Learning Differential Equations of Dynamical Systems Based on Discovery of Causal Networks from Multivariate Time Series

Abstract

Equation discovery identifies governing equations of dynamics from observations, which is significant for our more profound understanding of the systems. Among equation discovery methods, Sparse Identification of Nonlinear Dynamics (SINDy) has recently attracted considerable attention. SINDy identifies differential equations from the perspective of sparse regression in a high-dimensional nonlinear function space. However, SINDy often contains redundant terms requiring more criteria for selecting variables and functions. To eliminate dull terms based on causality and obtain equations that efficiently describe dynamics, we propose Parsimonious Equation Learning with Causality (PELC). PELC discovers causal networks from multivariate time series via adversarial generative networks and incorporates this topology as a constraint in the hypothesis space of SINDy. We compared the reproducibility of differential equations among SINDy, VAR-LiNGAM, and PELC. As a result, the reproducibility of PELC was the highest. PELC is expected to be a novel method that connects causal network discovery in continuous algebraic space by deep learning and equation discovery.