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GOODE: A Gaussian Off-The-Shelf Ordinary Differential Equation Solver
David John · Vincent Heuveline · Michael Schober

Wed Jun 12 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #214

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 an established benchmark of test problems.

Author Information

David John (Corporate Research, Robert Bosch GmbH)
Vincent Heuveline (University Heidelberg)
Michael Schober (Bosch Center for Artificial Intelligence)

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