Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy,...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Fung, Lloyd, Fasel, Urban, Juniper, Matthew P
Format: Article
Language:English
Subjects:
Bayesian analysis
Differential equations
Dynamical systems
Entropy (Information theory)
Learning
Mathematical models
Nonlinear dynamics
Parameter estimation
Robustness
System identification
Online Access:Get full text
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Summary:We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the 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.
ISSN:2331-8422