{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ODE-Solvers from Scratch\n", "\n", "All the other tutorials show how to use the ODE-solver with the `probsolve_ivp` function.\n", "This is great, but `probnum` has more customisation to offer." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from probnum import diffeq, filtsmooth, randvars, randprocs, problems\n", "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "plt.style.use(\"../../probnum.mplstyle\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we define the ODE problem. As always, we use Lotka-Volterra. Once the ODE functions are defined, they are gathered in a data structure describing the initial value problem." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def f(t, y):\n", " y1, y2 = y\n", " return np.array([0.5 * y1 - 0.05 * y1 * y2, -0.5 * y2 + 0.05 * y1 * y2])\n", "\n", "\n", "def df(t, y):\n", " y1, y2 = y\n", " return np.array([[0.5 - 0.05 * y2, -0.05 * y1], [0.05 * y2, -0.5 + 0.05 * y1]])\n", "\n", "\n", "t0 = 0.0\n", "tmax = 20.0\n", "y0 = np.array([20, 20])\n", "\n", "lotka_volterra = problems.InitialValueProblem(t0=t0, tmax=tmax, y0=y0, f=f, df=df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define a prior distribution and a step-size-selection rule. \n", "The former is almost always an integrated Wiener process.\n", "The latter can be an adaptive or constant rule." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "iwp = randprocs.markov.integrator.IntegratedWienerProcess(\n", " initarg=lotka_volterra.t0,\n", " num_derivatives=4,\n", " wiener_process_dimension=lotka_volterra.dimension,\n", " forward_implementation=\"sqrt\",\n", " backward_implementation=\"sqrt\",\n", ")\n", "\n", "firststep = diffeq.stepsize.propose_firststep(lotka_volterra)\n", "adaptive_steps = diffeq.stepsize.AdaptiveSteps(\n", " firststep=firststep, atol=1e-2, rtol=1e-3\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we construct the ODE filter and solve the ODE. Let's plot the solution." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "solver = diffeq.odefilter.ODEFilter(\n", " steprule=adaptive_steps,\n", " prior_process=iwp,\n", ")\n", "odesol = solver.solve(ivp=lotka_volterra)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "evalgrid = np.arange(lotka_volterra.t0, lotka_volterra.tmax, step=0.1)\n", "sol = odesol(evalgrid)\n", "\n", "plt.plot(evalgrid, sol.mean, \"o-\", linewidth=1)\n", "plt.ylim((0, 30))\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Predator / prey\")\n", "plt.title(\"Solution of the Lotka-Volterra system\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can take the customisation further. For example, we can choose the EK1 as an approximation strategy and a piecewise constant diffusion model. Other options are available, too." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "piecewise_constant = randprocs.markov.continuous.PiecewiseConstantDiffusion(t0=t0)\n", "rk_init = diffeq.odefilter.init_routines.NonProbabilisticFitWithJacobian()\n", "ek1 = diffeq.odefilter.approx_strategies.EK1()\n", "\n", "solver_ek1 = diffeq.odefilter.ODEFilter(\n", " steprule=adaptive_steps,\n", " prior_process=iwp,\n", " approx_strategy=ek1,\n", " diffusion_model=piecewise_constant,\n", ")\n", "odesol_ek1 = solver_ek1.solve(ivp=lotka_volterra)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sol = odesol(evalgrid)\n", "\n", "plt.plot(evalgrid, sol.mean, \"o-\", linewidth=1)\n", "plt.ylim((0, 30))\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Predator / prey\")\n", "plt.title(\"Solution of the Lotka-Volterra system\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }