{ "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, though `probnum` has more customisation to offer." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from probnum import diffeq, filtsmooth, statespace, randvars\n", "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\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 an `IVP` object." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "\n", "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", "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", "t0 = 0.\n", "tmax = 20.\n", "y0 = np.array([20, 20])\n", "\n", "ivp = diffeq.IVP((t0, tmax), initrv=randvars.Constant(y0), rhs=f, jac=df)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define a prior distribution and a measurement model. The former can be any `Integrator`, which currently restricts the choice to `IBM`, `IOUP`, and `Matern`. We usually recommend `IBM`.\n", "The measurement model requires a choice between EK0, EK1 (extended Kalman filters of order 0 or 1, respectively) and perhaps UK (unscented Kalman filter). The use of the latter is discouraged, because the square-root implementation is not available currently.\n", "\n", "The measurement model can either be constructed with `DiscreteEKFComponent.from_ode` or, perhaps more conveniently, with `GaussianIVPFilter.string_to_measurement_model`. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "prior = statespace.IBM(ordint=4, spatialdim=ivp.dimension, forward_implementation=\"sqrt\", backward_implementation=\"sqrt\")\n", "ekf = diffeq.GaussianIVPFilter.string_to_measurement_model(\"EK1\", ivp=ivp, prior=prior)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we construct the ODE filter. One choice that has not been made yet is the initialiation strategy. The current default choice is to initialise by fitting the prior to a few steps of a Runge-Kutta solution. An alternative is to use automatic differentiation, which is currently in development.\n", "An easy-access version of those initialisation strategies is to use the constructor `GaussianIVPFilter.construct_with_rk_init`. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "solver = diffeq.GaussianIVPFilter.construct_with_rk_init(ivp, prior=prior, measurement_model=ekf, with_smoothing=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can solve the ODE. To this end, define a `StepRule`, e.g. `ConstantSteps` or `AdaptiveSteps`. If you don't know which firststep to use, the function `propose_firststep` makes an educated guess for you." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "firststep = diffeq.propose_firststep(ivp)\n", "steprule = diffeq.AdaptiveSteps(firststep=firststep, atol=1e-2, rtol=1e-2)\n", "odesol = solver.solve(steprule=steprule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`GaussianIVPFilter.solve` returns an `ODESolution` object, which is sliceable and callable. The latter can be used to plot the solution on a uniform grid, even though the solution was computed on an adaptive grid. Be careful: the return values of `__call__`, etc., are always random variable-like objects. We decide to plot the mean." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "evalgrid = np.arange(ivp.t0, ivp.tmax, step=0.2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Done! This is the solution to the Lotka-Volterra model." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "tags": [ "nbsphinx-thumbnail" ] }, "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.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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 }