{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cahn-Hilliard with Primtive and Legendre Bases\n", "\n", "This example uses a Cahn-Hilliard model to compare two different bases representations to discretize the microstructure. One basis representaion uses the primitive (or hat) basis and the other uses Legendre polynomials. The example includes the background theory about using Legendre polynomials as a basis in MKS. The MKS with two different bases are compared with the standard spectral solution for the Cahn-Hilliard solution at both the calibration domain size and a scaled domain size. " ] }, { "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": "markdown", "metadata": {}, "source": [ "### Basis Functions for the Microstructure Function and Influence Function\n", "\n", "In this example, we will explore the differences when using the\n", "Legendre polynomials as the basis function compared to the primitive\n", "(or hat) basis for the microstructure function and the influence coefficients.\n", "\n", "For more information about both of these basis please see the [theory section](THEORY.html)." ] }, { "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", "### Generating Calibration Datasets\n", "\n", "Because the microstructure is a continuous field that can have a range of values and changes over time, the first order influence coefficients cannot be calibrated with delta microstructures. Instead, a large number of simulations with random initial conditions will be used to calibrate the first order influence coefficients using linear regression. Let's show how this is done.\n", "\n", "The function `make_cahnHilliard` from `pymks.datasets` provides a nice interface to generate calibration datasets for the influence coefficients. The function `make_cahnHilliard` requires the number of calibration samples, given by `n_samples`, and the size and shape of the domain, given by `size`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pymks\n", "from pymks.datasets import make_cahn_hilliard\n", "\n", "\n", "length = 41\n", "n_samples = 400\n", "dt = 1e-2\n", "np.random.seed(101)\n", "size=(length, length)\n", "X, y = make_cahn_hilliard(n_samples=n_samples, size=size, dt=dt)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `make_cahnHilliard` has generated `n_samples` number of random microstructures, `X`, and returned the same microstructures after they have evolved for one time step, given by `y`. Let's take a look at one of them." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cDgcuv/xy3HrrrZWyHmUWgseOF4p6KCAnfobfNlSd1wtvyonIQQPu0FdA2Xe7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\nEEKI7EYDgpRDdgQzMTvG/b0Z15n6S6+9TNf1g1uWmPqsf5p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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_concentrations\n", "\n", "\n", "draw_concentrations((X[0], y[0]),('Calibration Input', 'Calibration Output'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calibrate Influence Coefficients\n", " \n", "In this example, we compare the difference between using the primitive (or hat) basis and the Legendre polynomial basis to represent the microstructure function. As mentioned above, the microstructures (concentration fields) are not discrete phases. This leaves the number of local states in local state space `n_states` as a free hyperparameter. In the next section, we look to see what a practical number of local states for bases would be. \n", " \n", "### Optimizing the Number of Local States\n", " \n", "Below, we compare the difference in performance, as we vary the local state, when we choose the primitive basis and the Legendre polynomial basis.\n", "\n", "The `(X, y)` sample data is split into training and test data. The code then optimizes `n_states` between `2` and `11` and the two `basis` with the `parameters_to_tune` variable. The `GridSearchCV` takes an `MKSLocalizationModel` instance, a `scoring` function (figure of merit) and the `parameters_to_tune` and then finds the optimal parameters with a grid search." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pymks.bases import PrimitiveBasis\n", "from sklearn.grid_search import GridSearchCV\n", "from sklearn import metrics\n", "mse = metrics.mean_squared_error\n", "from pymks.bases import LegendreBasis\n", "from pymks import MKSLocalizationModel\n", "from sklearn.cross_validation import train_test_split\n", "\n", "\n", "train_split_shape = (X.shape[0],) + (np.prod(X.shape[1:]),)\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(X.reshape(train_split_shape),\n", " y.reshape(train_split_shape),\n", " test_size=0.5, random_state=3)\n", "\n", "prim_basis = PrimitiveBasis(2, [-1, 1])\n", "leg_basis = LegendreBasis(2, [-1, 1])\n", "\n", "params_to_tune = {'n_states': np.arange(2, 11),\n", " 'basis': [prim_basis, leg_basis]}\n", "Model = MKSLocalizationModel(prim_basis)\n", "scoring = metrics.make_scorer(lambda a, b: -mse(a, b))\n", "fit_params = {'size': size}\n", "gs = GridSearchCV(Model, params_to_tune, cv=5,\n", " fit_params=fit_params, n_jobs=3).fit(X_train, y_train)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal parameters are the `LegendreBasis` with only 4 local states. More terms don't improve the R-squared value." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MKSLocalizationModel(basis=,\n", " lstsq_rcond=2.2204460492503131e-12, n_jobs=None, n_states=4)\n", "1.0\n" ] } ], "source": [ "print(gs.best_estimator_)\n", "print(gs.score(X_test, y_test))\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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T7DX89faLG1WZ9dNTfNNMnxGXuKWKXq9n2rRpgOOW07lFu22pRdHr9S6P1Wp1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\nnTvHP/7xD7KystBoNERGRjJ58mT8/PxcHc3Bv/71L/bt24f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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_gridscores\n", "\n", "\n", "lgs = [x for x in gs.grid_scores_ \\\n", " if type(x.parameters['basis']) is type(leg_basis)]\n", "pgs = [x for x in gs.grid_scores_ \\\n", " if type(x.parameters['basis']) is type(prim_basis)]\n", "\n", "draw_gridscores([lgs, pgs], 'n_states', data_labels=['Legendre', 'Primitve'],\n", " colors=['#f46d43', '#1a9641'], score_label='R-Squared', \n", " param_label = 'L - Total Number of Local States')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see the `LegendreBasis` converges faster than the `PrimitiveBasis`. In order to further compare performance between the two models, lets select 4 local states for both bases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparing the Bases for `n_states=4`" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "prim_basis = PrimitiveBasis(n_states=4, domain=[-1, 1])\n", "prim_model = MKSLocalizationModel(basis=prim_basis)\n", "prim_model.fit(X, y)\n", "\n", "leg_basis = LegendreBasis(4, [-1, 1])\n", "leg_model = MKSLocalizationModel(basis=leg_basis)\n", "leg_model.fit(X, y)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's look at the influence coefficients for both bases.\n", "\n", "First, the `PrimitiveBasis` influence coefficients:" ] }, { "cell_type": "code", "execution_count": 8, "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(prim_model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the `LegendreBasis` influence coefficients:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_coeff(leg_model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's do some simulations with both sets of coefficients and compare the results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Microstructure Evolution\n", "\n", "In order to compare the difference between the two bases, we need to have the Cahn-Hilliard simulation and the two MKS models 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": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pymks.datasets.cahn_hilliard_simulation import CahnHilliardSimulation\n", "\n", "\n", "np.random.seed(66)\n", "phi0 = np.random.normal(0, 1e-9, ((1,) + size))\n", "ch_sim = CahnHilliardSimulation(dt=dt)\n", "phi_sim = phi0.copy()\n", "phi_prim = phi0.copy()\n", "phi_legendre = phi0.copy()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the inital concentration field." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MsCvIzFQQBJtjq2j+li1bkJCQYP57//79mD17NmJiYvDCCy/gww8/hK+vLwID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\ngg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_concentrations([phi0[0]], ['Initial Concentration'])\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 models." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "time_steps = 50\n", "\n", "for steps in range(time_steps):\n", " ch_sim.run(phi_sim)\n", " phi_sim = ch_sim.response\n", " phi_prim = prim_model.predict(phi_prim)\n", " phi_legendre = leg_model.predict(phi_legendre)\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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lnjrCev6RY0qLFJLABO/DD5qrv/HtbQDe37DeBuD1xre3AXh/MxS9DWD0N569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\n31jXbowehq4bqh6G1ijPxxvrzMRl9vw9exuA9ze+vQ3A+xv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_concentrations\n", "\n", "\n", "draw_concentrations((phi_sim[0], phi_prim[0], phi_legendre[0]),\n", " ('Simulation', 'Primative', 'Legendre'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By just looking at the three microstructures is it difficult to see any differences. Below, we plot the difference between the two MKS models and the simulation." