{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cahn-Hilliard Example\n", "\n", "This example demonstrates how to use PyMKS to solve the Cahn-Hilliard equation. The first section provides some background information about the Cahn-Hilliard equation as well as details about calibrating and validating the MKS model. The example demonstrates how to generate sample data, calibrate the influence coefficients and then pick an appropriate number of local states when state space is continuous. The MKS model and a spectral solution of the Cahn-Hilliard equation are compared on a larger test microstructure over multiple time steps." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cahn-Hilliard Equation\n", "\n", "The Cahn-Hilliard equation is used to simulate microstructure evolution during spinodial decomposition and has the following form,\n", "\n", "$$ \\dot{\\phi} = \\nabla^2 \\left( \\phi^3 - \\phi \\right) - \\gamma \\nabla^4 \\phi $$\n", "\n", "where $\\phi$ is a conserved ordered parameter and $\\sqrt{\\gamma}$ represents the width of the interface. In this example, the Cahn-Hilliard equation is solved using a semi-implicit spectral scheme with periodic boundary conditions, see [Chang and Rutenberg](http://dx.doi.org/10.1103/PhysRevE.72.055701) for more details." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pymks\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modeling with MKS\n", "\n", "In this example the MKS equation will be used to predict microstructure at the next time step using \n", "\n", "$$p[s, 1] = \\sum_{r=0}^{S-1} \\alpha[l, r, 1] \\sum_{l=0}^{L-1} m[l, s - r, 0] + ...$$\n", "\n", "where $p[s, n + 1]$ is the concentration field at location $s$ and at time $n + 1$, $r$ is the convolution dummy variable and $l$ indicates the local states varable. $\\alpha[l, r, n]$ are the influence coefficients and $m[l, r, 0]$ the microstructure function given to the model. $S$ is the total discretized volume and $L$ is the total number of local states `n_states` choosen to use.\n", "\n", "The model will march forward in time by recursively replacing discretizing $p[s, n]$ and substituing it back for $m[l, s - r, n]$.\n", "\n", "### Calibration Datasets\n", "\n", "Unlike the elastostatic examples, the microstructure (concentration field) for this simulation doesn't have discrete phases. The microstructure is a continuous field that can have a range of values which can change over time, therefore the first order influence coefficients cannot be calibrated with delta microstructures. Instead, a large number of simulations with random initial conditions are used to calibrate the first order influence coefficients using linear regression.