On solving Ordinary Differential Equations using Gaussian Processes

TL;DR

This paper introduces Gaussian Process based methods for solving non-linear Ordinary Differential Equations, including explicit and implicit probabilistic solvers with improved accuracy and a general approach for error estimation.

Contribution

It presents new Gaussian Process algorithms for ODE solving, enhancing accuracy and providing a general error estimation framework.

Findings

Greater accuracy than previous Gaussian Process ODE solvers

Development of explicit and implicit probabilistic methods

A general approach for error estimation from standard solvers

Abstract

We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the other to gradient matching. All methods have greater accuracy than previously suggested Gaussian Process approaches. We also suggest a general approach that can yield error estimates from any standard ODE solver.