A unified framework for equation discovery and dynamic prediction of hysteretic systems
This work addresses the need for flexible and accurate modeling of hysteresis in physical and mechanical systems, offering a novel approach that could improve predictions in fields like structural engineering and materials science, though it appears incremental as it builds on existing equation discovery methods.
The research tackled the problem of modeling hysteretic systems with memory effects by developing a unified framework that uses symbolic regression to automatically discover governing equations without predefined libraries, achieving effective equation recovery even in challenging settings with limited prior information.
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.