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RRVi/fj169OiBxMRErF+/HuFwWDuPy+VC9+7d8cEHHyA7Oxsejwe9e/fGgAEDcP755+OZ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\nPVRVVcHpdCIrKysylpOTgwM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Primative mse = 5.28727678594e-23\n", "Legendre mse = 4.3461487962e-28\n" ] } ], "source": [ "from sklearn import metrics\n", "from pymks.tools import draw_differences\n", "\n", "\n", "mse = metrics.mean_squared_error\n", "draw_differences([(phi_sim[0] - phi_prim[0]), (phi_sim[0] - phi_legendre[0])],\n", " ['Simulaiton - Prmitive', 'Simulation - Legendre'])\n", "\n", "print 'Primative mse =', mse(phi_sim[0], phi_prim[0])\n", "print 'Legendre mse =', mse(phi_sim[0], phi_legendre[0])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `LegendreBasis` basis clearly outperforms the `PrimitiveBasis` for the same value of `n_states`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Resizing the Coefficients to use on Larger Systems \n", "\n", "Below we compare the bases after the coefficients are resized." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "big_length = 3 * length\n", "big_size = (big_length, big_length)\n", "prim_model.resize_coeff(big_size)\n", "leg_model.resize_coeff(big_size)\n", "\n", "phi0 = np.random.normal(0, 1e-9, (1,) + big_size)\n", "phi_sim = phi0.copy()\n", "phi_prim = phi0.copy()\n", "phi_legendre = phi0.copy()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at the initial large concentration field." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6NilB5ocrgtZOKgq0Ou2MnHfVZwJAfx3/P30F9zkpmtfClj3ktL09eS7yv7UV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\n1D7ZWzdii3nm5CkRETlxEiazu++GEJ2SFa8AY4xBG3rvKGyfm+t0a65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MEZHQk7VXNeM8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\nO0D2XzyHJM2g2ovFrsa2Pn81t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TBj4RfdEENvXVz4Rbcw7Gy1HXbYYcdNYkHk+HzdK/Lj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\nfo5T3Yzr0x9bLIgc7bDDDjv+GMMuH7TDDjvsuEnYX4522GGHHTcJ+8vRD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_concentrations([phi0[0]], ['Initial Concentration'])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the resized coefficients.\n", "\n", "First, the influence coefficients from the `PrimitiveBasis`." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_coeff(prim_model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the influence coefficients from the `LegendreBases`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_coeff(leg_model.coef_)\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 models. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "for steps in range(time_steps):\n", " ch_sim.run(phi_sim)\n", " phi_sim = ch_sim.response\n", " phi_prim = prim_model.predict(phi_prim)\n", " phi_legendre = leg_model.predict(phi_legendre)\n", " " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sfWx+E8ttrH3o+Y6MR12//BzUcPO3n9/EchvrcBX2JmRrim2ZvYnkNkCY36wv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ZRjXy5qMBd1mAsR9QcJpU7FZPrlUB/bLkO2HSiERsLvHnCYXqEQiszPDbh9CI2MVcPF9Rrn4Xmb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_concentrations((phi_sim[0], phi_prim[0], phi_legendre[0]), ('Simulation', 'Primiative', 'Legendre'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both MKS models seem to predict the concentration faily well. However, the Legendre polynomial basis looks to be better. Again, let's look at the difference between the simulation and the MKS models." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ufE3aYgTQZDKZTCZT72kSDgAnk2wAaDKZTCaTqQdlA8BuGj8JpH+aq02b5Eyb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\ni58jPZuWpMFVLm4qLsqSGZNF+Rzesf+/vXMJteW6zvWox1pr7/OQHEn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oEpNA3209X6Nt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PgqtdMGeGrs+7R1j9yOCSD5Adb8e5mgjoPyHtqeRP6yKh64ryB9Fxe6HCqk9OdaKeVy2L7daOUc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\nteprlkptT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Primative mse = 4.43216831378e-23\n", "Legendre mse = 4.66632322173e-28\n" ] } ], "source": [ "draw_differences([(phi_sim[0] - phi_prim[0]), (phi_sim[0] - phi_legendre[0])], \n", " ['Simulaiton - Primiative','Simulation - Legendre'])\n", "\n", "print 'Primative mse =', mse(phi_sim[0], phi_prim[0])\n", "print 'Legendre mse =', mse(phi_sim[0], phi_legendre[0])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the resized influence coefficients, the `LegendreBasis` outperforms the `PrimitiveBasis` for the same value of `n_states`. The value of `n_states` does not necessarily guarantee a fair comparison between the two basis in terms of floating point calculations and memory used." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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 }