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

The pursuit of direct model equation discovery has been an ongoing and significant area of interest in scientific machine learning. The popular sparse identification of nonlinear dynamics (SINDy) framework [1] offers a promising approach to extract parsimonious equations directly from data. SINDy's promotion of parsimony by sparse regression allows for the identification of an interpretable model that balances accuracy with generalizability, while its simplicity leads to a relatively efficient and fast learning process compared to other machine learning techniques. The framework has been successfully applied in a variety of applications, such as model idenficiation in plasma physics [2], control engineering [3, 4], biological transport problems [5], socio-cognitive systems [6], epidemiology [7, 8] and turbulence modelling [9]. Furthermore, its remarkable extendibility has attracted a range of modifications, including the adaptation to discover partial differential equations [10], the extension to libraries of rational functions [11], the integration of ensembling techniques to improve data efficiency [12] and the use of weak formulations [13, 14] to avoid noise amplification when computing derivatives from discrete data. One major difficulty in using scientific machine learning methods in fields such as biophysics, ecology, and microbiology, is that measured data from these fields is often noisy and scarce.