Sparse identification of nonlinear dynamics in the presence of library and system uncertainty

TL;DR

This work tackles the limitations of SINDy, which assumes known variables and a fixed function library, by introducing Augmented SINDy that integrates causal discovery and sparse-coding–based basis learning to handle dual uncertainty. The approach is validated on real-world ecological datasets (e.g., Lynx–Hare and Sardine–Anchovy) and synthetic models, showing improved causal-structure recovery and dictionary element selection compared to standard SINDy. Key metrics such as FPIV and FDECS demonstrate that Augmented SINDy more reliably identifies governing dynamics and resists spurious associations even when parts of the system or library are unknown. The results suggest a practical, robust pathway for data-driven dynamical-system identification in uncertain, real-world settings, including ecological applications and beyond, by solving for dynamics with $\dot{\mathbf x} = \mathbf f(\mathbf x)$ using augmented dictionaries and causal information.

Abstract

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that can act as a basis for the system. In this paper, we demonstrate on real world data how the Augmented SINDy algorithm outperforms SINDy in the presence of system variable uncertainty. We then show SINDy can be further augmented to perform robustly when both kinds of uncertainty are present.