International Journal of Science, Engineering and TechnologyAuthors: S.Anto Nibiya, Sangeetha S
Abstract: The analysis of nonlinear differential equations describing chaotic dynamical systems continues to be a challenging problem at the nexus of mathematical theory and practical computation. Most previous data-driven discovery approaches have focused on sacrificing either interpretability for flexibility or making assumptions about which terms appear in the governing equations. In this work, we present DynamiFlow AI, a mathematically interpretable framework that combines multi-scale Koopman neural operators with differentiable physics constraints and sparse symbolic distillation. Our method learns latent linear representations of the nonlinear dynamics as well as explicit governing equations from a differentiable candidate library, while ensuring consistency in the identified equations when considered from multiple augmented views of the trajectories. DynamiFlow AI is applied to benchmark problems in chaotic dynamical systems including the Lorenz-63 system, the Kuramoto-Sivashinsky equation, and a reaction-diffusion system. We show that our framework discovers correct structural information in the governing equations and retains accurate long-horizon trajectory behavior, while simultaneously providing directly interpretable symbolic coefficients of chaotic flows.
DOI: https://doi.org/10.5281/zenodo.23906995
