{ "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": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] } ], "source": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "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": 14, "metadata": { "scrolled": true }, "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": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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IHAAAAIBYfInGD3R1mpxzh1v2cJ4zszrv/fTA5001szm559V77+/u0gQEYCAH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\ncKwKKnOrM3KMFQ8uk5m5l/xUZl594zWZuf5aXXrdtbJDZoZ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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": 16, "metadata": {}, "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": 17, "metadata": {}, "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": 30, "metadata": {}, "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": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "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": 29, "metadata": {}, "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": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "print(gs.best_estimator_)\n", "print(gs.score(X_test, y_test))\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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m2BIREZkusYKi8B5nnyQYLbrdzMbM7Ll0ebiS9eNmNkgQEBnBtFmutYymlA46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\nfI/ePKcoN5hLt2Vwiv3SQV13wb2mT1ntzvoQzTc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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": 21, "metadata": {}, "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": 22, "metadata": {}, "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": 23, "metadata": {}, "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": 24, "metadata": {}, "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": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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HFQzbEuc0vLPf9JJAV0kaJnv86koePD42wuad8NO2ph84+/r2aDttkwWdO0G2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\n4+zH24sIx5bUL+3UhlWjNmTH0O3tPOC8qawWPCw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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": 26, "metadata": {}, "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": 27, "metadata": {}, "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": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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G6fsZxhK8UEwwTuSTjA3/dmXNf5tZPT7no+OBmf2PdpyLuadtfUa/1zfknH+QUno7pfSp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\nSUVORK5CYII=\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": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }