A unified framework for equation discovery and dynamic prediction of hysteretic systems

TL;DR

This paper introduces a unified data-driven framework for discovering governing equations and predicting the dynamics of hysteretic systems using symbolic regression, overcoming limitations of traditional models and library-based methods.

Contribution

It develops a flexible, data-driven approach that reformulates hysteretic system equations in state-space form and employs symbolic regression to automatically recover explicit governing equations.

Findings

Effective in recovering equations in limited-data scenarios

Enables accurate dynamic prediction of hysteretic systems

Outperforms traditional methods in Full Equation Discovery tasks

Abstract

Hysteresis is a nonlinear phenomenon with memory effects, where a system's output depends on both its current state and past states. It is prevalent in various physical and mechanical systems, such as yielding structures under seismic excitation, ferromagnetic materials, and piezoelectric actuators. Analytical models like the Bouc-Wen model are often employed but rely on idealized assumptions and careful parameter calibration, limiting their applicability to diverse or mechanism-unknown behaviors. Existing equation discovery approaches for hysteresis are often system-specific or rely on predefined model libraries, which limit their flexibility and ability to capture the hidden mechanisms. To address these challenges, this research classifies equation discovery problems for hysteretic systems and develops a unified framework in which the state-space form is reformulated, and hysteretic variables are treated as trainable parameters from data. The framework further employs symbolic regression (SR) to automatically recover explicit governing equations without relying on predefined libraries, unlike methods such as sparse identification of nonlinear dynamics (SINDy). Experimental results demonstrate that the proposed method is effective in recovering governing equations for hysteretic systems, even in a challenging Full Equation Discovery setting, where prior information is extremely limited, and solving the equations naturally enables the dynamic prediction of hysteretic systems.