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Poster
Linear-Time Probabilistic Solution of Boundary Value Problems
Nicholas Krämer · Philipp Hennig

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @ Virtual

We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss-Markov prior and tailor it specifically to BVPs, which allows computing a posterior distribution over the solution in linear time, at a quality and cost comparable to that of well-established, non-probabilistic methods. Our model further delivers uncertainty quantification, mesh refinement, and hyperparameter adaptation. We demonstrate how these practical considerations positively impact the efficiency of the scheme. Altogether, this results in a practically usable probabilistic BVP solver that is (in contrast to non-probabilistic algorithms) natively compatible with other parts of the statistical modelling tool-chain.

Author Information

Nicholas Krämer (University of Tuebingen)
Philipp Hennig (University of Tübingen and MPI Tübingen)

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