Calibrated Adaptive Probabilistic ODE Solvers

Nathanael Bosch, Philipp Hennig, Filip Tronarp

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

Abstract

Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error. Addressing this issue, we introduce, discuss, and assess several probabilistically motivated ways to calibrate the uncertainty estimate. Numerical experiments demonstrate that these calibration methods interact efficiently with adaptive step-size selection, resulting in descriptive, and efficiently computable posteriors. We demonstrate the efficiency of the methodology by benchmarking against the classic, widely used Dormand-Prince 4/5 Runge-Kutta method.

Original languageEnglish
Title of host publicationInternational Conference on Artificial Intelligence and Statistics
PublisherML Research Press
Pages3466-3474
Number of pages9
Publication statusPublished - 2021
Externally publishedYes
Event24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States
Duration: 2021 Apr 132021 Apr 15

Publication series

NameProceedings of Machine Learning Research
PublisherML Research Press
Volume130
ISSN (Electronic)2640-3498

Conference

Conference24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021
Country/TerritoryUnited States
CityVirtual, Online
Period2021/04/132021/04/15

Subject classification (UKÄ)

  • Computational Mathematics

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