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Implicit probabilistic integrators for ODEs
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Teymur, Onur, Calderhead, Ben, Lie , Hancheng and Sullivan, T. J. (2018) Implicit probabilistic integrators for ODEs. In: NIPS'18 : Neural Information Processing Systems 2018, Canada, 3-8 Dec 2018. Published in: Proceedings of the 32nd International Conference on Neural Information Processing Systems pp. 7255-7264. doi:10.5555/3327757.3327827
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Official URL: https://dl.acm.org/doi/10.5555/3327757.3327827
Abstract
We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams–Moulton method. The implicit construction allows for dynamic feedback from the forthcoming time-step, in contrast to previous probabilistic integrators, all of which are based on explicit methods. We begin with a concise survey of the rapidly-expanding field of probabilistic ODE solvers. We then introduce our method, which builds on and adapts the work of Conrad et al. (2016) and Teymur et al. (2016), and provide a rigorous proof of its well-definedness and convergence. We discuss the problem of the calibration of such integrators and suggest one approach. We give an illustrative example highlighting the effect of the use of probabilistic integrators—including our new method—in the setting of parameter inference within an inverse problem.
Item Type: | Conference Item (Paper) | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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Journal or Publication Title: | Proceedings of the 32nd International Conference on Neural Information Processing Systems | ||||||
Book Title: | Advances in Neural Information Processing Systems 31 (NIPS 2018) | ||||||
Official Date: | December 2018 | ||||||
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Page Range: | pp. 7255-7264 | ||||||
DOI: | 10.5555/3327757.3327827 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Date of first compliant deposit: | 15 April 2020 | ||||||
Conference Paper Type: | Paper | ||||||
Title of Event: | NIPS'18 : Neural Information Processing Systems 2018 | ||||||
Type of Event: | Conference | ||||||
Location of Event: | Canada | ||||||
Date(s) of Event: | 3-8 Dec 2018 |
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