\n", "\n", "The function `make_cahn_hilliard` from `pymks.datasets` provides an interface to generate calibration datasets for the influence coefficients. To use `make_cahn_hilliard`, we need to set the number of samples we want to use to calibrate the influence coefficients using `n_samples`, the size of the simulation domain using `size` and the time step using `dt`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pymks\n", "from pymks.datasets import make_cahn_hilliard\n", "\n", "n = 41\n", "n_samples = 400\n", "dt = 1e-2\n", "np.random.seed(99)\n", "X, y = make_cahn_hilliard(n_samples=n_samples, size=(n, n), dt=dt)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `make_cahnHilliard` generates `n_samples` number of random microstructures, `X`, and the associated updated microstructures, `y`, after one time step `y`. The following cell plots one of these microstructures along with its update." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HR6Nfv36IiooqkeUotBGcPeVDUc/9Q37ge3iHWuq0OrfsIOphBg/GXjjlE1H3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\nrsQsnSYk5xrgqWHXt2iKJL49/BDQlHgoyK+zgN++FhIJ3kZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_concentrations\n", "\n", "draw_concentrations((X[0], y[0]), labels=('Input Concentration', 'Output Concentration'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calibrate Influence Coefficients\n", "\n", "As mentioned above, the microstructures (concentration fields) does not have discrete phases. This leaves the number of local states in local state space as a free hyperparameter. In previous work it has been shown that, as you increase the number of local states, the accuracy of MKS model increases (see [Fast et al.](http://dx.doi.org/10.1016/j.actamat.2010.10.008)), but, as the number of local states increases, the difference in accuracy decreases. Some work needs to be done in order to find the practical number of local states that we will use. \n", "\n", "### Optimizing the Number of Local States\n", "\n", "Let's split the calibrate dataset into test and training datasets. The function `train_test_split` for the machine learning Python module [sklearn](http://scikit-learn.org/stable/) provides a convenient interface to do this. 80% of the dataset will be used for training and the remaining 20% will be used for testing by setting `test_size` equal to 0.2. The state of the random number generator used to make the split can be set using `random_state`. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import sklearn\n", "from sklearn.cross_validation import train_test_split\n", "\n", "split_shape = (X.shape[0],) + (X[0].size,)\n", "X_train, X_test, y_train, y_test = train_test_split(X.reshape(split_shape), y.reshape(split_shape),\n", " test_size=0.5, random_state=3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now going to calibrate the influence coefficients while varying the number of local states from 2 up to 20. Each of these models will then predict the evolution of the concentration fields. Mean square error will be used to compare the results with the testing dataset to evaluate how the MKS model's performance changes as we change the number of local states. \n", "\n", "First we need to import the class `MKSLocalizationModel` from `pymks`." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pymks import MKSLocalizationModel\n", "from pymks.bases import PrimitiveBasis\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we will calibrate the influence coefficients while varying the number of local states and compute the mean squared error. The following demonstrates how to use scikit-learn's `GridSearchCV` to optimize `n_states` as a hyperparameter. Of course, the best fit is always with a larger value of `n_states`. Increasing this parameter does not overfit the data." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "GridSearchCV(cv=5, error_score='raise',\n", " estimator=MKSLocalizationModel(basis=,\n", " lstsq_rcond=2.2204460492503131e-12, n_jobs=None,\n", " n_states=array([0, 1])),\n", " fit_params={'size': (41, 41)}, iid=True, n_jobs=1,\n", " param_grid={'n_states': array([ 2, 3, 4, 5, 6, 7, 8, 9, 10])},\n", " pre_dispatch='2*n_jobs', refit=True, scoring=None, verbose=0)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.grid_search import GridSearchCV\n", "\n", "parameters_to_tune = {'n_states': np.arange(2, 11)}\n", "p_basis = PrimitiveBasis(2, [-1, 1])\n", "model = MKSLocalizationModel(p_basis, n_jobs=4)\n", "gs = GridSearchCV(model, parameters_to_tune, cv=5, fit_params={'size': (n, n)})\n", "gs.fit(X_train, y_train)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MKSLocalizationModel(basis=,\n", " lstsq_rcond=2.2204460492503131e-12, n_jobs=None, n_states=10)\n", "0.99999908222\n" ] } ], "source": [ "print(gs.best_estimator_)\n", "print(gs.score(X_test, y_test))\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ry2g0UlZWRmxsLCUlJZSXl7N06VIURcFsNmMwGHjggQd47rnnWow8bO3Dra2t\n7fBncKUEBwdf0Zy7T+UCMFjbx6H3vdI5O8oTcnpCRpCczuZJOTtyFxGHC9fcuXNtj1988cWLrqdS\nqWz36LoUX19fkpOTycjI4IEHHuDkyZPk5OTwzDPPtFh3woQJrFu3jvHjxxMaGsrWrVuZNGlSu9pJ\nTk7mzTffJDs7m+HDh7N582bi4+Pp1asXFovFbuj7sWPH2LBhAy+++KLH/NbibsyWJg5WWO+/Jddv\nCSGcx+HCNXDgwFZnhL8c9913H+vWrWPBggVotVruv/9+YmNj0el0LF68mJUrV9KjRw+GDRvG9OnT\nWbZsGSaTiZSUFFJTU9tsB0Cr1bJ48WLS09NZvXo1CQkJPPzwwwB4eXkREvLzqaygoCBUKhVardap\n+9mdfF9dSH1TI738exATGOnqOEKILkSltNWhI9rl/GH17upKnj7YePxj1h7N5H9iRvPMiLsd2taT\nTnO4e05PyAiS09k8JWevXr06tJ1cESo6Rc65G0cOl+u3hBBOJoVLOJ3JYuZQ5QlArt8SQjhfh6d8\nqqysJDc3l4qKiove4mTGjBkdDiY815GqAoxNjcQGRNArIKLtDYQQwgEdKlwZGRm8++67NDU1XXI9\nKVzd075zpwmvDe+Ht8xPKIRwMocL15dffsmWLVsYPHgwN910EytWrGDixIkMHTqUvLw8duzYQUpK\nityPqxvbd25i3eHh0r8lhHA+hwvXJ598Qnh4OH/605/w9m6+m21UVBTjxo1j3LhxJCcns3z5csaN\nG+f0sML9NTaZyK04CcBouX5LCNEJHD6PU1hYyPDhw21FC8BisdgeDxs2jKFDh/L+++87J6HwKN9V\n5dNgMdE7MIrogHBXxxFCdEEOF66mpia72SQ0Gk2LOQKtUzOJ7idH+reEEJ3M4W+WsLAwKisrbc8j\nIiJsd0G2qqystDsiE91Hztnm+28NC7vaxUmEEF2Vw4UrPj6eoqIi2/OkpCSOHj1KVlYWRqOR/fv3\n880339C3b1+nBhXur6HJRG7lSVTA6Ejp3xJCdA6HC9fIkSMpKirizJkzQPNs8QEBAaxZs4a77rqL\nv/71rwDMmjXLuUmF28utPEmjxUyfoKu4yj/M1XGEEF2Uw6MKJ02aZJuRHZpPFb7wwgu8//77lJWV\nERkZyU033UTv3r2dmVN4ANv1W2HSvyWE6DwdnjnjfFFRUdx3333OaEp4sP3W67fC5PotIUTnkV+L\nhVMYzY3X6KdFAAAgAElEQVTkVuajAkZFyfyEQojO4/ARl06na/e6F945WHRdhypPYFaa6Bfck0i/\njt8RWwgh2uJw4Vq0aFG71mvvHZBF17D/3DD4a8P6Sv+WEKJTOVy4JkyY0OodkOvq6sjPz0en0zFo\n0CAiI+Wut92JdWCG9G8JITqbU4+4LBYLW7Zs4dNPP233kZnwfAazkbyqfLxQMTJS+reEEJ3Lqed0\nvLy8SE1NJTIykv/85z/ObFq4sUMVJ2hSLPQN7kkPX62r4wghurhO6Yy45pprOHToUGc0LdxQjq1/\nqx9qL5nqSwjRuTqlcOn1ehoaGjqjaeGGrBPrjpD7bwkhrgCnF67Dhw+zZ88e4uLinN20cEN1ZiPf\nVxfipVIxIkIKlxCi8zk8OGPZsmWtLrdYLOh0Ott1XjNmzLi8ZMIjHDz7E02KhQHaGMKlf0sIcQU4\nXLiOHDly0deCgoIYNmwYt956K4MHD76sYMIz5Jyb5mmI9G8JIa4QhwvX22+/3Rk5hIfaJ/1bQogr\nTKY4EB2mN9VzrLoIb5UXw8LlxpFCiCtDCpfosAMVP2JBob82hnA/6d8SQlwZDp8q3LVrV4ffbOLE\niR3eVrif8++/Jf1bQogrxeHCtXbt2g6/mRSursV6/ZacJhRCXEkOF66FCxeSnZ1NTk4OgwYNYtCg\nQYSGhlJVVUVeXh7ff/89I0eOJDk5uTPyCjdR02jgh5pTqKV/SwhxhTlcuLRaLQcPHuSRRx5h1KhR\ndq+lpqby7bffsmrVKm688UaGDRvmtKDCvRyoOI6CwgBtHGG+wa6OI4ToRhwuXO+88w7JycktipbV\n6NGjGT16NFu2bGl34dLr9axbt47Dhw+j1WqZM2cO48ePb3Xdbdu2kZmZSWNjIykpKSxYsAC1Wt2u\ndnJzc9mwYQM6nY7+/fuTlpZmu9nl9u3b+eijj6ipqcHf35+xY8cyb948vLxk/Epr9unOzU8YLv1b\nQogry+Fv5fz8fKKjoy+5TnR0NAUFBe1uc/369fj4+JCens5DDz3E+vXrKS4ubrHewYMHyczMZOnS\npaxdu5aysjIyMjLa1U5tbS0rVqxg9uzZbNy4kX79+rFq1SrbtqNHj+aFF17gn//8JytWrCA/P58P\nP/yw3fvQ3VgvPB4upwmFEFeYw4VLrVaTn59/yXUKCgrw9m7fb+ENDQ1kZ2cze/ZsNBoNiYmJjBo1\niqysrBbrZmVlMXnyZGJiYggICOCOO+5g586d7Wpn7969xMXFMWbMGNRqNampqRQUFHD69GkAoqKi\nCAoKApqnr1KpVJSWlrbzU+leqhr1HK85hY+XmqFhUriEEFeWw4VryJAhHDhwgI8++ghFUexeUxSF\nDz/8kAMHDjBkyJB2tVdSUoK3t7fdUVx8fHyrR1xFRUX06dPHbr3q6mr0en2b7RQXF9tt6+vrS3R0\ntN37fPXVV9x1110sWLCAwsJCpk6d2q596G72n/0RgGu0sYT4Brk4jRCiu3G4j+vOO+8kLy+PjRs3\nsn37dhITEwkJCaG6upqjR49y5swZgoKCmDt3brvaMxqNBAQE2C3z9/envr6+zXX9/f1ty9tqx2g0\notVqL/o6wPjx4xk/fjylpaVkZWUREhLSrn3obnJs12/1lf4tIcQV53Dhio6O5rnnnmP9+vXk5uZy\n5swZu9evvfZa7rvvPq666qp2tefn54fBYLBbZjAYbEXpwnXPLzTW7fz8/Nps58JtL/U+0dHRxMbG\n8tprr/HHP/6xxet5eXnk5eXZns+cOZPgYPcfWafRaJyS80DlTwCkxA7plP12Vs7O5gk5PSEjSE5n\n85ScgN04haSkJJKSktrcxuHCBc1f7E8++SQVFRWcPHkSg8FAQEAAffv2JTw83KG2evbsicViobS0\n1Haar6CggNjY2BbrxsXFkZ+fT0pKCtA8UCQ0NJSgoCB8fHwu2U5sbKzdrB9Go5GysrJW3wfAbDa3\nKMpWrX24tbW1Du23KwQHB192zsqGWo5XF6PxUjPAr2en7Lczcl4JnpDTEzKC5HQ2T8o5c+ZMh7e