LES-SINDy: Laplace-Enhanced Sparse Identification of Nonlinear Dynamical Systems

Abstract: Sparse Identification of Nonlinear Dynamical Systems (SINDy) is one of the go-to workhorses for data-driven discovery of governing equations. However, it still encounters challenges when modeling complex dynamical systems that involve high-order derivatives or discontinuities, particularly in the presence of noise. These challenges limit its applicability across a broad range of applications in applied mathematics and physics. To mitigate these issues, we propose Laplace-Enhanced SparSe Identification of Nonlinear Dynamical Systems (LES-SINDy), which enhances the identification process by transforming time-series measurements from the time domain to the Laplace domain. By leveraging the Laplace transformation and integration by parts, LES-SINDy not only enables more accurate approximations of derivative and discontinuous terms but can also handle unbounded growth functions and accumulated numerical errors in the Laplace domain, thereby effectively addressing challenges in the identification process. The model evaluation process subsequently selects the most accurate and parsimonious dynamical systems from multiple candidates. Experimental results across diverse ordinary and partial differential equations show that LES-SINDy achieves superior accuracy and parsimony in discovering nonlinear dynamical systems compared to existing methods.

[arxiv]