An interpretable data-driven identification of dynamical systems via universal neural ordinary differential equations

Abstract

Interpretable data-driven techniques are of significant research value in dynamical system identification. This paper develops an interpretable identification framework based on universal neural ordinary differential equations (UNODEs), symbolic regression, and parameter refinement. In the proposed framework, UNODEs are used as a front-end model to learn state- and time-dependent vector fields, while symbolic regression is employed to transform the learned black-box vector field into an explicit governing equation. After the symbolic structure is identified, model parameters are further refined at the trajectory level to improve the numerical consistency of the mechanistic model. Theoretical justification for the uniqueness and identifiability of the recovered model is provided via the regularized Neural ODE framework. Comparative experiments against SINDy, PNODE, and ODENet demonstrate that the proposed method is competitive on autonomous polynomial systems and more effective in recovering compact symbolic structures for non-polynomial and explicitly time-varying dynamics.