\n",
       " 'wvw_{x}',\n",
       " 'wuw_{x}',\n",
       " 'w^2w_{x}',\n",
       " 'vw_{y}',\n",
       " 'uw_{y}',\n",
       " 'ww_{y}',\n",
       " 'v^2w_{y}',\n",
       " 'uvw_{y}',\n",
       " 'u^2w_{y}',\n",
       " 'wvw_{y}',\n",
       " 'wuw_{y}',\n",
       " 'w^2w_{y}',\n",
       " 'vw_{xx}',\n",
       " 'uw_{xx}',\n",
       " 'ww_{xx}',\n",
       " 'v^2w_{xx}',\n",
       " 'uvw_{xx}',\n",
       " 'u^2w_{xx}',\n",
       " 'wvw_{xx}',\n",
       " 'wuw_{xx}',\n",
       " 'w^2w_{xx}',\n",
       " 'vw_{xy}',\n",
       " 'uw_{xy}',\n",
       " 'ww_{xy}',\n",
       " 'v^2w_{xy}',\n",
       " 'uvw_{xy}',\n",
       " 'u^2w_{xy}',\n",
       " 'wvw_{xy}',\n",
       " 'wuw_{xy}',\n",
       " 'w^2w_{xy}',\n",
       " 'vw_{yy}',\n",
       " 'uw_{yy}',\n",
       " 'ww_{yy}',\n",
       " 'v^2w_{yy}',\n",
       " 'uvw_{yy}',\n",
       " 'u^2w_{yy}',\n",
       " 'wvw_{yy}',\n",
       " 'wuw_{yy}',\n",
       " 'w^2w_{yy}']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve for $\\xi$\n",
    "\n",
    "TrainSTRidge splits the data up into 80% for training and 20% for validation.  It searches over various tolerances in the STRidge algorithm and finds the one with the best performance on the validation set, including an $\\ell^0$ penalty for $\\xi$ in the loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_t = (0.015199 +0.000000i)w_{yy}\n",
      "    + (-1.019123 +0.000000i)uw_{x}\n",
      "    + (-0.999854 +0.000000i)vw_{y}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "lam = 10**-3\n",
    "d_tol = 5\n",
    "c = TrainSTRidge(X,wt,lam,d_tol,l0_penalty=1)\n",
    "print_pde(c, description, ut = 'w_t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_t = (0.011135 +0.000000i)w_{xx}\n",
      "    + (0.012373 +0.000000i)w_{yy}\n",
      "    + (-1.016748 +0.000000i)uw_{x}\n",
      "    + (-1.006065 +0.000000i)vw_{y}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "lam = 10**-6\n",
    "d_tol = 5\n",
    "c = TrainSTRidge(X,wt,lam,d_tol,l0_penalty=1)\n",
    "print_pde(c, description, ut = 'w_t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_t = (-0.101250 +0.000000i)w_{x}\n",
      "    + (-0.074977 +0.000000i)w\n",
      "    + (-0.794783 +0.000000i)uw_{x}\n",
      "    + (-0.069146 +0.000000i)v^2w_{x}\n",
      "    + (-0.104433 +0.000000i)u^2w_{x}\n",
      "    + (0.025134 +0.000000i)wvw_{x}\n",
      "    + (-0.846570 +0.000000i)vw_{y}\n",
      "    + (-0.023193 +0.000000i)uvw_{y}\n",
      "    + (0.010162 +0.000000i)wuw_{y}\n",
      "    + (0.044960 +0.000000i)vw_{xy}\n",
      "    + (0.008823 +0.000000i)ww_{xy}\n",
      "    + (0.013746 +0.000000i)uw_{yy}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "lam = 10**-1\n",
    "d_tol = 5\n",
    "c = TrainSTRidge(X,wt,lam,d_tol,l0_penalty=1)\n",
    "print_pde(c, description, ut = 'w_t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import h5py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "hf = h5py.File('../Datasets/nv_noiselv1.h5', 'w')\n",
    "hf.create_dataset('X', data=X.real)\n",
    "hf.create_dataset('wt', data=wt.real)\n",
    "hf.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "hf = h5py.File('../Datasets/nv_noiselv1.h5', 'r')\n",
    "Xr = np.array(hf.get('X'))\n",
    "wtr = np.array(hf.get('wt'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.0)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(wtr-wt), np.sum(Xr-X.real)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "description = ['',\n",
    "             'w_{x}',\n",
    "             'w_{y}',\n",
    "             'w_{xx}',\n",
    "             'w_{xy}',\n",
    "             'w_{yy}',\n",
    "             'v',\n",
    "             'u',\n",
    "             'w',\n",
    "             'v^2',\n",
    "             'uv',\n",
    "             'u^2',\n",
    "             'wv',\n",
    "             'wu',\n",
    "             'w^2',\n",
    "             'vw_{x}',\n",
    "             'uw_{x}',\n",
    "             'ww_{x}',\n",
    "             'v^2w_{x}',\n",
    "             'uvw_{x}',\n",
    "             'u^2w_{x}',\n",
    "             'wvw_{x}',\n",
    "             'wuw_{x}',\n",
    "             'w^2w_{x}',\n",
    "             'vw_{y}',\n",
    "             'uw_{y}',\n",
    "             'ww_{y}',\n",
    "             'v^2w_{y}',\n",
    "             'uvw_{y}',\n",
    "             'u^2w_{y}',\n",
    "             'wvw_{y}',\n",
    "             'wuw_{y}',\n",
    "             'w^2w_{y}',\n",
    "             'vw_{xx}',\n",
    "             'uw_{xx}',\n",
    "             'ww_{xx}',\n",
    "             'v^2w_{xx}',\n",
    "             'uvw_{xx}',\n",
    "             'u^2w_{xx}',\n",
    "             'wvw_{xx}',\n",
    "             'wuw_{xx}',\n",
    "             'w^2w_{xx}',\n",
    "             'vw_{xy}',\n",
    "             'uw_{xy}',\n",
    "             'ww_{xy}',\n",
    "             'v^2w_{xy}',\n",
    "             'uvw_{xy}',\n",
    "             'u^2w_{xy}',\n",
    "             'wvw_{xy}',\n",
    "             'wuw_{xy}',\n",
    "             'w^2w_{xy}',\n",
    "             'vw_{yy}',\n",
    "             'uw_{yy}',\n",
    "             'ww_{yy}',\n",
    "             'v^2w_{yy}',\n",
    "             'uvw_{yy}',\n",
    "             'u^2w_{yy}',\n",
    "             'wvw_{yy}',\n",
    "             'wuw_{yy}',\n",
    "             'w^2w_{yy}']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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