{ "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": [ "%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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VHHYFiw27nZ7mwdjDKMHZ0AD8daZkd8NN47YZ4O1eONuW69PofeUscgDA31iR\n1L08vdgYO2P7o2Rrw1m6KLYBY7mTmcPbfsHK3PA1JbcjUmn5diuNvZFOS1vh3AoyEogr0gMoCIIg\nCIJbI6+AXZEEUBAEQRAEt0YSQFckARQEQRAEwa2RBNAVSQAFQRAEQXBrpAjEFUkABUEQBEFwa8pj\nD2BOTg5iY2Nx8OBBGI1G9O7dGy1atCDn/eqrr5CUlASTyYRatWqhf//+CA6mCxCLS5EJ4OsL3iV1\nTwNdAdfohVbssn5M3ETqRm9fNsa7WTVSt+fyA33HfvMZqWsre7MxNqbC6tP4ODbGw5eu6Bs0fggb\nY7fQ252zPZWNaTIqktSVqlltTBWg5TxfMTr0A/pYHz1zgo354hO6fd4YO4yNWbwqntSbPhzFxlgv\n0VVzGVcvsTFc1d6qH9eyMTsXrCd1fVgFNqbqw7VI/YFa97MxPUbS1dMrZ9NtAwCfzJxH6g+2f4SN\ncdjpm15Y9VA2JvP706T+RdUVpN62+qN4ol1TdnnFRasu2e9RrrpQ6bpgUSgQZKtzFdaj1+lJ3Waj\nq0IBwMJUs5oVqoC5bXNY+PWAeQ5m5/L3Bq5CWOOhZmO4/dErVHjmmejr/Er2VTbGxtxTbaWoNtZp\nPdkYg54+pkr7k5N3jdQvZV4ucYxSNS1b8cxc/wBgN9PniIp/tEKlZY63h0JbM9OUKtVvR8Wugzvx\n7yJxcXHQarWIi4tDSkoKpk2bhtDQUJfEbteuXfjxxx8xadIkBAYG4quvvsK8efMwffr0W1p/yev+\nBUEQBEEQ/odwOBx39F9RmEwm7Nu3D7169YJer0d4eDgiIyOxY8cOl3kvXryI8PBwVK5cGR4eHvjP\nf/6D1FS+06i4SAIoCIIgCIJbU94SwLS0NKjValStWtWphYaG4ty5cy7zNm/eHBcuXEBaWhqsViu2\nb9+Ohx566JbbRL4BFARBEATBrSlvRtAmkwmenoU/OTAYDDCZTC7zVqhQAffffz+GDBkCDw8PBAYG\nYswYelCJkiAJoCAIgiAIbs3dqAJOTEx0/j8iIgIRERHOvw0GA/LyCn/zmpubCwNRX/H111/j1KlT\niI2NRYUKFbBjxw5MnDgRH330EXS60o+aIgmgIAiCIAhuzd2oAu7Rowc7LSgoCDabDenp6c7XwGfP\nnkVISIjLvGfOnEHz5s3h7+8PAHjsscewZMkSpKamIiwsrNTbJ98ACoIgCILg1pS3bwANBgOioqKQ\nkJCA/Py89KBSAAAgAElEQVR8HD16FPv370fLli1d5q1Tpw52796NzMxM2O127NixAzabrdD3g6Wh\nyB7AjXt+IPXU3cfpAIX9bt+nM6mvmvMlG1O3I/2hY+oZ1w8lC8j7I4PUZ8+by8YMnzyK1Js2b8bG\n/BhL24l8vm45G/PK8/1I3fcx16y/gH6Pdyd1Y4dQNib3l3RS7znsZTbm4IkjpN74/kZsTH5qNqnP\nHjCBjen1/iBS/ybuKzbmhRlvkPqUuJlsjCOP9jN4st0TbMxzY2l7lsR3FrExqRm0dUWTobw9y7Fz\nJ0k9oCVtKQMAl3ak0DFGfzbm9z0/kfqb43ibHt+W9Lmo0dC3Cw912fyOzM2n25GDtUBRuvlamWkK\nu6ACY3GhsBrWosbCW8dYGYuY0vRcOLj9BAAr/S2UyU7bjwC85Y1BT9uBAYCBscJR2p9rebmkbslW\nsPZh9kelV7CoYaxJAoy8DYwHY3ljtfK+KZztT57CuW7l9lXpfNMyJ7DSucPYsDjsvKULVMx3dAo2\nMKV59Wq2WEocUxTl0QcwOjoasbGxiI6OhtFoRExMDIKDg5GRkYGhQ4di1qxZCAgIQNeuXZGZmYmR\nI0fCZDIhKCgIw4YNg5eX1y2tX14BC4IgCILg1pTHBNDHxwcjRoxw0QMDAxEf/68nrFarRf/+/dG/\nf/8yXb8kgIIgCIIguDUyFJwrkgAKgiAIguDWlMcewLuNJICCIAiCILg1kgC6IgmgIAiCIAhujSSA\nrhSZAKYl05WHC2JjSf1IylF2WZ8uXUzqtiuuztcFnE9LI/WPx89iY/p16kXqh079wcY4mIqoHz5c\nxcY8+Ta9ns/X81XAnvUCSD37x7/YGN92oaSu86Sr7ABgwmfzSP2dESPZmGdf6knqc79YwMaojbQJ\npUrHV+B9NY6uqFWqhOYu3lGvDGVjTGb6vPp8A398/t7yJ6mr/fi21lb1JvW1q79lY/JP0YPb26+Z\n2ZjWbz5D6hun8PtjbF2T1CuF8PYB6Ufoc/Gkha78f1BVg11WSbDmuVb+aTy17PxaDT3NbOHb0OFB\nn0daHb8ejZqexp1fAH++cpW+AOCw0zF6PX/ucaMb5Hvwlal2Zj2wKIyUoKanmT34trZY6UpO7rgB\ngOkaXR3rMCu0G1MFrFSbrmLOK6Vt06rpxyVX8Q0Adju9bRaFymHYmOp2Zj+LmsbCbLZKo1AFzJw7\nbBUywFcIK1SqOyz88S4tDpSvkUDKA9IDKAiCIAiCWyM9gK5IAigIgiAIglsjVcCuSAIoCIIgCIJb\nIz2ArkgCKAiCIAiCWyMJoCuSAAqCIAiC4NZIAuiKJICCIAiCILg1kgC6UmQCmHv4IqkP+3B0iVcW\n/mA9Ur9Wh7aqAIDgKtVJnRtkGwC0VWhbjiXL4kkdAJr+pxmpJ/2xjo3p2Za25cg18QN9/zhrNakb\n6ldiYypVpqed/HwPG7O+7mZSN6dmszHVKweRuiWdHyTecoEevN3Ylj+meQfpc6pZZFM2Jiw4lNTf\nj53Bxgx6IZrUuz/elY258kgrUq9SsTIbM3UAfS14P0K3JwCMnjeJ1Hcm72Zjftm3j9S9wmlrIQCY\n/s5kUs83MwPOA1hXdROpb526ktTzVJfYZZUEyvrBpjDIPBh3FL2Ot01Rq2i7Cq2Wt//gsDMWLABv\nDaK0bZx9jV5LWy0pYdbwx1fFWLpAwc4EjE2W3Vpyuw7OGgXgH9IqpfNAw1iQcDoAHdOmNju/Pzl5\n9H1Qp3DucOeIVsM/es06ehs4m6D/XxEpqxTagLNnUan5tubsvTw9vdgYB+htM9n556TDVPaWLVIE\n4or0AAqCIAiC4NZID6ArkgAKgiAIguDWcKbp9zKSAAqCIAiC4NZID6ArkgAKgiAIguDWSALoiiSA\ngiAIgiC4NeUxAczJyUFsbCwOHjwIo9GI3r17o0WLFuS8Fy5cwOeff44///wTGo0GrVu3xgsvvHBL\n6y8yAVyatIrUo2PoCsvHn3uCXdbfF9OKuVn/0veJHqT+cpc+bMxDLzCVnP58JWc+U4HnUdHAxgx6\n41VSD46sw8ZM/PIjUh/3ygg25i+m0vbl2UPYmP1HD5C6NoiukAaAhcsXk/rI90axMbOXfkzqmd+d\nZmPCnn+E1L0UKsnOM+eO0iDodYPDSN2qUEH+Ru8Yej0mhZjZ75D6F6u+ZGMm9hlO6rqaRjamQlQI\nqb/z1ntszIVLdMX1pFfeZmPaDXuO1L2jqpG6vlYFdlklgqhCVTq+NjV9TDRq/rbmoVaoimSwWCyk\nrtPw1Z9clakSGg+6wpKrKAb4ffX05q/zXAdT1a/Q1iptyduNKf5URO9FV0mbFSpTuXNEpaXbU4mr\n2ZnsNK6KVK/jjzXnVmEx0+eUElwFLkBX0APK1w9bIezBH2u9gX4eeiico9c4VwylT/IUir5Li700\nJ+RtJi4uDlqtFnFxcUhJScG0adMQGhqK4ODgQvNZrVZMnjwZTzzxBIYOHQoPDw+cP3/+ltdfiqta\nEARBEAThfweHw3FH/xWFyWTCvn370KtXL+j1eoSHhyMyMhI7duxwmTcpKQn+/v7o2LEjdDodNBoN\natSoccttIq+ABUEQBEFwa8rbK+C0tDSo1WpUrVrVqYWGhuLIkSMu8x4/fhyVKlXC1KlTcfLkSdSo\nUQMvv/zyLSeB0gMoCIIgCIJbUx57AD09PQtpBoMBJpPJZd7Lly/j559/xpNPPolFixbhoYcewowZ\nM2C1Wm+pTaQHUBAEQRAEt+Zu9AAmJiY6/x8REYGIiAjn3waDAXl5hb+PzM3NhYH4zlKn06FevXpo\n1KgRAKBLly5YvXo1zp8/f0u9gJIACoIgCILg1igN3Xi76NGDLmIFgKCgINhsNqSnpztfA589exYh\nIa7FfjVr1sSxY8ecf5dVMiuvgAVBEARBcGvK2ytgg8GAqKgoJCQkID8/H0ePHsX+/fvRsmVLl3n/\n85//4MSJEzh06BDsdjs2bNgAo9GI6tWr31KbFNkD2LfZM6Re48XGpL59y4/ssu5vHEHqlf0rsTH9\nn+tL6l4PVWFjjp86QetHj7Mxr784kNQvts9gY+qH1SP1tEsX2JjLWVdJPW7dMjZm9opYUo8fvYCN\nWfJ9Iqn3W9GLjfGpT9vk1A6uxcY0frARqf+u5y0L2kY9Ruo7k3ezMUfiXCujAEBb1YeNGdj5RVIP\n7HQ/G+PIp+0UFq1bysYM6Eqvx7Mhf15TlicAsGgJbcUDAC+36Unqjhf4m830qdPobWvMXz+Xs66Q\net7Bf0jdHJjFLqtEEAPaK95GmWOVj3x+FXbezodDp6FtPrQKNjBaDX1rVTNWLwCgVpfctoSz3/Ay\neJI6ADiYVjXlu3575IQ4NgDgoeG32W6ne1yULHK8DbQVlE3PHzfOakXpIXzNRFtrOUz8N1UOG728\nawoWKCpNyf1MVMy9U2Xje7A4ixOHkteKB7NtzLEGAIuVtq8xO2gbNcXlKTXNbbCBKW9FIAAQHR2N\n2NhYREdHw2g0IiYmBsHBwcjIyMDQoUMxa9YsBAQEoFq1ahg8eDA+/fRTZGZmIiwsDCNHjizVPeNG\n5BWwIAiCIAhuTXlMAH18fDBihKsHcGBgIOLj4wtpUVFRiIqKKtP1SwIoCIIgCIJbUx4TwLuNJICC\nIAiCILg13Egu9zKSAAqCIAiC4NZID6ArkgAKgiAIguDWSALoSpEJ4Mtz3yL1xK9XkrrpT75qNuRJ\numR585dr2BhtiJHU+3Tjq1kzc7JJ3ceLHyC9TnAYqZ86SlcUA8C1PLqSrF9Hftumz5tJ6jnbz7Ex\nbUfT1Z+eCpXQMdHRpD5w2lA2Zs2O70h90GuD2Bj/+tVIfe5QuvoUAL7YsILUj6/bz8YY6lQkdU0l\numoQAGxZdGXahZWH2ZjQFyJJfdW2tWzMrIRPSP2HX5LYmO0+P5H6a/99nY2xm+kKxWXff83HZNIV\nsSot7wClVdPVrXrmGGgr89dVSfAwuFa02ZlKXwBwmLkKR4UqRqaSUq3nK3r1Oj2pa5hKXwBQMWWM\nXGUsANbV36ZQuaxiKlDzzXxVJvcg5CpwAcDKbINDwVvNg6n25doGAKw2ug24YwAAGqZqlqv0vb4i\npmqWPacAh0J1LL8eel89vPjzzZOp4OYqvgGlqmaF64e5FpT2087EqLiKYihXirPcI1XAdxvpARQE\nQRAEwa3h7I/uZSQBFARBEATBrVHqrb5XkQRQEARBEAS3RqqAXZEEUBAEQRAEt0a+AXRFEkBBEARB\nENwaSQBdkQRQEARBEAS3RhJAV4pMAM0WZvDnc/QA8PrQCuyy1k3/ktSNLUPYmOnDJpP6ojVL2Jhj\nyX+Quo2xxACA5ep4Un+ye2c2Zs2c5aQ+ZR9vHaOt5kPqDV9rw8Y0rf8Iqe/Z/jMbE7d4Man37/8K\nG2Ngjt206dPZmPeXfETqV7Iz2Zjfjh0g9cWJ9DEAgAExMaTe7skObMzhU3+S+sk/eKuiq5lXSd1g\nMLAxY+fR52hko8ZsjOnkFVKPHvYqG7Ng0BRSD6tWk40ZvuINUj9wgrfCmT9/PqmPmTie1GuhMrus\nkqD3crW/MNl4Kw+7hbYMcShYx3h40PY3Bi1vM8LFcLYtAJBroW1YODsVJczMsgD+ocZtMwB46uhz\nWckmi/t+ymbj9yfrGv2MsClY4aiZ7VZqA5sHbTNittLPLgAA1zxq3n+EtTrhm5q16YGGX49OS1vE\nsMsC4OmgrWPy7EpWONzy+ERJzVi6KFkIcShZIqm9SmEdUwSSALoiPYCCIAiCILg1UgTiiiSAgiAI\ngiC4NdID6IokgIIgCIIguDWSALoiCaAgCIIgCG6NGEG7IgmgIAiCIAjCHSYnJwexsbE4ePAgjEYj\nevfujRYtWijGTJw4EUeOHMGKFSsUi72KQ5EJ4Jq1a0h92ryZpP72gLfYZXGDxrd4lN/hkR+8R+qP\ntWjFxjR8LoLUv167mo2x5dBVZhu+4GOGzaC37cO36WpNAPCqF0jqh+J/YmO6t+lK6hPfGcfGcFgz\nTOy03GsXST1hC98GOWcvkfqIgW+yMfq6FUl94IABbIw5NZvUv33vMzZmfAJdoTw7k95mAKhZla5I\n333oFzamRo0apN6zzdNsTE5uDql/PPB9NmbaNx+T+uiXhrIxOw/sJfXMP9PZmP6v08fh1N+nSd3H\nWwVUZxdXbHQa1+pHq5eOnd9iZX7R20r+qsdi4ytGDQ6+ApxfHl0hnG/mnQi4Kk+lmzz3WourplVa\nj0bNPw60xLEBAFM+fz+xcFXS3HEDcM2hULXK4LCX3as9labkD1SVVqGt1fQ0H0++4po7PkqvMDVq\numrWg6naBQC7ij4OOh19rAHAg6m4VoKr9tVp+Wv7VhMbivL4CjguLg5arRZxcXFISUnBtGnTEBoa\niuDgYHL+n376SbHyvqSUfSsLgiAIgiCUIxwOxx39VxQmkwn79u1Dr169oNfrER4ejsjISOzYsYOc\nPzc3F19//TVeeOGFMmsTeQUsCIIgCIJbY1fwN7wbpKWlQa1Wo2rVqk4tNDQUR44cIedfvnw5OnTo\nAD8/vzLbBukBFARBEATBrSmPPYCenoUNvA0GA0wm188qTp06hRMnTuCJJ54os/YApAdQEARBEAQ3\n5258A5iYmOj8f0REBCIi/q1PMBgMyMvLKzR/bm6uy6hTdrsdcXFx6NevX5l/GykJoCAIgiAIbs3d\nSAB79OjBTgsKCoLNZkN6errzNfDZs2cRElK4EDEvLw+nT5/G7NmzAfxbVDNo0CAMHToU4eHhpd4+\nSQAFQRAEQXBrylsVsMFgQFRUFBISEjBo0CCkpKRg//79mDy58Njy3t7eWLRokfPvjIwMvPvuu5g+\nfTp8fX1vaRuKTAA1AbQFgl5HD57u4c2Xdqt96PLyzQt5mxHPB2jblAdrP8DGzJo9i9QfaNqAjTm6\nn/7wct6iT9iY1/oPJPUPP5vPxhw5/SepL7uwnI05/fcZUv/yo8VszPQFH5K6tgo/aLcl7Rqpn0n7\ni43xruFP6nm+/HmQe4C2m4kZN5iNUTM2BxV8+A9iJw0cRepvzHyHjXEwHwqv2fEdG3N4KW3h89Zv\nx9gYWzZtB7JoG38evLeIthfqNSaajQmuXI3UZ6zlLYS4fc26Rlvx2Oo8jlcinmGXV1woWwjuuAPA\nVQttM+LIV7BJYCxDWMsSAFbG0qU0DxSl/eGsW5S2zaDj7s8KFhsqej1K9hJcGyhtG2dnoujawlnE\n0Iv6/wUyupoP8vRk7oOetAwA+Rb6mrXbeFsbbwO9HoOetxbijgO3fkDZxojDm2kD7tkOADot/Qy3\nMVYvAJDNWF7ZFCyEtJqy75sqj2MBR0dHIzY2FtHR0TAajYiJiUFwcDAyMjIwdOhQzJo1CwEBAYUK\nP/Lzr58Hfn5+t98HUBAEQRAE4X+Z8tYDCAA+Pj4YMWKEix4YGIj4+HgypnLlykhISCiT9UsCKAiC\nIAiCWyNDwbkiCaAgCIIgCG5NeewBvNtIAigIgiAIglsjCaArkgAKgiAIguDWSALoSpEJ4PgBdCXl\nXxdSSb1Kk1rsssb1f5vUX30xho0ZNuBNUp85h65yBYD5M+eS+oCe/diYWh0bkfqcBL4KWOVFN9+4\nT6eyMfOGTaeXpVDmtmJNIqlPmz+TjRk1jG7raR/N4GPepatjr+XS1cEAYL1MV3J56Plqx2EfvEvq\nOXn8egIrBJD6gq8/ZWN0YRVIPe1SOhtj9DaSusnMV+CN++wDUo/95nM25vLOM6Q+8Mm+bEzTN54i\n9Z8P7WVjalenr8ca3ejzHQAuHDhL6rYr9LE2azPZZZUEqqJNqRrQ28ub1K955LIxDjNdYelQKE3l\njr1eYTB7Dq7SF+AfUA6FKlOTmT4mGoVqYzCTcvPz6AkK22a28tWnXIVyvoq/lkrTBtx4Vjcb6t6I\nl4Eu91VKEsxWMz3BxsfkMcdHuRqcnqZlKnCV0Kr5GK4S2ceTvq4A+hoFALOFaRsAGmZ/uLYBAJud\nry4vLeWxCvhuIz2AgiAIgiC4NdID6IokgIIgCIIguDWSALoiCaAgCIIgCG4NZ/J/LyMJoCAIgiAI\nbo30ALoiCaAgCIIgCG6NXYygXZAEUBAEQRAEt0Z6AF0pMgEcM308PUHHDCiezZeDL91Ej19neIC2\n+ACACS+4jpMHAE+N7sPGvDHkDVJ/+s3n2ZgNX60h9bHjxrEx758+TepX155kY17ZQ9t8aPz5Ucgf\nbBNJ6iNeHMzGWC/Tlg7xG79iYxYtWEjqShfOG+8PJ/Vrv/JWKx++NZnUvZtWY2PUBvpUtSsMQp53\n+CKpr/prKRtz3zONSf3tF/7LxoxfQNv+5B+/wsZM/+QjUleym/nlz99JXWkg+A6PPk7qU5J5O6Au\nfZ4l9bVLV5G6h2fJ7SkoLJSliIZfNmeloWSxYQVjA8PYwwCARU23L2dvAQA6ZrvzLfzxtXHnsoJF\njd1C22Vk27LZGA8Nvd1K1jFWG90+KhVvX+Vt8CJ1vY63z7Ex6+HsbgDe3kPJWstqo9uNWz8A2Kz0\nNLuZtyzhpmUyywIAH8beSKNgieTJ2Nr4evmwMXqdntS1an49FqbdyGv3/2HPawVuR7ImCaAr0gMo\nCIIgCIJbIwmgK5IACoIgCILg1kgC6IokgIIgCIIguDUyEogrkgAKgiAIguDWSA+gK5IACoIgCILg\n1pTHBDAnJwexsbE4ePAgjEYjevfujRYtWrjMl5SUhE2bNiEtLQ1eXl5o3rw5+vTpw47NXFyKTADn\nTPiQ1Nft3ETqBi1dWQQAK2fHk7rayFeFefjQ1XRXsq6yMcNG0pXDPx/cy8bUaRJB6mMG0FWuAFCl\n/f2kbnngGhsz6r13ST3XxA/Enrj1W1LvOao/G7Pu+w2k/p+GTdmYfm27k7rhgUA2RqWnT8DRcyex\nMVX8K5H6zgN72Jjtv/1M6gF+/mzMyfpZpG75m6+QPLGBrrQdungnG1OlR31Snxo7no35Kz2V1D9J\n/IyNGf/aKFLftPsHNmba0tmkbknPYWM2/7yV1Ks0DiV13xp8FX9JUBNVtVw1LcBXoCpVjFqZylCH\nja9UtDMVmx4G/uarZbabq6IEALuJdlBQtC/jKoSVKoeZfTUrVGtqmQpUTz3vXuDFVKbm5fPHh3tI\ne3vSlbEAYGCqWZUwW+iq1XwL72JRGhwWuk3tDr5qNsdBX5t+Rj82xodpHy+F48NVFWtKUQWs9PzK\ny8ulJyjlY7qy75sqjwlgXFwctFot4uLikJKSgmnTpiE0NBTBwcGF5jObzXjppZdQt25dZGZm4oMP\nPsDatWvx9NNP39L6by19FARBEARBKOc4HI47+q8oTCYT9u3bh169ekGv1yM8PByRkZHYsWOHy7zt\n27dHeHg41Go1/P390aJFCxw7duyW20ReAQuCIAiC4NY4ytlIIGlpaVCr1ahatapTCw0NxZEjR4qM\n/eOPPxASEnLL2yA9gIIgCIIguDV2OO7ov6IwmUzw9Cz8it5gMMBk4j+RAIBt27YhJSUFXbp0uaX2\nAKQHUBAEQRAEN+dufAOYmJjo/H9ERAQiIv6tNTAYDMjLK/ztZG5uLgwGA7u8ffv2YcWKFRg7dix8\nfPhRXoqLJICCIAiCILg1dyMB7NGjBzstKCgINpsN6enpztfAZ8+eZV/tJicnY9GiRRg1alSZvP4F\n5BWwIAiCIAhuTnkrAjEYDIiKikJCQgLy8/Nx9OhR7N+/Hy1btnSZ9/Dhw5g7dy6GDx+O2rVrl1mb\nFNkD+O4ntJ3Hyx37kPpPybvZZbXp35nUuQHrAWBEv8Gkvjv2Ozbm8JHDpD5/DG1pAwDvLJhA6uoA\nvoz++Q60bcrcw7T1BgBMHUO3p65ORTYma9NpUj8XyH8sOn0xvQ1KJ2ar/9LfFGyfv46NWfDt56S+\nZgd/fHZ8t43U7SbeIsORS08bFfsWG/NR3sek7hvFd50f3fArqS/asoyNGTr5HVL/7dgBNiZhxVek\n/mK/l9iYDTs3k3rTBlFszKm/z5D6ycMn2Bjf+yqTesapNFLP8cpkl1USrplc7SI4+xGAt4jx9fJl\nY7iB6a15vP2Hw0ZfM2Yrb+Wh0/LWViWGdq4BwF/PDjP/wbvKg5nG2OoAAJjj4OvFX0v6MrRnMXrz\nx5Q7R5SsSaw2eppF4Zhyx0GlUehHYc4dpU/EVGp6eZztEcBvN3VNFeBt8CJ1q5W/D+fk0hY12bm8\ntZbSfZ3lNvTWlUcbmOjoaMTGxiI6OhpGoxExMTEIDg5GRkYGhg4dilmzZiEgIACrVq1CXl4e3n//\nfWdsvXr1MGoUbQ1WXOQVsCAIgiAIbk15HArOx8cHI0a4+hYHBgYiPv5f3+Rx48bdlvVLAigIgiAI\ngltTHnsA7zaSAAqCIAiC4NZIAuiKJICCIAiCILg15c0IujwgCaAgCIIgCG6N9AC6UmQC+M/6o6Q+\nfd1YUn/p/TfYZQX60YPGv/PaMDbmi7UrSP3zdXxV5s/f0IPZf6tQmXrxZ7rS1qtRFTbmk6/iSN16\nnq6UAoBxn0wj9fGv8dU8Hr50Nd17c+mKYgA48dcpUg+uUo2NOZ32F6k/2M+1LL2AlLSzpN6l5ZNs\nTDOmanX7b7vYmN0/uI6PCACjZ45nY4YPHELqEwbRVbsAoK1KVzUeP0e3JwDE9O1P6l9sWM7GWK/Q\nbu/31eBL/Lfs+5HUd4zYxMaMnT2F1Kck0+c7AOScziD1OpEPkHql6vw1UhJMua6VmdkqvsKyorEC\nqesVKnA9mEpKxUpO5rlhtfHVjdw0xYeQmqnytPMxSpWhHA4rvTyVjl+WXkvfg5TWb2cqrlUKZc3c\nsVOr1WyMRk1Xg+t1fI+PyZxP6orHh6voVcDBHDsVd6wVtsFms7ExmTlZpK5RqKLnMFv4iviMzEt0\nTK5CFb2J324Ou1LpeymRBNAV6QEUBEEQBMGtKY9VwHcbSQAFQRAEQXBrpAfQFUkABUEQBEFwayQB\ndEUSQEEQBEEQ3BqH0vAr9yiSAAqCIAiC4NZID6ArkgAKgiAIguDWSBGIK0UmgG98RFtmfLbiC1LX\naXgLBn+/inRMbdrOAQD6PdGT1B1mvrR84XdLSf3TtfGkDgB9h8eQ+u5Dv7AxaRfSSH3O8oVszJCX\nXyd1jR8/cPqoyWNIfc/hX9mYpATaGqT7oBfYmNQNh0k95OUObMzs96aT+qtj32Jjln+/ktR7tHmG\njcluRg82fmDjHjbmwy/nk7otm7cs8G9TmdQ/eoO33Bk8i7bwydyawsYYHw8l9d+OHmBj6tW8j9T/\nDuLXM37ASFJXuhXar9Hto3qEsVAphRUJvaCSzc7ZYtgUDF+5h4DDUnKTWLWBt47h2sSg469zu53e\nH4vNwsY4OPsaK78/Kg1zHHW81QoHZz8CAFoNbc9isfL7w8VYmbYBeOsYJZue0vQGOZg2ddgUzp1S\n5BzcuZiTd63EMWCONcC3AWffAwDmPNo+x57LH1M786xWum+odGWfrEkPoCvSAygIgiAIglsjI4G4\nIgmgIAiCIAhujfQAuiIJoCAIgiAIbo0kgK5IAigIgiAIglsjCaArkgAKgiAIguDWlMcq4JycHMTG\nxuLgwYMwGo3o3bs3WrRoQc67fv16rF27Fvn5+WjSpAliYmJKNdbzjRQZvXDqXFKPfKYlqX+zYwO7\nrKt7z5H6oNFvsjGL8Tmpm8/x1WfDJtGVyyH3hbIx3K+DqgF0VSgAHFu5j9TfOjCYjanW5n5Sv3Lx\nMhvz4Sezaf29aWzMjh+SSP2bdd+yMfV7Nif1lPNn2ZhKLcJI/fNvv2RjMtedJPVDoXTbAMCR3w6R\nuj2Xr/SDB11l5tW4KhtittDVbI37P87GPFjnAVJ3mPmPjvP+yCD1tTb++nnkwUhSVytUkGuCvEnd\nfo2v2jPc70/qB5fsIPX7H6sItGEXd0uo1Xxlaj4zaH2+ma5UBJQrHPkg+t7AnSsAoNeWvPKxLFFp\nSwNBAWcAACAASURBVF7Ry+0nAOTm59EhCu3p4UFXKGsUjimHTaEKODcvl9SVqqfVHvSjrzTnh4q5\nzwAAuCptpRgGh4VvA7uJOd8UqoCzPXJInavEVkRhd1Rqug1UfBH9baE89gDGxcVBq9UiLi4OKSkp\nmDZtGkJDQxEcHFxovuTkZKxZswbjxo1DxYoVMXPmTCQmJqJPnz63tP47fAgEQRAEQRDuLA6H447+\nKwqTyYR9+/ahV69e0Ov1CA8PR2RkJHbscP2hvX37drRp0wbBwcHw9vZGt27dkJSUdMttIgmgIAiC\nIAhuTXlLANPS0qBWq1G16r9vpEJDQ3HunOub0tTUVNSsWdP5d82aNZGZmYmcHLoXt7jIN4CCIAiC\nILg15e0VsMlkgqenZyHNYDDAZDKR83p5eTn/LogzmUzw8fEp9TZIAigIgiAIglvjKM2wLLdIYmKi\n8/8RERGIiIhw/m0wGJCXV/jb2tzcXBgMBpfl3Dxvbm6uU78VJAEUBEEQBMG9uQsdgD169GCnBQUF\nwWazIT093fka+OzZswgJCXGZNyQkBGfOnEGTJk2c8/n5+d1S7x8g3wAKgiAIguDuOBx39l8RGAwG\nREVFISEhAfn5+Th69Cj279+Pli1dHVZatmyJbdu2ITU1FTk5OVi1ahUee+yxW26SInsAq7aoQ+r9\nu/Ql9dcGDWKXNWvhPFJ//al+bMyURNqG5r3+w9iYTq88R+oXr9DWGwCw5L0FpG7Ppq0mAGDG2oWk\nPmvFx2zMQ/c1IPVGHeuzMR99TrfboE4vsjHGJ2l7Fn9jRTbmj42/knr3115gY5o1iCL1EaNGsjFR\nQ54k9Y7NO7AxlSsGkvrmTZvYmJmDJ5H6q71fYWPMZ2l7oXRvXzZmYFf6OHD2BwCQf+oqqetrVeBj\nGHsT6yXaogMAXn49htTX/7yZjalRJZjUvR73IvV6AfQ5XVLUWtfbEWclAgBmxgbGbOWvWdZKQ8mV\noxTOLdz3RmYrb01iYyxI1Dr+Nm2z0fuj1G6c1YnDwlug2MzMdqv5xrGrmTZQsFrh7FnUCg9UzqJG\n6ZsvtboUdi+cpYvS+eHBrYcP4pyCHFaFbWb3VWk99DSNB2/TY2bshTw8SRkA4FCX/JpT6UphY/Q/\nSHR0NGJjYxEdHQ2j0YiYmBgEBwcjIyMDQ4cOxaxZsxAQEIBGjRqhS5cumDBhAsxmM5o0aaLYu1hc\n5BWwIAiCIAhuTTmrAQEA+Pj4YMSIES56YGAg4uPjC2mdOnVCp06dynT9kgAKgiAIguDelMcM8C4j\n3wAKgiAIgiDcY0gPoCAIgiAI7o10ALogCaAgCIIgCO6NvAJ2ocgE8MKBs6S+Zsd3pB63eDG7rP79\n6OrLx0d0Y2Penz2N1DUBdEUiAKyb/xWpL1i6iI25nHWF1NtFtWZjxo4fS+p5R/hqY1X9SFKf/MZ7\nbEzIU3SFcH6NTDbGepmujEs/l83GRD3jWn4OACtGf8LG/N7vIKn71q3ExuybvZHUD3y7m43x8KJP\n1ce7P8HGDHl3KKkPnzmGjUn95zypf/PtN2zMU8N6kfr3X61nY7q9QseEVKnOxixc9TmpT55AVzsD\nwMj+b5I6VwEIABlBqaSuq2kk9Wp1ab0ssFqt7LR8C10Vbc6ldQBwWLmHAP9wUKrmZmOY9tVrdWyM\nQacn9Xym2hkAPJj1KB1fM1cJbePbwGGnpymsBvCgJ6rVfIWn1UZXG1uZTQb4bVOsamarcxVQ3Fka\nDz1939Jq+EevhTvnmfYEADDnqMagZUP8vOnrVunc0TPn6GUH/fwEANiYtlaqAlaoLhfKDukBFARB\nEATBvZEOQBckARQEQRAEwa0pb2MBlwekClgQBEEQBOEeQ3oABUEQBEFwb6QD0AVJAAVBEARBcG8k\nAXRBEkBBEARBENwcyQBvpsgEcMAbr5L6vj9+I/V+T9H2FgCg0tOfHP7wfiIfw5S3x25eysZo1PRu\nDer2Ehvz6MvtSD3j6iV+Pf4GUm8zlLe12X80mdRVnvyhOL/rBKlXigplY4b2fo3U3333XTYmpGoI\nqc9dy1v7DB82jNRbdG3DxlwNPUfqsz+dz8a89V/azuT7Rd+yMU1foI/prHHT2Zipc2eQerMxUWzM\n3MSFpH7/Yw3ZmO2//0zqkwaOZmNydv9N6uqBvK3GY/3psSN3/7CTjfHwoa0jmjdqQuq1/cPYZZUE\n6iPtnGs57Px2E+0N4uBsTgD2GaBkO6Ey0PcgJSsPk9lE6gYdfc8AeIsNnYJ1DGfZYVawjjFbaKsV\nKDQbtx6VRuEzcqZNvfSeJV7PNVOuwsYxspKVCDeNtQkCHIydiUrBnsUBOkat488dbhpnewSAfZJ7\nKpxvnB2Pkg2MTkPfG2x2/uTJtNN2ZQ5rKax4bgXJ/1yQHkBBEARBENwbSQBdkARQEARBEAQ3RzLA\nm5EEUBAEQRAEt0ZsAF2RBFAQBEEQBPdGEkAXJAEUBEEQBMHN+d/LAHNychAbG4uDBw/CaDSid+/e\naNGiBTlvUlISNm3ahLS0NHh5eaF58+bo06cPPDz4Qq0iE0Cuonb/NztI3atxFXZZDzSoT+q92/FV\ns2M+mkDq5zPS2Zipb44l9QlxdIUnAIx7ZTipD9ywgo3RaemKqMbhjdgYPx96AO4hplFsTGT4Q6S+\nbdkGNmb8xffp9T9QlY1p0fBRUv9o+cf8tj3RnNT37tzFxrR/pSupb9qzlY3pEfM8qR/76yQbsz9p\nD6nb85nB1gFM+JSuEHbk81Vu2Ul0VfOIRfS5CwBHTh+l17+Yr1Du9XZ/Us838xWfl7Ovknrrjm3Z\nmA2Tl5H6939+Q+rG5hbg0RfZ5RUXm8m1OlWp3R2WUlQRchWbCpWPsNMPDouZqaZVWJ7Fylc1c1WZ\n3gYvNsagp6s8bTaFdmPehWXmZPExZmZ5Cu/V1Myzg9tPALDb6WPKPYcAfl+VKm21TDVrvoqvtHXk\n09tmN/PnoUpDnwd5pjw2hmtTh0KFskpLP+SVqqetTOWu0vkGpt24CnYA0Bvoc9SUw7cBe77dCv97\n+R/i4uKg1WoRFxeHlJQUTJs2DaGhoQgODnaZ12w246WXXkLdunWRmZmJDz74AGvXrsXTTz/NLl+G\nghMEQRAEQShHmEwm7Nu3D7169YJer0d4eDgiIyOxYwfd+da+fXuEh4dDrVbD398fLVq0wLFjxxTX\nIQmgIAiCIAhCOSItLQ1qtRpVq/771i40NBTnztFvnG7mjz/+QEgI7e1bgCSAgiAIgiC4N447/O8W\nMZlM8PQsbJpuMBhgMtEm8zeybds2pKSkoEuXLorzSRGIIAiCIAjuzV3wgUlM/HeUs4iICERERDj/\nHj9+PP78808yLjw8HC+//DLy8gp/J5mbmwsD801lAfv27cOKFSswduxY+Pj4KM4rCaAgCIIgCG7N\n3agB6dGjBztt/PjxirEmkwk2mw3p6enO18Bnz55VfK2bnJyMRYsWYdSoUUW+/gXkFbAgCIIgCO7O\n/9grYIPBgKioKCQkJCA/Px9Hjx7F/v370bJlS3L+w4cPY+7cuRg+fDhq165drHWoHJwnwP8T8PwD\npK5mBoy3pF9jl2XNoMu+1X58CbmdsYEw1KnIxrwzmrZUmfYBb7Fhu0xvm4ee7yRVedHT/O8LYmNq\nVKWz8ofrNWBjNu2m7VHObjzExmgC6QHXrVf47wcefKYpqf++iLdnMdT1pyconFamI5dIfe7mL9iY\nA8fpff18zHw2RhvkTepdX3qOjTmSQldNHfv2FzaGG9Q8sF1dNubCqiOk7uHJn2+eDSuTeoWQQDZm\nXP+RpB6/MYGN6dXuWVKfsWweqT9ZswVmdKTXUxKCRjVx0RQHjGfsWRQtXTgXGA3/W1ilo6epOEsZ\nAA4bvW0qNR+jMtDH3teLf43D2UrptDo2xpRP3wM4yyAAMOUq2JYwaPX0M8Lbk74uAd7Sxapga2O1\n0XY8diWLGsYbzZzPWyrZcxn7KIX1qPS05Y3S+cad84rXArcJCk93bhuU7kE+zLFTsvbJZaxozHm8\n5Y7dRB/v85N4e7GiCHqbtjm7XaRN33vLy7jZB7BPnz5o3vy69VpGRgaGDh2KWbNmISAgABMmTMDR\no0ehvcGerl69ehg1ireYk1fAgiAIgiAI5QwfHx+MGDGCnBYYGIj4+Hjn3+PGjSvx8iUBFARBEATB\nvfkfNIK+3UgCKAiCIAiCe3MXqoDLO1IEIgiCIAiCcI8hPYCCIAiCILg30gHoQpEJYNTTdMnxnmV0\nZahvC957pmebZ0g9bsJcNuaB7nTlzuDuA9iYQW2fJ3WlHuCeHwwk9avZmWzMj19+R+qh1WqwMZH1\nHiJ1rjIPAE4voytQR8ZNYmNiExaT+vBRb7Mxej1dOTisz+tsTDJTnVuBqU4E+Iq+EYOGsDH5qfRA\n9T4tqrMx9hy6OnB9who2pt+AV0i9om8FNsZipdfz29c/sTFcBWu7/9IVuACw5/B+Uk/fwo/3+OZh\nuk2tl/hB4nd/uomOYSrIL7ULBjqyiys+XFUvg0rLvMBQqM7lHgJKFb1gii/tJqYqFICD2RcPptIX\nAFRWOiY3n6/A1etoBwUlcwe7g94htYp/IeTp5UWvR+GpamC2TalCWc1VXCtUdlts9HHIzePP8WvM\nNIe55FXn3LEGADCVu4pV5wrTOOx5zLnIVKMDYN//OSx8G2Tbc+hFqflttpvp+z1X6QsADibmVijC\n8OSeRF4BC4IgCIIg3GPIK2BBEARBENwb6QB0QRJAQRAEQRDcG0kAXZAEUBAEQRAEN0cywJuRBFAQ\nBEEQBPdG8j8XJAEUBEEQBMG9kQTQhSITwF2MJYQ+jLbF6NP+OXZZC8fMJvX63ZuxMafPppD6Gz2j\n2RjPxlVI3Z7FD/S9Jm4lqbfu9QQbU63lfaTevAE/6PSciTNJvUXPdmxMt/G0NcmRlKNsTFhoLVL/\n+BvaHgYAMn/6i9Ttl3iLmsGxo0n92x20RQ4AHNpAD5Id0LQmG/P8E91J/eO4T9gYh4W2ElDp+dPe\n6O1LxyjYUFTw9SN1w/3+bIw5NZvUd/+yh41p/xh9jqz57Ss25uXX6Oukgg+9zQD+r717D4+qPNcG\nfs8xM0kISIKCgkRLS/ziWYy0QTz1K9RWelARULeNgLKpeEg3oFYhoG7BU+phE63xAFoVLrC7VCu7\nuwqEKpaKpSCCKCdBQAjIIWTOM98ffmJ1nvsFoqiZ3L/r4rrMM/OsWbPWO2te15rnWZh8Q40ZH/nw\nzWb8+HApXdbBsNppONtlBNkN6PmR3uO1l5dJ89YXrDVIxtVig7ScYGMSADKkrU2KtE0CeDuTpshe\nmhPw2ePf52PbE/A7xj/jJW1lYvEYzQn4A2Y8Py9Mc1h7j3QL2n54/Px9ZpLksZSjdQxp7ZMhcdc6\nuD4LXvJZcLV0occ0V28QkuJ3jJ24l4xfV/scV1umFnK1LGqrdAZQREREcpvmf1k0ARQREZHcpglg\nFk0ARUREJMdpBvh5mgCKiIhIbtP8L4smgCIiIpLbWuEEsKmpCXV1dVi6dCmKioowePBg9OnTZ795\nEydOxPLly/Hss8/CSwrfgAOYABac3sWMn3fOeWb86Rem02WlIgkz3u+Mc2nOQ28+ZMY9Yb7qwSPt\nSs7Qt3kl2Y5X15nx15e/QXNYxeiaTfayACCxza7Om//kizSny7k9zfi2JXbVLgAcdvyRZnzMpdfS\nnL0X2hWFW3dsozlvvrPUjLsG3QXD7IreWRMepzkLjyo14z1OsLcNAKx8+R9mvPNJvNq4duLdZjz9\nEa+Evmvag2acjQ8A+J/Qy2a86bWNNKe5d8SMn3X5+TTnO92/bcaffolXDqeb7RvL/+8b88y49