{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem formulation\n", "\n", "This section defines a problem that the later section tries to solve. If\n", "you want to go straight to the solving, see the sections:\n", "[Monte Carlo integration](./monte_carlo_integration.ipynb),\n", "[point collocation](./point_collocation.ipynb),\n", "[pseudo-spectral projection](pseudo_spectral_projection.ipynb), and\n", "[intrusive Galerkin](./intrusive_galerkin.ipynb). They all are based on the\n", "problem described here.\n", "\n", "At the core of any forward problem, stochastic or otherwise, you will find\n", "the model predictor or model solver. Typically most problems starts with a\n", "set of governing equations that needs to be solved. The model predictor will\n", "in this case represent the forward predictor that allows the user to create\n", "predictions. However as we are trying to address uncertain parameter, making\n", "a single solution will likely not do. Instead the parameters needs to be an\n", "input in the model predictor, and the governing equations have to be solved\n", "specifically for the provided input.\n", "\n", "In other words, we expect the model predictor to be deterministic. It should\n", "typically expect some form of `parameters` vector as input. And to keep\n", "things simple, we assume that the return value for the predictor is either\n", "scalar or some sort of `numpy.ndarray` vector.\n", "\n", "As these tutorials are all meant for demonstrative purposes only, we keep\n", "things simple. We limit our problem to a simple ordinary linear equation:\n", "\n", "$$\n", "\\tfrac{d}{dt} u(t, q) = - \\beta u(t, q) \\qquad u(0, q) = \\alpha\n", "$$\n", "\n", "the number of parameters to two: initial condition $\\alpha$ and rate $\\beta$.\n", "We define this model over the domain $t\\in [0, 10]$. For simplicity and to\n", "assess accuracy, we use the analytical solution to this problem:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:40.905417Z", "iopub.status.busy": "2021-05-18T10:56:40.905048Z", "iopub.status.idle": "2021-05-18T10:56:40.913970Z", "shell.execute_reply": "2021-05-18T10:56:40.913558Z" } }, "outputs": [], "source": [ "import numpy\n", "\n", "coordinates = numpy.linspace(0, 10, 1000)\n", "\n", "\n", "def model_solver(parameters):\n", " \"\"\"\n", " Simple ordinary differential equation solver.\n", "\n", " Args:\n", " parameters (numpy.ndarray):\n", " Hyper-parameters defining the model initial\n", " conditions alpha and growth rate beta.\n", " Assumed to have ``len(parameters) == 2``.\n", "\n", " Returns:\n", " (numpy.ndarray):\n", " Solution to the equation.\n", " Same shape as ``coordinates``.\n", " \"\"\"\n", " alpha, beta = parameters\n", " return alpha*numpy.e**-(coordinates*beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then use the model by passing only the two model parameters:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:40.916738Z", "iopub.status.busy": "2021-05-18T10:56:40.916410Z", "iopub.status.idle": "2021-05-18T10:56:40.990308Z", "shell.execute_reply": "2021-05-18T10:56:40.990581Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib import pyplot\n", "\n", "pyplot.plot(coordinates, model_solver([1.5, 0.1]))\n", "pyplot.plot(coordinates, model_solver([1.7, 0.2]))\n", "pyplot.plot(coordinates, model_solver([1.7, 0.1]))\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Changing the model parameters changes the shape of the solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Uncertain parameters\n", "\n", "Even though `model_solver` is assumed to be deterministic, we are here going\n", "to assume that there are uncertainty in the model parameters, which in turn\n", "means there is uncertainty in the model.\n", "\n", "For our tiny example, we assume that the `parameters` can be described\n", "through a bivariate uniform probability distribution:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:40.993156Z", "iopub.status.busy": "2021-05-18T10:56:40.992834Z", "iopub.status.idle": "2021-05-18T10:56:41.000839Z", "shell.execute_reply": "2021-05-18T10:56:41.000528Z" } }, "outputs": [], "source": [ "import chaospy\n", "\n", "alpha = chaospy.Normal(1.5, 0.2)\n", "beta = chaospy.Uniform(0.1, 0.2)\n", "joint = chaospy.J(alpha, beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This distribution can be visualized as follows:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.003405Z", "iopub.status.busy": "2021-05-18T10:56:41.003091Z", "iopub.status.idle": "2021-05-18T10:56:41.094603Z", "shell.execute_reply": "2021-05-18T10:56:41.094258Z" } }, "outputs": [ { "data": { "image/png": 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uTkhOZYFXtc8jrxar2kdaTclfJE6seL+UFe+XAoHn8BVpCXX7iASRM208xSsf4swHSyle+RA508Y7HZJIxOiyQSSAnGnjWTQ/m7xV29m0+0NXXf38bAAK1nzkcHQibacrf5EAcudOJ2/V9qZDRs+d7nRoIhGh5C8SgBncN8iQ0X0dikgkspT8RQKwZUcD1tXbsqMORSQSWUr+IgHkv/gOi2eO8q2rnzmK/BffcTo0kYjQDV+RABpu6i6YOx0z+Cps2VEWLi3UzV7pMJT8RYIoWPORkr10WOr2kYSj+n0RXfkntIlDezLj8v4M6d2ZvccreH3zQd4rPeF0WFHVkvr9nGnjyZ07HTO4L7bsKPkvvqNvAtJhKPknqIlDe3LT6AE8sGKLZ3KQJbPHAvDnHcdCtI5f3vX7gKd+f8Hc6T6JXQ95SUenbp8E9Y1R/XlgxRafh5geWFHCzeMudDq0qAq3fr+jPeR14xUXsfrBa9n51Nd5c/6X+XrWBU6HJA7TlX+CGtyrc8AkOCSzi0MRtY99R04xYVim58ofAtfvu04SH/qsc50krmqXOCPpW1cO5P4ZhtyVJZ5vefmzxpKS0onVWw85HZ44RFf+Cars5LmADzHtPV7hUETRlzM1i86d01gye6xP/f6SWWOa1O9H4yGvnKlZFL9yL2fWP0zxK/eSM2VMq/fVEvfccCm5K0t8vsXkrixh7nXD2+X4Ept05Z+g3tp+mCWzs5r0+f+h+IDToUVN7p1Tmbe8hH7d03n4m6MY2b8bZccrOF9X26QfP//Fd1js6fN3T5g+cxQLlxa26tg5U7NYdO+Nvvu7+wZISaVg3SeR+PWCGjmge8BveSP6dYvqcSW2hZX8jTHXA9nAYeC8tfaRANvMAR4H5llr3/Jab4BvA+eA64CHrbUfRCB2aYONe8oBeHzWWE+1zx+KD3Toah8zpA+bdm+itv48/73FdZJLSeqEffSGJttG+iGv3DunBr7RfPs1UU/+Ow+dDtjVVXrkTFSPK7EtZPI3xnQBngdGWWurjDErjTFTrLVrvbYZjuvEUObXNhl4GrjRWltvjHkZqI3obyCttnFPOes/d10RVlXXORxN9Nm9x8Lq728QyYe8Gk483jbtPo4Z1Dsi+2/Oc6t3kD9rbJM+/+fW7oz6sSV2hXPlPwnYY62tci//FZgBeJK/tXYXsMsY83O/thOATsA97pPIMeDf2xy1SCvk/7aIxf5dL23oymmJoCeefdH/pvVG8X6SkpN5+MZRjBzQjc8Pn2Hpmn/w508PR/3YErvCSf79gdNey6fc68IxFNfJ49vW2nJjzCtANfBSS4IUiYSCoi1QV+PIeD3/+8EOnv+XCXTLSGXn4TOs2XaQb2VdyMIX1oZuHAFvfnyANz92dXWlpaW4f6reI5GFk/wPA929lnu414XjFPCZtbbcvfw+8M8o+YtDnBivJ2dqFjMmj+UHr3zk+cbxzC3jWLlmc9T7+0WCCefUvwEYaoxJdy9/BXjbGJNpjOkRou3fgT7uvn9wfRPY0bpQReKT983ehlLL+17bzD9fNdLp0CSBhUz+1toK4IfAs8aYx4AS983ePOBHAMaYTsaYn+FK7nOMMdPcbY8DucAzxpiFQD9gaVR+E5EY5brZG+ip4swgLUSiL6xST2ttEVDkt+5Br9fngcfc//m3XQWsaluY4rQppi+3/Z/BDO/blV1Hz/Lb93azZnv83TB0YrC24FVGx5tpJRJdeshLQppi+vL9rwzlwdcbSwWfuNk1CNxbmw86HF34fB+0ar/B2oJWGS1bHbVjioSi5C8h3TZxMA++XuLzgNKDr5ew6Fuj4yr5B33Qym9Ez0grKNoCwII7p2KGXIUtO87CZaspWLsV0jKidlyR5ij5S0jD+3QNMjxAV4ciap2gD1q1w2BtBUVbXCeB1PTQG4u0AxX6Ski7jp0NOMhZ6ZGzDkXUOg19797aOlibSLxS8peQfr+xjCdu9h0J84mbx/Kf7+92OrQWyf9tEYtnjvL5PRbPHNVkRE+RRKBuHwlprXVdGT9602hPtc+v15XGXbWPk0/4isQaJf8I690lhcxuqfTqksqJszUcPV3N8bPxP5bdWnuU1dsak31NTXwOBOfEE76x5MYrLuLHXxvJxf27UXrkDC+u38Xaz9TtlYiU/COoZ5dkuqYncfd/NT7G/6tvj2PkgC6cqKjlUHkVR87UOB2mJKgbr7io6YxeN48lJTkp7r7FSdupzz+CenVJ4b7XNvs8xj/vD5vZefgs97z6EX26pdKvW6rTYUqCunvqyKYzer1ewr9ePczp0MQBSv4R1KtLasCSyJH9u7Gh9Bjzl29mQE+V+okzRg7o1iFKdiUylPwj6GRFTcBSwp2HXTMmbdp9nMwuuvIXZ+w8dKZDlOxKZCj5R9DJilqeuWWcTylh/qyxLFvnmjFpwrBMjleoz1+csaxoJ/mzfEt28+OwZFciQzd8I6i8oo76+vMs+854enVJ5XRlLf/vr7v409aDTBrRh6VzxnGovCr0jkSioGEyl0e+OcpT7fPcn3eq2idBKflH2ImKWk5U1ALn6JGRzHcmDuPHUy7h+NkaVft0AE6MChpJb358wFPZ0zCTV2pqcnNNpINS8o+i42drPTX+VXX1DkcjbZUzbTyL5me3+6igItGgPn+RMOXOnd5kRq68VdvJnTvd6dBEWkzJXyRMZnDfIDNy9XUoIpHWU/IXCZMtO6pRQaXDUPIXCVP+i++0aFTQnKlZFL92P2f+9kuKX7ufnKlZLTpezrUjKV52C2f+eBfFy25h9tUjIvFriAC64SsStoabuuGMCuo7ZeQm183he2+E5FTXDF4h5FxnWHTHJPIKtzVO/XjbBABWvF8a2V9MEpKSf4wa3CuDS/p2pV/XdI6cqeLTI2fYoScxHRfuqKBBp4z83uSwkn/urRPJK9zm275wKwtmj1Pyl4hQ8o9BA3tmMKR3Bvf9YbPnqu/pOVnU1p2n9HiF0+FJGIJPGZkZpIVf+0G9At9cvqhHxGKUxKY+/xg0vE8XfrJ8i09J4U+Wb2H0Bd2dDk3CFHzKyONBWvi133cycPsDpyIWoyQ2Jf8Y1LdrWsCrvv7dNCJovAg6ZeTv1oXX/tWNLM4e7ds+ewz5KzZHN3BJGOr2iUFHz1YzYVimp78XXFd9h89oXKD21JahHAqKtgCw4M6pmCFXYfceY+Gzb1Lwv5+F1369hZRUFsz5EmZgT+z+chb+fpP6+yVilPxj0K5jFTw9J4ufLN/i0+e/7YvTToeWMCIxlENB0RbPScAjNfxvbwXv7qTg3Z2e5U4taCsSipJ/DNpfXknN+Xqe+fY4n2of3extP95DOYBXtc7c6RrHRzoEJf8YVXaykrKTlVRrQDhHuIZy+NBnnata5yqHIoptE4f25MZR/RnUqzP7Tp6j6B/HKN4X+pvqZf27ctXgXgzons6h01VsP3RaFzntRMlfJICGoRz877toKIemJg7tyU2jB/DAisZuyidzXE8zb/si+LMpl/XvyoRBPfnJct+SZoD9pyrbJfZEpmofkQBaOpRDIvvGqP48sMK3NPn+gi187dLmB7ybMLgnPy1QSbNTdOUvEkBLhnJIdIN7dQ5YmjywZ0az7S7onqGSZgcp+YsEEe5QDomu7OS5gF1k+8ub77r54nSlSpodpG4f6XBypoxp02ia0jJvbT/MktlZPl1kT+Zk8T87mr8/sqmsnKdyfNuppLn96MpfOpScKWNYdPcNTUfThKY19xIRG/eUA7D45rGeap937FGK950mPSX49eWnh103g5+eM65JtU9z7SQylPylQ8n93uTA9fl3TlXyj6KNe8r5aH/jFXt6mJPCf3r4LHtOnvMsZyjptxt90tKhmMGZgUfDHNLHoYhEYlNYV/7GmOuBbOAwcN5a+0iAbeYAjwPzrLVv+b3XGfg78D/W2vvbHLVIELbseOD6/L3HmmklknhCXvkbY7oAzwPzrbUPA2ONMVP8thmO68RQFmQ3jwEfty1UkdDyf7cucH3+b4ucDk0kpoRz5T8J2GOtbai/+iswA1jbsIG1dhewyxjzc//Gxpjb3G3GAt3aHLFIMxpmyVpwxz/7jqap/n4RH+Ek//6Ad+3VKfe6kIwxlwOXWWv/zRgzthXxiTQrZ/Ll5N52NWawa6KU/N+to2DtVgpWfxi6sUgCCyf5Hwa8n7fu4V4XjplApTEmD7gaSDPG3GetfaZFUYoEkDP5chbddT15q7wmOb/7BgAlf5EQwkn+G4Chxph0d9fPV4BfG2MygVprbdB55ay1v2h4bYzJALop8Uuk5N5+DXmrtgWeJF3JX6RZIW/4WmsrgB8CzxpjHgNKrLVrgTzgRwDGmE7GmJ8BQ4E5xphp3vswxswCrgUmGmO+HeHfQRKUGdQ7cFlnmJOkiySysEo9rbVFQJHfuge9Xp/HVdHzWJD2K4GVrQ9TpCm770SQYZfDmyRdJJHpIS+JW/kvv8fimaNbPUm6SCLT8A4StwrWfQLAAq9qn4XLVnvKPUUkOCV/iWsF6z7RsMsiraBuHxGRBKTkLyKSgJT8RUQSkJK/iEgCUvIXEUlASv4iIglIyV9EJAEp+YuIJCAlfxGRBKTkLyKSgJT8RSIgZ9p4ilc+xJkPllK88iFypmY5HZJIszS2j0gb5Uwbz6L52eSt2s6m3R+6ZhS790YAzR0sMUtX/iJtlDt3OnmrtrOh9Bi19ec9M4rl3jnV6dBEglLyl7iUM/lyin93F2eK8ih+5V5ypoxxLBYzuG/gGcWG9HEoIpHQ1O0jcafZidsdGMvflh0NPKPY3mPNtBJxlq78Je54T9zu083yvcmOxJP/4jssnjmq6Yxivy0K3VjEIbryl7gTaxO3N0wms2DudMzgq7BlR1n47Ju62SsxTclf4k4sTtxesOYj3xnFUjMci0UkHOr2kbijidtF2k5X/hJ3PBO3334NZlBvTdwu0gpK/hKXCtZ94jkJUF3pbDAicUjdPiIiCUjJX0QkASn5i4gkICV/EZEEpBu+IhIXBvbMYHifLvTtmsaxs9XsPXGOg6eqnA4rbin5i0jMG9wrg6G9OzPvDx97xnNaOmccAMfO1jgbXJxSt4+IxLxL+nZl/vLNPuM5zV++mSG9OzsdWtxS8heRmNeva3rA8Zz6dE1zKKL4p+QvIjHvyNkqJgzzHbhvwrBMjp2tdiii+KfkLyIx7x9Hz7J0zjif8ZyWzhnH3hPnnA4tbumGr4jEvLKTlaR2SuJX376iSbVPWrKuYVsjrORvjLkeyAYOA+ettY8E2GYO8Dgwz1r7lnvdxcBjwEfAIOCYtXZRhGIXkQSyv7yS/eWucZyU8Nsu5CdojOkCPA/Mt9Y+DIw1xkzx22Y4rhNDmV/zTOA1a+0Sa+084BZjzJURiVwkAc2+egQf/iqbE6/ext+f/CbZE4c6HZLEqXCu/CcBe6y1DU9T/BWYAaxt2MBauwvYZYz5uXdDa+0mv30lAWdbH65I4pp99QgW3TaBvMKtjXMXu2vdCzfucTY4iTvhfHfqD5z2Wj7lXtcixpiZwBpr7WctbSsikDt7HHmFW33nLi7cyk9vGu10aBKHwrnyPwx091ru4V4XNmPMZGAycF9L2olII3NRj4C17pde2MOhiCSehXPlvwEYaoxJdy9/BXjbGJNpjAn5V2eMmQFMA+YBFxhjJrU6WpEEZg+cCljrvuPgKYcikngWMvlbayuAHwLPGmMeA0qstWuBPOBHAMaYTsaYnwFDgTnGmGnu9VcCy4GJwDrgDcBE4xcR6ejyV2xmcfYY37mLs8fw1B+3OR2axKGwSj2ttUVAkd+6B71en8dV0vmY3zbFQLe2hykiK94vBWDB7HGYi3qy40A5jy7frJu90ip6yEskjqx4v5QV75eSkur6p9vwU6Sl9KSEiEgC0mWDQwZ0T2NgrwwyuzQ+qr5H45SISDtR8nfAgO5pDOiezj2v+k5MUVt/3vP4uoi/2VePIHf2OMxFPdhx4BRLCkv446Z9ToclcUrJ3wEDe2Vwz6sfs6H0GIBnYopfffsKJX8JKOfakU2f7r31SpKSk3XDV1pFff4OyOySFvBhnb6amEKCyJ3zJT3dKxGl5O+A4xXVAR/WOaqJKSQIM7Cnnu6ViFLyd8D+k5UBJ6bYdazC6dAkRtn95Xq6VyJKff4OOHTadYX/3K1X+FT7qL9fgslf/iGL7/iyb59/9hgeXb45ZNtvXTmQe24wjBzQjZ2HzvD8ulL+tOWL6ActMU3J3yGHTldz6HQ11XX1TocicaDg3Z2QnOp+utdV7fPIq8Uhq32+deVAHvzmZeSubDxp5M8aC8CfP23R+IwtcuWg7nzt0r4M7JnBgfJK3tt9gpKDZ6J2PGk5JX+RONHwdC8Q9hO+99xwKbkrt/pUluWuLOGRb46KWvK/akhPppu+3F+wxXPCeTInC4AdRzSdR6xQ8pcWmXpZP+748hCG9+1K6ZGzvLi+lNVbDzkdlgQxckD3gDeKL+4fvSG3pv+TK/F7n3DuL9jCkpwsJf8YouQvYZt6WT/uunYYD75e0tiFcLOrC+G/iw86ElPO5MvJve1qzOBMbNlx8n+3joK1Wx2JJRbtPHSaCcMyPYkYXDeKPz8cvS6YQb06BzzhXNgjI2rHlJZTtY+E7Y4vD+HB10t8as1zXy9h7nXDHYknZ/LlLLrreh5dsxPzs9U8umYni+6+gZwpYxyJJxY9t3oH+bN8h4HOnzWW3/ylNGrH3HfyXMDKpIOnVNAQS3TlL2Eb3rdrwCu6Ef2cGbU79/ZryFu1zad7IW/VdhZ8bzIFqz90JKZY80bxfgAevnGUp9pn6Zp/8KctX5CWFp1rv3c+O8qTOVlN+vzX7zoRleNJ6yj5S9h2HT0bsAuh9IgzVRxmUO+AJyMzODNIi8T0RvF+3i5pvC+Tlhbdf/Yf7C0nJbkT+bOzPNU+63e5qn0yUjpF9dgSPiV/CdtLf9vLEzePbdLn/9yfdzoSj913IuDJyJYdb6aVtIfifacp3nea9BTXt4uMVPUwxxolfwlb0adHAHj0ptGeap/n/rzTsWqf/JffY/Fd15O3alvjg08zR7Fw2WpH4hGJJ0r+0iJFnx6h6NMj1NTUAXh+OqFg3ScALPCq9lm4bLWqfUTCoOQvca1g3ScUrPnI6TBE4o464kREEpCSv4hIAlLyFxFJQEr+EvNyrh1J8Qvf5czb8yh+4bvkTL7c6ZBE4p5u+EpMy7l2JIvumEReoVc5513XA43VPk7LmTae3LnTMYP7YsuOkv/iOxT8JTZiEwlGyV9immvuWv8hHLax4PZrYiL550wbz6L52eSt2s6m3R+6Tk7zsyE5lYKiLU6HJxKUun0kpgWbu9YM6u1QRL5y504nb9V234nVV20n986pTocm0iwlf4lpweautftiY5AwM7hv4JPTkD4ORSQSHiV/iWn5yz9kcfZonyGJF88cTf7L7zkdGgC27Gjgk9PeY0FaiMQG9flLTCt41zVo3IKcKzGDemH3nWThC3+Oif5+gPwX32Gxp8/fa3yhZ990OjSRZin5S8wreHcnBWu3Na6oPudcMH4ahpZYMHc6ZvBV2LKjLFxaqGofiXlK/iJtVLDmo6bjC6VqykKJberzFxFJQEr+IiIJSN0+ErNyrh1J7pwvYQb2xO47Sf6rGylYb50OK67deMVF/PhrI7m4fzdKj5zhxfW7WPvZUafDEgco+UtMmn31CBbd9iXfYR2+fy0ABUWbnQ0uTt14xUXcP8OQu9J3Gs6U5CTWbD/sdHjSzsJK/saY64Fs4DBw3lr7SIBt5gCPA/OstW+1pK2Iv9zZ45oO61C4jQW3TlTyb6W7p44kd2WJz2ea+3oJi741Wsk/AYVM/saYLsDzwChrbZUxZqUxZoq1dq3XNsNxJfeylrYFSEnq1HyQfu/X1p9vuk1yctD2tXVNtyfVd7Gmrp7mboEEOmaz+wdq6+ubrKsLsG2gffvv039fgY5ZVee7TXV94xSL1f7v+S1X1Yd4v7ZxubLW972Kat9l//cra31jraxp+rlU+bUxFwUf1mHW92Y0ae/aR+gpJauqoz/tZHpa8L9FzzYpwbdJS2n6d5ie2nT79ADb+U+UnpHS+G9n5IBuAT/Ti/t15Y6vDndv79ve+xhpyX7vJfku+7/fZDnJ93dI93s/Jdn333lKUvPvu7Zpui45wHaB9hdsn83t21tqcuhbps3tvzXHjKRwrvwnAXustVXu5b8CMwBPArfW7gJ2GWN+3tK2AN0z2vE3lrhwurJm94RhmUMbrlLB9eRsRXXtnlf+JWuYc5HFr2Cf6dnq2j33Xj18mHORiRPCSf79gdNey6fc68LRlraSwLpnpA77w9yJTofRoegzFW/hlHoeBrp7LfdwrwtHW9qKiEiUhJP8NwBDjTHp7uWvAG8bYzKNMT1a07Z1oYqISKR0On8++I3MBsaYqcDNwBGgxlr7iDHmCeC4tXaxMaYT8BBwJ/A+8Iq1dk2wttH5VUREJFxhJf9IMMZcADwGZFlrJwR4PwlXqehpYBjwW2vtxnYJrp2F8VncAUwEPgfGA89Za//WrkG2k1Cfhdd21+EqFBhnrd0WbLt4Fs5nYYz5LtDH/V+WtfYb7Rhiuwnj30hv4AVgC3Ap8L619t/bN8r2YYy5GNdn8REwCDhmrV3kt00G8CSwH7gEWGyt3dHcfttzeIergTeAYJU9OUAPa+0vgFzgZWNM6Jq5+BTqsxgI3GetXQI8g+uPvKMK9VlgjOkPzAH2tVdQDmn2szDGXAMMtdY+ba19CPi39gyunYX6u5gLHHTni/uA59wXkB1RJvCatXaJtXYecIsx5kq/be4D9lprfwksBX4baqft9mFZa1/Ht/LH3wxc9wiw1h4HKoFR7RBauwv1WVhrf2GtrXQvJgFn2iUwB4T6LLy+ET7UbkE5JIx/I98Bkowx84wxjwMd9eIonM/iENDP/bofsNla2/QBkg7AWrvJWvuG16ok4KzfZt75cyuQFeqebCydKVUW6sd9L2Ue8BOnY3FQHvDv1trYmLfRWUOBIdbaX+H6ir/K3f2RiF4B0owxvwZeBH7tcDztwhgzE1hjrf3M760W589YSv4qC/XiTvxLgJestRucjscJ7n7M0cBkY0we0BO40xgzxdnIHHMK+Dt4vh1/AWQ5GpFzngCKrbU/AqYDvzDGdMieggbGmMnAZGB+gLdbnD8dHdjNGNMV6GKtPYKrBPRa4PfGmEwgA9juZHztyfuzcN/rWAqstNauN8bMstaudDjEduP3d3Gr1/of4CoE6JA3fAPx+yzWAhe71ycBFwClDobXrvw+i8FACYC19pwxphxIb659PDPGzACuwdUTcKExZihggVpr7Slc+XMS8J4xZgywxb0+qPas9rkOuB24AfgN8BTwr8AYa+0P3H/MvwQqgCG4vup31GqfUJ/F07jKYxv+YV9srR3sSLBRFuqzcG+TiqsI4KfA74HnrbUdbp7EMP4u0oB84BiuooC/W2tfcijcqArjs7gMVwXMx7i6N45bax92KNyoct/cXQ986F7VFVgGXE5juX1nXF2BB4GRwOOhqn3aLfmLiEjsiKU+fxERaSdK/iIiCUjJX0QkASn5i4gkICV/EZEEpOQvIpKAlPxFRBLQ/wd9BX6wHt/gPwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "grid = numpy.mgrid[1:2:100j, 0.1:0.2:100j]\n", "contour = pyplot.contourf(grid[0], grid[1], joint.pdf(grid), 50)\n", "\n", "pyplot.scatter(*joint.sample(50, seed=1234))\n", "\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model evaluations\n", "\n", "Random samples created from the distribution can be passed to the model\n", "solver, creating random realizations of the model solutions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.096935Z", "iopub.status.busy": "2021-05-18T10:56:41.096620Z", "iopub.status.idle": "2021-05-18T10:56:41.314850Z", "shell.execute_reply": "2021-05-18T10:56:41.314473Z" } }, "outputs": [], "source": [ "parameter_samples = joint.sample(10000, seed=1234)\n", "model_evaluations = numpy.array([model_solver(sample)\n", " for sample in parameter_samples.T])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.317299Z", "iopub.status.busy": "2021-05-18T10:56:41.316866Z", "iopub.status.idle": "2021-05-18T10:56:41.891705Z", "shell.execute_reply": "2021-05-18T10:56:41.891418Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.plot(coordinates, model_evaluations[:1000].T, alpha=0.03)\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reference solution\n", "\n", "Our goal here is to describe the behavior of ``model_predictor`` with only\n", "having a black-box evaluation of the function available.\n", "\n", "To be able to assess how well the various methods works for this example, we\n", "asses how well the various methods is to estimate the _mean_ and _variance_\n", "for the model solution. To do so, we need the reference value to compare\n", "against. For such a simple problem, this can be done analytically:\n", "\n", "$$\n", " \\begin{align*}\n", " \\mbox E(u) =& \\frac{15 (e^{-0.1t}-e^{-0.2t})}t &\n", " \\mbox{Var}(u) =& \\frac{11.45 (e^{-0.2t}\\!-\\!e^{-0.4t})}t - \\mbox E(u)^2\n", " \\end{align*}\n", "$$\n", "\n", "or numerically:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.894255Z", "iopub.status.busy": "2021-05-18T10:56:41.893945Z", "iopub.status.idle": "2021-05-18T10:56:41.901041Z", "shell.execute_reply": "2021-05-18T10:56:41.901321Z" } }, "outputs": [], "source": [ "_t = coordinates[1:]\n", "\n", "true_mean = numpy.hstack([\n", " 1.5, 15*(numpy.e**(-0.1*_t)-numpy.e**(-0.2*_t))/_t])\n", "true_variance = numpy.hstack([\n", " 2.29, 11.45*(numpy.e**(-0.2*_t)-numpy.e**(-0.4*_t))/_t])-true_mean**2" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.903545Z", "iopub.status.busy": "2021-05-18T10:56:41.903230Z", "iopub.status.idle": "2021-05-18T10:56:41.960327Z", "shell.execute_reply": "2021-05-18T10:56:41.960014Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "std = numpy.sqrt(true_variance)\n", "pyplot.fill_between(coordinates, true_mean-2*std, true_mean+2*std, alpha=0.4)\n", "pyplot.plot(coordinates, true_mean)\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Error analysis\n", "\n", "To summarize how close a particular estimator is, we use the average absolute\n", "difference between estimated and true value. We can create a couple of helper\n", "functions to calculate this for us:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.962513Z", "iopub.status.busy": "2021-05-18T10:56:41.962195Z", "iopub.status.idle": "2021-05-18T10:56:41.969161Z", "shell.execute_reply": "2021-05-18T10:56:41.968821Z" } }, "outputs": [], "source": [ "def error_in_mean(predicted_mean, true_mean=true_mean):\n", " \"\"\"\n", " How close the estimated mean is the to the true mean.\n", "\n", " Args:\n", " predicted_mean (numpy.ndarray):\n", " The estimated mean.\n", " true_mean (numpy.ndarray):\n", " The reference mean value. Must be same shape as\n", " ``prediction_mean``.\n", "\n", " Returns:\n", " (float):\n", " The mean absolute distance between predicted\n", " and true values.\n", " \"\"\"\n", " return numpy.mean(numpy.abs(predicted_mean-true_mean))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.971268Z", "iopub.status.busy": "2021-05-18T10:56:41.970947Z", "iopub.status.idle": "2021-05-18T10:56:41.978143Z", "shell.execute_reply": "2021-05-18T10:56:41.977846Z" } }, "outputs": [], "source": [ "def error_in_variance(predicted_variance,\n", " true_variance=true_variance):\n", " \"\"\"\n", " How close the estimated variance is the to the true variance.\n", "\n", " Args:\n", " predicted_variance (numpy.ndarray):\n", " The estimated variance.\n", " true_variance (numpy.ndarray):\n", " The reference variance value.\n", " Must be same shape as ``predicted_variance``.\n", "\n", " Returns:\n", " (float):\n", " The mean absolute distance between\n", " predicted and true values.\n", " \"\"\"\n", " return numpy.mean(numpy.abs(predicted_variance-true_variance))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which we can apply to our little problem:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.980188Z", "iopub.status.busy": "2021-05-18T10:56:41.979876Z", "iopub.status.idle": "2021-05-18T10:56:41.987877Z", "shell.execute_reply": "2021-05-18T10:56:41.987539Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.003705159671179502, 0.0006474753373452826)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(error_in_mean(numpy.mean(model_evaluations[:100], 0)),\n", " error_in_variance(numpy.var(model_evaluations[:100], 0)))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:41.990206Z", "iopub.status.busy": "2021-05-18T10:56:41.989897Z", "iopub.status.idle": "2021-05-18T10:56:43.659316Z", "shell.execute_reply": "2021-05-18T10:56:43.659022Z" } }, "outputs": [], "source": [ "indices = numpy.arange(100, 10001, 100, dtype=int)\n", "eps_mean = [error_in_mean(numpy.mean(model_evaluations[:idx], 0))\n", " for idx in indices]\n", "eps_variance = [error_in_variance(numpy.var(model_evaluations[:idx], 0))\n", " for idx in indices]" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2021-05-18T10:56:43.661468Z", "iopub.status.busy": "2021-05-18T10:56:43.661194Z", "iopub.status.idle": "2021-05-18T10:56:43.903571Z", "shell.execute_reply": "2021-05-18T10:56:43.903842Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pyplot.semilogy(indices, eps_mean, \"-\", label=\"mean\")\n", "pyplot.semilogy(indices, eps_variance, \"--\", label=\"variance\")\n", "pyplot.legend()\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This solution will be used as a reference in the later sections like:\n", "[Monte Carlo integration](./monte_carlo_integration.ipynb),\n", "[point collocation](./point_collocation.ipynb),\n", "[pseudo-spectral projection](pseudo_spectral_projection.ipynb), and\n", "[intrusive Galerkin](./intrusive_galerkin.ipynb)." ] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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": "3.9.5" } }, "nbformat": 4, "nbformat_minor": 4 }