Champneys, M.D. orcid.org/0000-0002-3037-7584 and Rogers, T.J. orcid.org/0000-0002-3433-3247 (2025) BINDy: Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte Carlo. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481 (2319). 20240620. ISSN: 1364-5021
Abstract
Model parsimony is an important cognitive bias in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse representations of complex dynamics directly from data, given a basis of library functions. In this work, a novel Bayesian treatment of dictionary learning system identification, as an alternative to SINDy, is envisaged. The proposed method—Bayesian identification of nonlinear dynamics (BINDy)—is distinct from previous approaches in that it targets the full joint posterior distribution over both the terms in the library and their parametrization in the model. This formulation confers the advantage that an arbitrary prior may be placed over the model structure to produce models that are sparse in the model space rather than in parameter space. Because this posterior is defined over parameter vectors that can change in dimension, the inference cannot be performed by standard techniques. Instead, a Gibbs sampler based on reversible-jump Markov-chain Monte Carlo is proposed. BINDy is shown to compare favourably to ensemble SINDy in three benchmark case-studies. In particular, it is seen that the proposed method is better able to assign high probability to correct model terms.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
Keywords: | Bayesian statistics; nonlinear dynamics; reversible-jump; Markov-chain Monte Carlo |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > School of Mechanical, Aerospace and Civil Engineering |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 Aug 2025 10:40 |
Last Modified: | 12 Aug 2025 10:40 |
Status: | Published |
Publisher: | The Royal Society |
Refereed: | Yes |
Identification Number: | 10.1098/rspa.2024.0620 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:230272 |