A Fourier State Space Model for Bayesian ODE Filters

Fourier ODE filters are designed to capture the periodic components of ODEs

Abstract

Gaussian ODE filtering is a probabilistic numerical method to solve ordinary differential equations (ODEs). It computes a Bayesian posterior over the solution from evaluations of the vector field defining the ODE. Its most popular version, which employs an integrated Brownian motion prior, uses Taylor expansions of the mean to extrapolate forward and has the same convergence rates as classical numerical methods. As the solution of many important ODEs are periodic functions (oscillators), we raise the question whether Fourier expansions can also be brought to bear within the framework of Gaussian ODE filtering. To this end, we construct a Fourier state space model for ODEs and a `hybrid’ model that combines a Taylor (Brownian motion) and Fourier state space model. We show by experiments how the hybrid model might become useful in cheaply predicting until the end of the time domain.

Publication
Workshop on Invertible Neural Networks, Normalizing Flows, and Explicit Likelihood Models, ICML 2020
Hans Kersting
Hans Kersting
Postdoctoral Researcher

My research interests include Bayesian inference, dynamical systems, and optimization.

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