Enhancing sparse identification of nonlinear dynamics with Earth-Mover distance and group similarity

The sparse identification of nonlinear dynamics (SINDy) algorithm enables us to discover nonlinear dynamical systems purely from data but is noise-sensitive, especially in low-data scenarios. In this work, we introduce an advanced method that integrates group sparsity thresholds with Earth Mover's distance-based similarity measures in order to enhance the robustness of identifying nonlinear dynamics and the learn functions of dynamical systems governed by parametric ordinary differential equations. This novel approach, which we call group similarity SINDy (GS-SINDy), not only improves interpretability and accuracy in varied parametric settings but also isolates the relevant dynamical features across different datasets, thus bolstering model adaptability and relevance. Applied to several complex systems, including the Lotka-Volterra, Van der Pol, Lorenz, and Brusselator models, GS-SINDy demonstrates consistently enhanced accuracy and reliability, showcasing its effectiveness in diverse applications.