There are two types of ordinary differential equations (ODEs): initial value problems (IVPs) and boundary value problems (BVPs). While many probabilistic numerical methods for the solution of IVPs have been presented to-date, there exists no efficient probabilistic general-purpose solver for nonlinear BVPs. Our method based on iterated Gaussian process (GP) regression returns a GP posterior over the solution of nonlinear ODEs, which provides a meaningful error estimation via its predictive posterior standard deviation. Our solver is fast (typically of quadratic convergence rate) and the theory of convergence can be transferred from prior non-probabilistic work. Our method performs on par with standard codes for on an established benchmark of test problems.
David John (Corporate Research, Robert Bosch GmbH)
Vincent Heuveline (University Heidelberg)
Michael Schober (Bosch Center for Artificial Intelligence)
Related Events (a corresponding poster, oral, or spotlight)
2019 Poster: GOODE: A Gaussian Off-The-Shelf Ordinary Differential Equation Solver »
Wed Jun 12th 06:30 -- 09:00 PM Room Pacific Ballroom