GOODE: A Gaussian Off-The-Shelf Ordinary Differential Equation Solver


David John, Vincent Heuveline, Michael Schober ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:3152-3162, 2019.


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.

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