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Implicit Probabilistic Integrators for ODEs

Teymur, Onur, Lie, Han Cheng, Sullivan, T.J., Calderhead, Ben (2018) Implicit Probabilistic Integrators for ODEs. Advances in Neural Information Processing Systems 31, . pp. 7244-7253. (KAR id:90456)

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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: Article
Uncontrolled keywords: initial value problems, Adams-Moulton method, ODEs
Subjects: Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Onur Teymur
Date Deposited: 29 Sep 2021 09:25 UTC
Last Modified: 13 Oct 2021 10:42 UTC
Resource URI: (The current URI for this page, for reference purposes)
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