Implicit probabilistic integrators for ODEs

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Title: Implicit probabilistic integrators for ODEs
Authors: Teymur, O
Calderhead, B
Lie, HC
Sullivan, T
Item Type: Conference Paper
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.
Issue Date: 2-Dec-2018
Date of Acceptance: 5-Sep-2018
ISSN: 1049-5258
Publisher: Massachusetts Institute of Technology Press
Journal / Book Title: Advances in Neural Information Processing Systems
Copyright Statement: This paper is embargoed until publication.
Conference Name: Neural Information Processing Systems
Keywords: 1701 Psychology
1702 Cognitive Science
Publication Status: Accepted
Start Date: 2018-12-02
Finish Date: 2018-12-08
Conference Place: Montreal, Canada
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Mathematics
Faculty of Natural Sciences

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