7\nrLHe4eHhjBw5kuuvv56RI0c6XLSgua8pOTmZjIwMGhoaOHr0KDk5OUyYMKHFuhMmTGDHjh0UFxej\n1+vZunUrkyZNalc7ycnJFBcXk52djclkYvPmzcTHx9OrVy8AvvjiC2pqaoDm/rD33nuv3f103UnO\n2eZh8IkhvQnRBLo4jRCiO+rQEVdrTp06xYEDB/D19WXcuHEt+psu5b777mPdunUsWLAArVbL/fff\nT2xsLDqdjsWLF7Ny5Up69OjBsGHDmD59OsuWLcNkMpGSkkJqamqb7UDzhdOLFy8mPT2d1atXk5CQ\nwMMPP2zb9ujRo/z3v/+loaEBrVbLddddx6xZs5z18XQZ1sI1JCxe+reEEC6hUi4cGtiGzZs388kn\nn7By5Urb8PHDhw/z17/+FbPZDDQPLX/++ec95hyrM1iH1bszZ5w+SN3xDPn6Uv5v1ANM7Hmtk5LZ\n86TTHO6e0xMyguR0Nk/JaT3j5SiHTxUeOHCAmJgYW9EC+O9//4tKpWLmzJnceOONnDlzhg8++KBD\ngYT70hmrydeX4uvlw5CweFfHEUJ0Uw4XrvLycmJiYmzPKyoqOHHiBDfeeCN33HEH9913H4MHD+bb\nb791alDhevvP69/SSv+WEMJFHC5cdXV1dkdbR48eBWDkyJG2ZX379kWn0zkhnnAn1v6ta8Pl+i0h\nhOs4XLi0Wi0VFRW253l5eajVavr3729bZjabW8yqITyf9caRI8ITXJxECNGdOTyqsE+fPuzbt4/C\nwkI0Gg179uwhMTERjUZjW6e8vJzQ0FCnBhWuVW6sorDuDH7eGgaFxrs6jhCiG3P4iOuXv/wlBoOB\nRx55hN/97ncYDAZuueUW2+sWi4Vjx45x9dUy+WpXknPuNiaDQnqj1bT/UgchhHA2h4+4Bg4cyOOP\nP85nn32GSqXi+uuvZ/jw4bbXjx07Rnh4uNwBuYvZd+42JkOkf0sI4WIdugB52LBhF71J5MCBA3nx\nxRcvK5RwP9aJdYdL/5YQwsUu+/a+BoNBRhB2caX1lRQbdPh7+zIopE/bGwghRCe67MK1fft2Fi1a\n5Iwswk3tP3e0lRTah2Dp3xJCuNhlFy7R9dn6t+T+W0IINyCFS7Rpn61/S0aKCiFcTwqXuKTThrOU\n1FcQqPYjMVT6t4QQrnfZhUtmyOjacs7+3L8V5OPn4jRCCOGE+3Hdcsst3HDDDc7IItyQ9cLjIWF9\nUaukf0sI4XqXfcQVEBBAZGRki+XWuwkLz6Uoiu2Ia1j41ahUKhcnEkKITujjMhgM/Oc//+Ghhx5y\ndtPiCjtlOEtpfSXBan+uCYlzdRwhhAAcPFVYXl7OiRMn8Pb2JiEhwW4i3cbGRrZv3877779PXV2d\n3aS7wjPZ+rfC4gny8XdxGiGEaNbuwrVhwwY++eQT22AMtVrN/Pnzuemmm8jLy2PNmjWcPXsWtVrN\ntGnT+NWvftVpocWVYR0GL/1bQgh30q7CtXPnTj7++GNUKhWxsbEAnDp1io0bN+Lr68trr72GxWJh\n6tSp3H777YSHh3dqaNH5zu/fGi79W0IIN9KuwrVr1y7UajVLly5lwIABABw5coRnn32Wf/zjH/To\n0YPHHnuM3r17d2pYceUU1ZVTbqxG6xNAgjbG1XGEEMKmXYMzCgoKGD16tK1oAQwaNIjRo0ejKAoL\nFy6UotXFWKd5GhzWV/q3hBBupV2Fy2AwEB0d3WJ5z549AewKmugarLcxGRwaL/1bQgi30q7CpSgK\nanXLs4re3s1faDKCsGs5v39rRI8E6d8SQrgVmatQtFCgL+NsQy2hmiCuDu7l6jhCCGGn3cPhN23a\nxKZNm1p9bdasWS2WqVQq3nrrrY4nEy5j698KjSdA7eviNEIIYa/Tjrhk8l3PZZ2fcHBYX3y8Lns6\nSyGEcKp2fSu9/fbbnZ1DuAm5fksI4e6kj0vYOaEvobJRT7gmmH7BPV0dRwghWpDCJez8fJowHn9v\nGS0qhHA/UriEnfPnJ9R4+7g4jRBCtOQWPe96vZ5169Zx+PBhtFotc+bMYfz48a2uu23bNjIzM2ls\nbCQlJYUFCxbYrjFrq53c3Fw2bNiATqejf//+pKWlERERAUBmZia7du1Cp9Oh1WqZOnUq06dP7/yd\ndyMWxcL+s81HXMPl+i0hhJtyiyOu9evX4+PjQ3p6Og899BDr16+nuLi4xXoHDx4kMzOTpUuXsnbt\nWsrKysjIyGhXO7W1taxYsYLZs2ezceNG+vXrx6pVq+zaf+ihh9i4cSNPPPEEH3/8MXv27OncHXcz\nJ2pLqDbVEeGrpXdglKvjCCFEq1xeuBoaGsjOzmb27NloNBoSExMZNWoUWVlZLdbNyspi8uTJxMTE\nEBAQwB133MHOnTvb1c7evXuJi4tjzJgxqNVqUlNTKSgo4PTp0wBMnz6d+Ph4vLy86NWrF6NGjeLY\nsWNX7HNwB9bThIPD+hLgLddvCSHck8sLV0lJCd7e3nZzIcbHx7d6xFVUVESfPn3s1quurkav17fZ\nTnFxsd22vr6+REdHt/o+AEePHiUurnvd9dfWvxUq/VtCCPfl8sJlNBoJCAiwW+bv7099fX2b6/r7\n+9uWt9WOI++TkZGBoihMmjSpQ/vkiSyKhf0V5/q3IuT6LSGE+3L54Aw/Pz8MBoPdMoPBYCtKF657\nfqGxbufn59dmOxdue7H3+eijj/jyyy/5y1/+0urEwgB5eXnk5eXZns+cOZPg4OC2dtXlNBrNRXN+\nX1lArameq/zDSIyMJ9jfdftzqZzuxBNyekJGkJzO5ik5AbtxCklJSSQlJbW5jcsLV8+ePbFYLJSW\nltpO8xUUFNjutHy+uLg48vPzSUlJASA/P5/Q0FCCgoLw8fG5ZDuxsbHs2rXL1pbRaKSsrMzufb74\n4gvee+89/vKXvxAWFnbRzK19uLW1tR38BK6c4ODgi+bMKjgIQFJoHyxGM7Vm1+3PpXK6E0/I6QkZ\nQXI6myflnDlzpsPbufxUoa+vL8nJyWRkZNDQ0MDRo0fJyclhwoQJLdadMGECO3bsoLi4GL1ez9at\nW22n89pqJzk5meLiYrKzszGZTGzevJn4+Hh69Wqe/fzLL7/krbfeYsmSJURGRl6x/XcX355tHogi\n/VtCCHenUtxgNtwLr7+aO3cuY8eORafTsXjxYlauXEmPHj0A2L59O++++y4mk6nN67is7Vh99913\npKeno9PpSEhIYNGiRbbruB588EEqKirw8fFBURRUKhXXX389CxYsaNc+WEcnurOL/RbWpFiY8tEj\n1JmNbBz/RwaH9XVBup950m+L7p7TEzKC5HQ2T8lpPXBwlFsUrq7AkwvX91WFzP/yr1zlH8a/r3+M\nMF/Xnhv3lH90npDTEzKC5HQ2T8nZ0cLl8lOFwvWs998aEirXbwkh3J8ULsG+8nP9WzI/oRDCA0jh\n6ubMliYOVvwEwNDwfnL9lhDC7Unh6uaOVRdhaGqgl38PegX0cHUcIYRokxSubs7avzU4LF76t4QQ\nHkEKVzcn8xMKITyNFK5u7Pz+rWE9ZH5CIYRnkMLVjR2pKsDY1EhsQARX+V98iishhHAnUri6sZzz\n+rf8pX9LCOEhpHB1Y9+e17/lK/1bQggPIYWrmzJZzORWngBgaLj0bwkhPIcUrm4qrzIfY5OJ3oFR\nRPmHujqOEEK0mxSubmrf2ea7HSeF9pH+LSGER5HC1U3t050/P6HL7ycqhBDtJoWrG2psMpFbeRKA\nYeFX46WS/wyEEJ5DvrG6oe+q8mm0mIkPuooIvxBXxxFCCIdI4eqGrNM8JYXG4+etcXEaIYRwjBSu\nbujb8/q35PotIYSnkcLVzRibGsmrzEeFimHh/aR/SwjhceRbq5v5rjIfk9JE36CrCPfVujqOEEI4\nTApXN2M9TTg4rK/0bwkhPJIUrm7Gev3W4NB46d8SQngkKVzdSL25gSNVhahQMVT6t4QQHkq+ubqR\nA7rjmJUmrg7uSZhvsKvjCCFEh0jh6ka+KT0CNN9/S/q3hBCeSiapcxKTxYyK5luDqFTNj1So3Op2\nId+UNRcuuf+WEMKTSeFykkVPP8L9c+8iJi4OBQWVogIUQGX937lChq3AwQVFzrbu+QVQhde5Amhd\n1wsvvGzPWxZL6/PzGcxG8iry8ULFkPC+0r8lhPBYUricJOdaAz/8bRmrFj9DbGysQ9sqgHLu/1Hs\nX1AUBeXcqyjKeesCqGzLUHHJYrn/7I80KRYGaGMI1QRd5t4KIYTrSOFyEi9fNbVTovjzP5Yz4zdz\n8fFSo/H2QeOlPvfHB413y8c+Xj+v09ppxfOPqujgWcfi4mJWrV1Fjb6MM0FnOdO7lLC+MjhDCOGZ\npHA5kZevmp9qTrPu2LYObe9jK3ItC52Plxpfb/tC1/z6udes63k3P7auV112ln+sf5XGG2PQ+oZT\n0WBm4UuP8/oTq+gd19vJn4AQQnQ+KVxOZGkwExcUyfjYMZgsZhosJkwWM41NZhotJhot5uY/Tc2P\nTeeeNzSZMCtNmM4tq3NiptptRwm8MQEv3+a/ai9fNdWTI1i5cS1/e2q5E99JCCGuDLcoXHq9nnXr\n1nH48GG0Wi1z5sxh/Pjxra67bds2MjMzaWxsJCUlhQULFqBWq9vVTm5uLhs2bECn09G/f3/S0tKI\niIgAIC8vj82bN3Py5EmCgoL4+9//7tA+WBrMBH9+hpc60McFYFEsmCxNzQWu6VyBu0Sxsz5v8fjc\nNqZzxXKPdwEqX/u/Zi9fNeX1VQ5nFEIId+AWhWv9+vX4+PiQnp7OiRMnWL58OfHx8S0KwMGDB8nM\nzGTp0qWEhYXx0ksvkZGRwZ133tlmO7W1taxYsYKFCxcycuRI3nrrLVatWsVzzz0HgK+vL5MnT6ax\nsZF33nnH4X0YnRvIAx0sWgBeKi98vb2ah6k7caT6kg9P8G1Dne2IC5qLbKR/mPPeRAghriCXj4lu\naGggOzub2bNno9FoSExMZNSoUWRlZbVYNysri8mTJxMTE0NAQAB33HEHO3fubFc7e/fuJS4ujjFj\nxqBWq0lNTaWgoIDTp08DkJCQwPXXX09UVFSH9uOpx/7MVT2jMTWZbaf8zJYmmqx/FAsWxYKiKG03\n5kQP/Ppegj8/g6XBDDQXrZAvdPzhnrQrmkMIIZzF5UdcJSUleHt7Ex0dbVsWHx/PkSNHWqxbVFTE\n6NGj7darrq5Gr9ej0+ku2U5xcTF9+vSxvebr60t0dDTFxcX06tXrsvcjyi8U+HmousViQQEsNP9U\nFOXc0PZzy84VMNvQdgUUzhv6fm4b6zqKbTXr0Hjr/zUPNVRUzUPpVQAq67B4iO7VkxW/f5pX3/wn\n1aY6ov3C+MMTf5aBGUIIj+XywmU0GgkICLBb5u/vT319fZvr+vv725a31Y7RaESr1V709cul9vK2\nX3AFjmXtrvHiwkLX/MeCQki/a1i55HlCg7WY6hs7P5gQQnQilxcuPz8/DAaD3TKDwWArSheue36h\nsW7n5+fXZjsXbnup92lLXl4eeXl5tuczZ84kONj9r4vSaDQ0qt2/cGk0Go/5PN09pydkBMnpbJ6S\nEyAjI8P2OCkpiaSkpDa3cXnh6tmzJxaLhdLSUttpvoKCglYHOcTFxZGfn09KSgoA+fn5hIaGEhQU\nhI+PzyXbiY2NZdeuXba2jEYjZWVlHRpM0dqHW1tb63A7V1pwcLDkdCJPyOkJGUFyOpsn5Zw5c6bD\n27l8cIavry/JyclkZGTQ0NDA0aNHycnJYcKECS3WnTBhAjt27KC4uBi9Xs/WrVuZNGlSu9pJTk6m\nuLiY7OxsTCYTmzdvJj4+3ta/pSgKJpMJs9ls91gIIYR7USlXephbKy68/mru3LmMHTsWnU7H4sWL\nWblyJT169ABg+/btvPvuu5hMpjav47K2Y/Xdd9+Rnp6OTqcjISGBRYsW2a7jOnLkCMuWLbPLNWjQ\nIJYuXdqufbCOTnRnnvRbmOR0Dk/ICJLT2TwlZ0cHxrlF4eoKpHA5j+R0Hk/ICJLT2TwlZ0cLl8tP\nFQohhBCOkMIlhBDCo0jhEkII4VGkcAkhhPAoMjhDCCGER5EjLic4/8pvdyY5ncsTcnpCRpCcztbV\nc0rhEkII4VGkcAkhhPAo3k8//fTTrg7RFXT0Pl5XmuR0Lk/I6QkZQXI6W1fOKYMzhBBCeBQ5VSiE\nEMKjSOESQgjhUaRwCSGE8Cguv5GkpzKbzaxfv57c3Fz0ej3R0dHMmTOHYcOGuTpaC6tXryY3N5fG\nxkZCQ0OZPn06kydPdnWsiyopKeGPf/wj1113HQ8++KCr47Tw9NNPc/z4cdRqNYqi0KNHD1atWuXq\nWK3avXs3mzdvRqfTERYWRlpaGomJia6OZTN//nxUKhXQfE+8xsZGbrrpJu655x4XJ7NXXl7O+vXr\n+eGHH9BoNIwZM4a7774bLy/3+t3/1Kl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_gridscores\n", "\n", "draw_gridscores(gs.grid_scores_, 'n_states',\n", " score_label='R-squared', param_label='L-Number of Local States')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the accuracy of the MKS model monotonically increases, as we increase `n_states`, but accuracy doesn't improve significantly as `n_states` gets larger than signal digits. \n", "\n", "In order to save on computation costs, let's set (calibrate) the influence coefficients with `n_states` equal to 6, but realize that, if we need slightly more accuracy, the value can be increased." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "model = MKSLocalizationModel(basis=PrimitiveBasis(6, [-1, 1]))\n", "model.fit(X, y)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the first 4 influence coefficients. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_coeff\n", "\n", "draw_coeff(model.coef_[...,:4])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Microstructure Evolution\n", "\n", "With the calibrated influence coefficients, we are ready to predict the evolution of a concentration field. In order to do this, we need to have the Cahn-Hilliard simulation and the MKS model start with the same initial concentration `phi0` and evolve in time. In order to do the Cahn-Hilliard simulation, we need an instance of the class `CahnHilliardSimulation`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pymks.datasets.cahn_hilliard_simulation import CahnHilliardSimulation\n", "np.random.seed(191)\n", "\n", "phi0 = np.random.normal(0, 1e-9, (1, n, n))\n", "ch_sim = CahnHilliardSimulation(dt=dt)\n", "phi_sim = phi0.copy()\n", "phi_pred = phi0.copy()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to move forward in time, we need to feed the concentration back into the Cahn-Hilliard simulation and the MKS model." