WyNDA: A method to discover mathematical models of dynamical systems from data

Abstract

This paper introduces a novel method called Wide-Array of Nonlinear Dynamics Approximation (WyNDA) for extracting mathematical models of dynamical systems from data. A key advantage of this method over existing approaches lies in its suitability for online implementation. Moreover, WyNDA stands out by not relying on optimization or machine learning, ensuring computational efficiency. The fundamental concept revolves around approximating the unknown function of a dynamical system through a diverse set of basis functions that encapsulate the available data. An adaptive observer is then employed to iteratively refine this approximation and estimate the associated parameters. The efficacy of the proposed method is demonstrated through numerical simulations encompassing linear systems, nonlinear systems, and control systems. The results underscore the method’s ability to successfully unveil the governing equations of dynamical systems, highlighting its potential for extracting intricate system dynamics from observational data.•WyNDA represents a novel approach for uncovering mathematical models of dynamical systems from data.•Utilizing a series of basis functions, WyNDA effectively approximates the unknown structure inherent in dynamical systems.•The validation of WyNDA involves benchmark equations of dynamical systems, confirming its efficacy in diverse scenarios.