+jv\nAcfRxR0wj1H55wk6qoBJVaS1nE+wakl2w3oASKft7eF6nQyrDHVUPmbYOjgKIiNp+zPrEvfb2yAc\nDB30slyVw8mUvd1Y1a7rMbYsgFd3el2Vy2wdHDken/1YhjeXQCZJKsib7e9CAPCQanCv4zuPfR96\nAo4KZTKwvGR8ALza1+vlOS3iqhBusdY3A6yvr0cgEEB9fT3Wrl2LSZMmobS0FF27dqU5CxYscHYO\n+Feugm8RERGR1i/zFf/7gqLRKBYtWoRBgwYhLy8PZWVl6NWrFxoaGmhOc3MzZs6cicsuu+yAXkOX\ngEVERCSntaAt5Ndq8+bN8Pl86Ny5875YaWkpli9fTnOeeeYZ9OvXD+3b8z6v/0pnAEVERES+QaLR\nKMLhz/5sLRQKIRq1f460evVqvPvuu+jfn9+84vN0BlBERERy29dwCnDGjBn7/ru8vBzl5eX7/q6p\nqcGKFSvMvLKyMlRVVSES+ezvvpubmxEKZf9WN51Oo76+HldccYXz9/efpwmgiIiI5Lav4RLwwIED\n6WM1NTXO3Gg0ilQqhS1btuy7DLx+/Xp069Yt67mRSARr1qzBb37z8e120///1pYjRoxAdXU1ysrK\nzNfQBFBERETkGyQUCqGiogLTp0/HiBEjsHbtWixevBi333571nMLCgrw29/+dt/fjY2NuPnmmzF5\n8mS0a8e7Uex3Atj89y1m/Pybv2/GX17wCl3WtbU3mfG6Zx6lOaNGjjLjU57lOef2PsuMv/nOP2lO\napd9g/I983mrld3kht5bFrxHc35YfYkZ/2j3TpqzbrO9Dv5i3tZm6IDLzfivr6ymOazNQP4pR9Cc\ngedfaMYX/OM1mvPSoj+Z8cBRfKBu2bHVjPc48hias3TjHjO+YZPdugYAgt3sdYjtsFuwAMAtt/za\njFeNGEZzWHuTifX30Jypf3rWjK+f/zbNWbbafiwW4W1t7niq1oz/evB1ZnzbuV2AA//ZCWW1QfGQ\nti0Ab8tRUFBAc/x+e4wng7zNyF6v3bopk+KnFDys/UfC0ZaDLK4lOZ48vt1Yuxe2bQDensXVbmJv\nhLSocVyKCwQDZrwg7NinPtICxdUGhrXwcbUfIePN1aaHjRGP63JkC9aNbTdPwNESibRuSaf5Po0n\nSPuaNO+F4xy/hKstU4u1tioQAMOGDUNdXR2GDRuGoqIiDB8+fF8LmMbGRlRXV6O2thbFxcWfKfyI\nxT6ez7Rv3/6L9QEUERERadVa3/wPhYWFGD16tPlYSUkJpk2bZj52+OGHY/p03pP5E5oAioiISE5r\nhfO/Q04TQBEREcltrfAS8KGmCaCIiIjkNs3/sqgRtIiIiEgbs/8zgKSa7KrvX2rGC07vbMYB4Phj\nyR3jyU3dAaC4fUczvvuV9TQnXmFXJLluQn74+XafnI/++QH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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, loss_func=None, 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, score_func=None, scoring=None,\n", " 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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UlA4fZ3fCmjZtml3lOtJeodVqSUhIYNWqVTz22GMUFBSQm5vLn//85zZlJ06c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\n1YU1NDQo999/v7J//35nh2LT66+/rix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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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ZxIvy9yWUIu9zkl/jHXvdpV6iUfevB+spCoszfmMMwONMyogXLM74jTEAv89Z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\nePXVV5FOGxU0AKxYsQK///3vcfvtt6O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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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PNjy8AcQo1TnRSDbpqpzD6b+l31eCacXMvL+8WSalu4w3Xhom2LTVZatmjdF4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wAAAg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\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": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }