{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Forward Euler, continued\n", "\n", "First, revisit the simulations with large time steps. On the board, we determined that, in order for the simulation to be constantly shrinking, that the time step should be < 1. \n", "\n", "Let's try that with our single-state degradation model. Here is copy-pasted code from Tuesday." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Run the 1D model to see where the steps break down..\n", "import numpy as np\n", "import scipy.integrate\n", "import matplotlib.pyplot as plt\n", "\n", "def degradation_model1D( t, y, params ):\n", " dydt = -params[0] * y;\n", " return dydt\n", "\n", "def forwardEuler1D( fn, t, y0, params ):\n", " \"\"\" [t,y] = forwardEuler1D( fn, t, y0, params )\n", " Given a function handle fn for dydt, find the value of\n", " y at timepoints t, given y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (1,NT) (NOTE WE ASSUME WE HAVE JUST ONE VARIABLE)\n", " \"\"\"\n", " y = np.zeros( (1,t.size) )\n", " y[0,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[0,i-1],params);\n", " y[0,i] = y[0,i-1] + h*yprime;\n", " \n", " return (t,y)\n", "\n", "dt = 1\n", "y0 = 1\n", "params = (2,)\n", "t = np.arange(0,10,dt)\n", "tru_y = np.exp( -params[0]*t)\n", "(t,y) = forwardEuler1D( degradation_model1D, t, y0=y0, params=params)\n", "\n", "plt.plot(t, tru_y)\n", "plt.plot(t, y.T);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rewrite the forward Euler method to work for multi-state models\n", "\n", "Rewrite the method so that y0 can have more than one value and fn can return a vector of more than one value.\n", "\n", "The return value should be NY x NT (number of states by number of time steps) big, so it gets filled in one column at a time. Adjust the 1D code to account for multiple states." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "def forwardEuler( fn, t, y0, params ):\n", " \"\"\" [t,y] = forwardEuler( fn, t, y0, params )\n", " Given a function handle fn for dydt, find the value of\n", " y at timepoints t, given y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (NY,NT)\n", " \"\"\"\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[:,i-1],params);\n", " y[:,i] = y[:,i-1] + h*yprime;\n", " \n", " return (t,y)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, make a 2-state degradation model." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def degradation_model( t, y, params ):\n", " y1 = y[0]\n", " y2 = y[1]\n", " dydt = np.zeros( (2,) )\n", " dydt[0] = -params[0] * y1\n", " dydt[1] = -params[1] * y2\n", " return dydt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run the 2-state degradation model with forward Euler.\n", "\n", "Use 2 and 2.5 as the degradation rates. Simulate from t=0 to t=4 with a time step size of 0.1.\n", "\n", "Then plot the true solution and the approximate solution (indicate simulated with dashed lines). And in another plot, show the difference (between the true and approximate solutions) over time." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "params = np.array([2,2.5])\n", "y0 = np.array([1,1])\n", "(t,y) = forwardEuler( degradation_model, np.arange(0,4,0.1), y0, params)\n", "tru_y1 = y0[0]*np.exp(-params[0]*t)\n", "tru_y2 = y0[1]*np.exp(-params[1]*t)\n", "\n", "plt.subplot(2, 1, 1)\n", "plt.plot( t, tru_y1)\n", "plt.plot( t, tru_y2 )\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( t, y.T, '--' );\n", "plt.legend(['True y1','True y2','Approximate y1','Approximate y2']);\n", "\n", "plt.subplot( 2, 1, 2 )\n", "plt.plot( t, tru_y1 - y[0,:])\n", "plt.plot( t, tru_y2 - y[1,:]);\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Determine how the error depends on the step size\n", "\n", "When we compute the difference between the true and approximate solutions, we have one value at each state for each time step. I would like to summarize this as one number, so that we can plot \"error\" versus step size.\n", "\n", "Let's explore different measures for the error." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-norm across states, then mean across time 0.025902904858696563\n", "2-norm across states, then mean across time 0.018549186024476992\n", "inf-norm across states, then mean across time 0.01460706848790066\n", "1-norm across states, then max across time 0.09120215528866388\n", "2-norm across states, then max across time 0.0650221500659531\n", "inf-norm across states, then max across time 0.051473191171442334\n" ] } ], "source": [ "import scipy.linalg\n", "\n", "tru_y = np.vstack( (tru_y1,tru_y2))\n", "d = tru_y - y\n", "print( \"1-norm across states, then mean across time\", np.mean(scipy.linalg.norm( d, ord=1, axis=0 )) )\n", "print( \"2-norm across states, then mean across time\", np.mean(scipy.linalg.norm( d, ord=2, axis=0 )) )\n", "print( \"inf-norm across states, then mean across time\", np.mean(scipy.linalg.norm( d, ord=np.inf, axis=0 )) )\n", "print( \"1-norm across states, then max across time\", np.max(scipy.linalg.norm( d, ord=1, axis=0 )) )\n", "print( \"2-norm across states, then max across time\", np.max(scipy.linalg.norm( d, ord=2, axis=0 )) )\n", "print( \"inf-norm across states, then max across time\", np.max(scipy.linalg.norm( d, ord=np.inf, axis=0 )) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Determine how the error changes with the time step. Plot two figures - one with the simulations and one with the errors. Compute the error using two methods:\n", "- Compute the Euclidean distance between the true solution and the approximate solution (2-norm of the difference) at each time point, then take the mean across time.\n", "- Compute the infinity norm (max value) of the difference between the true solution and the approximate solution at each time point, then take the mean across time.\n", "\n", "Make an array of time steps. For each time step, plot each solution in a separate subfigure, and keep track of the error in an array. Then plot the errors in a second figure, with each error computation in a separate subfigure." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# range from smallest timestep that doesn't take way too long to run to largest time step with qualitatively correct answer.\n", "dts = np.linspace(1e-4,1e-1,10)\n", "err1 = np.zeros( (dts.size,) )\n", "err2 = np.zeros( (dts.size,) )\n", "params = (2,2.5)\n", "y0 = np.array((1,1))\n", "\n", "for i in range(dts.size):\n", " t = np.arange(0,4,dts[i])\n", " sol = scipy.integrate.solve_ivp(fun=degradation_model, t_span=(0,150), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", " (t,y) = forwardEuler( degradation_model, t, y0, params)\n", " plt.subplot( dts.size, 1, i+1 )\n", " plt.plot( t, sol.y.T )\n", " plt.plot( t, y.T, '--')\n", " err1[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " err2[i] = np.mean(scipy.linalg.norm( sol.y-y, np.inf, axis=0) )\n", " \n", "plt.figure()\n", "plt.subplot(2,1,1)\n", "plt.plot( dts, err1, '.-' );\n", "plt.subplot(2,1,2)\n", "plt.plot( dts, err2, '.-' );\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus Content\n", "\n", "Here, we use Forward Euler to solve the Goodwin oscillator (coded up in Lecture 9). This code is hear as an example to follow when working on Project 3. Aside from being more interesting than the degradation model, the most important difference is that we don't have an analytical solution. So, we use solve_ivp's LSODA method with really tight error controls (i.e. we allow only tiny little errors) to generate the reference \"true\" solution." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Here is the model, copied from a notebook from earlier in the course\n", "def goodwin_oscillator( t, statevars, params ):\n", " X = statevars[0];\n", " Y = statevars[1];\n", " Z = statevars[2];\n", " alpha_1 = params[0]\n", " K = params[1]\n", " n = params[2]\n", " gamma_1 = params[3]\n", " alpha_2 = params[4]\n", " gamma_2 = params[5]\n", " alpha_3 = params[6]\n", " gamma_3 = params[7]\n", " \n", " dydt = np.zeros( (3,) )\n", " dydt[0] = alpha_1*K**n/(K**n+Z**n) - gamma_1*X\n", " dydt[1] = alpha_2*X - gamma_2*Y;\n", " dydt[2] = alpha_3*Y - gamma_3*Z;\n", "\n", " return dydt" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simulate the model for a given time step size.\n", "# SRT reran this many times, adjusting the time step.\n", "import scipy.integrate\n", "\n", "alpha_1 = 1\n", "K = 0.61\n", "n = 11\n", "gamma_1 = 0.15\n", "alpha_2 = 1\n", "gamma_2 = 0.15\n", "alpha_3 = 1\n", "gamma_3 = 0.25\n", "\n", "params = (alpha_1,K,n,gamma_1,alpha_2,gamma_2,alpha_3,gamma_3)\n", "\n", "# Find a point on the limit cycle and start all subsequent simulations from that point.\n", "sol = scipy.integrate.solve_ivp(fun=goodwin_oscillator, t_span=(0,300), y0=(.1,.1,.1), method='LSODA', rtol=1e-8, atol=1e-8, args=[params] )\n", "y0 = sol.y[:,-1]\n", "\n", "# Run this with a time step of 0.1 (which is the biggest that looks like it is still qualitatively correct)\n", "# Run this with a smaller time step - the smallest you are willing to wait for, as well. \n", "t = np.arange(0,150,.1)\n", "sol = scipy.integrate.solve_ivp(fun=goodwin_oscillator, t_span=(0,150), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", "(t,y) = forwardEuler( goodwin_oscillator, t, y0, params)\n", "\n", "plt.plot( sol.t, sol.y.T );\n", "plt.plot( t, y.T, ':' );" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Determine how the error changes with the time step. Since we don't know exactly what the region of absolute stability is, we want to make sure we plot every solution (and not just the error we compute from it). So plot each solution in one figure, but keep track of the error in an array. Then plot the error in a second figure. Here, I compute the error by first computing the Euclidean distance between the true solution and the approximate solution at each time point, then take the mean across time." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Determine how the error changes with the time step.\n", "# range from smallest timestep that doesn't take way too long to run to largest time step with qualitatively correct answer.\n", "dts = np.linspace(1e-4,1e-1,10)\n", "err = np.zeros( (dts.size,) )\n", "\n", "for i in range(dts.size):\n", " t = np.arange(0,150,dts[i])\n", " sol = scipy.integrate.solve_ivp(fun=goodwin_oscillator, t_span=(0,150), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", " (t,y) = forwardEuler( goodwin_oscillator, t, y0, params)\n", " plt.subplot( dts.size, 1, i+1 )\n", " plt.plot( t, sol.y.T )\n", " plt.plot( t, y.T, '--')\n", " err[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " \n", "plt.figure()\n", "plt.plot( dts, err, '.-' );" ] } ], "metadata": { "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }