Pentland, Kamran, Tamborrino, Massimiliano, Sullivan, T. J., Buchanan, James and Appel, L. C. (2023) GParareal : a time-parallel ODE solver using Gaussian process emulation. Statistics and Computing, 33 (1). 23. doi:10.1007/s11222-022-10195-y ISSN 1573-1375.
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Abstract
Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion, “predicting” the solution serially using a cheap (coarse) solver and “correcting” these values using an expensive (fine) solver that runs in parallel on a number of temporal subintervals. In this work, we propose a time-parallel algorithm (GParareal) that solves IVPs by modelling the correction term, i.e. the difference between fine and coarse solutions, using a Gaussian process emulator. This approach compares favourably with the classic parareal algorithm and we demonstrate, on a number of IVPs, that GParareal can converge in fewer iterations than parareal, leading to an increase in parallel speed-up. GParareal also manages to locate solutions to certain IVPs where parareal fails and has the additional advantage of being able to use archives of legacy solutions, e.g. solutions from prior runs of the IVP for different initial conditions, to further accelerate convergence of the method — something that existing time-parallel methods do not do.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
| SWORD Depositor: | Library Publications Router |
| Library of Congress Subject Headings (LCSH): | Gaussian processes, Initial value problems, Parallel programs (Computer programs) |
| Journal or Publication Title: | Statistics and Computing |
| Publisher: | Springer US |
| ISSN: | 1573-1375 |
| Official Date: | 2023 |
| Dates: | Date Event 2023 Published 21 December 2022 Available 7 December 2022 Accepted |
| Volume: | 33 |
| Number: | 1 |
| Article Number: | 23 |
| DOI: | 10.1007/s11222-022-10195-y |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Open Access (Creative Commons open licence) |
| Date of first compliant deposit: | 22 June 2023 |
| Date of first compliant Open Access: | 22 June 2023 |
| RIOXX Funder/Project Grant: | Project/Grant ID RIOXX Funder Name Funder ID EP/S022244/1 [EPSRC] Engineering and Physical Sciences Research Council |
| URI: | https://wrap.warwick.ac.uk/173571/ |
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