Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data
Year: 2025
Type: 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.
Authors: Lloyd Fung, Urban Fasel, Matthew Juniper
Institutions: University of Cambridge, Imperial College London
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4407525277