Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data
File(s)
Published version
Author(s)
Fung, Lloyd
Fasel, Urban
Juniper, Matthew
Type
Journal Article
Abstract
We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the sparse identification of nonlinear dynamics (SINDy) method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as lynx–hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy.
Date Issued
2025-02-13
Date Acceptance
2024-12-13
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2025, 481 (2307)
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
481
Issue
2307
Copyright Statement
© 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.
License URL
Subjects
active learning
Bayesian inference
EQUATIONS
model discovery
Multidisciplinary Sciences
Science & Technology
Science & Technology - Other Topics
SELECTION
SINDy
sparse regression
system identification
Publication Status
Published
Article Number
20240200
Date Publish Online
2025-02-13