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "time_steps = 10\n", "\n", "for ii in range(time_steps):\n", " ch_sim.run(phi_sim)\n", " phi_sim = ch_sim.response\n", " phi_pred = model.predict(phi_pred)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at the concentration fields." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hpZdeQiKRwGWXXYYvfvGLJdkPDQBFREQkdAbqAHD16tVIJBJ48MEHsWvXLnz7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\n43DxxRc7X/enP/0JH/3oR3t+Hjt2LI4cOYKOjg5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_concentrations_compare\n", "\n", "draw_concentrations((phi_sim[0], phi_pred[0]), labels=('Simulation', 'MKS'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The MKS model was able to capture the microstructure evolution with 6 local states. \n", "\n", "## Resizing the Coefficients to use on Larger Systems \n", "\n", "Now let's try and predict a larger simulation by resizing the coefficients and provide a larger initial concentratio field." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "m = 3 * n\n", "model.resize_coeff((m, m))\n", "\n", "phi0 = np.random.normal(0, 1e-9, (1, m, m))\n", "phi_sim = phi0.copy()\n", "phi_pred = phi0.copy()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again we are going to march forward in time by feeding the concentration fields back into the Cahn-Hilliard simulation and the MKS model. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "for ii in range(1000):\n", " ch_sim.run(phi_sim)\n", " phi_sim = ch_sim.response\n", " phi_pred = model.predict(phi_pred)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at the results." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vwgxheF+Yj+mXQt52kvjLQtvW3LthGRDxSGvWyTSmOQpGQ/NByFnn9R2yHFTT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gtZTcTIzJA6ALyGs+WbKL2WHbAFnI3aozaUr63qKY6r0CsPxI5cb2ZNgDSSvZrpz0IrgRpQU8bp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\nB6wMolFqQ67HhQCZQIY4C6hz6Hp+dmzFI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u3AcVB673OsYtHomNgOJoy31p6khsSWqRRV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\nHIN/ADocDofD4XA8x/D/AaUdoXtKvxjcAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_concentrations_compare\n", "\n", "draw_concentrations_compare((phi_sim[0], phi_pred[0]), labels=('Simulation', 'MKS'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The MKS model with resized influence coefficients was able to reasonably predict the structure evolution for a larger concentration field. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }