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

2025-12-02

AI Summary

Existing hysteresis modeling approaches rely heavily on predefined assumptions or fixed model libraries, limiting mechanistic interpretability and generalizability. To address this, we propose a unified framework integrating latent-variable learning with prior-free symbolic regression. Our method employs neural networks to autonomously discover unobservable internal state variables and directly performs symbolic regression on the learned latent representations—without prescribing model structures or candidate equation sets—enabling end-to-end discovery of interpretable, explicit governing equations. Dynamic response prediction is further achieved by numerically solving the identified differential equations. Experiments across diverse canonical hysteresis systems demonstrate that the framework accurately recovers ground-truth control laws and yields long-term stable predictions, significantly enhancing model interpretability, universality, and out-of-distribution generalization.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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, this research develops a unified framework that integrates learning of internal variables (commonly used in modeling hysteresis) and symbolic regression to automatically extract internal hysteretic variable, and discover explicit governing equations directly from data without predefined libraries as required by methods such as sparse identification of nonlinear dynamics (SINDy). Solving the discovered equations naturally enables prediction of the dynamic responses of hysteretic systems. This work provides a systematic view and approach for both equation discovery and characterization of hysteretic dynamics, defining a unified framework for these types of problems.

Problem

• Automatically discovers governing equations for hysteretic systems from data
• Integrates internal variable learning with symbolic regression for flexibility
• Enables dynamic response prediction without predefined model libraries

Innovation

• Integrates internal variable learning with symbolic regression
• Discovers governing equations without predefined model libraries
• Enables dynamic response prediction from discovered equations