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

TL;DR

This paper introduces Bayesian-SINDy, a fast probabilistic method that identifies sparse nonlinear differential equations from limited, noisy data, providing uncertainty quantification and robustness, especially useful for biological and real-time systems.

Contribution

The paper presents Bayesian-SINDy, a novel Bayesian framework that accelerates sparse nonlinear dynamics identification while quantifying uncertainty and improving robustness over existing methods.

Findings

Effective in learning correct models from limited noisy data

Demonstrates robustness and efficiency on synthetic and real data

Enables active learning through entropy calculation

Abstract

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.