NeurIPS 2021: Linear-Time Probabilistic Solutions of Boundary Value Problems
Linear-Time Probabilistic Solutions of Boundary Value Problems
Nicholas Krämer, and Philipp Hennig
Advances in Neural Information Processing Systems (NeurIPS) 2021
► 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.