NeurIPS 2021: Linear-Time Probabilistic Solutions of Boundary Value Problems

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Linear-Time Probabilistic Solutions of Boundary Value Problems
Nicholas Krämer, and Philipp Hennig
Advances in Neural Information Processing Systems (NeurIPS) 2021
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► Paper: https://arxiv.org/abs/2106.07761
► Code: https://github.com/pnkraemer/probabilistic-bvp-solver

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.

► Find out more about our research at https://uni-tuebingen.de/en/134428.

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