A Physics‐Informed Hysteretic Neural Network for Duhem Hysteresis Modeling and Parameters Identification

Abstract

The Duhem model is widely used for modeling hysteresis in smart materials due to its explicit differential equations and accuracy in capturing Preisach‐like nonlinearities. However, its non‐smooth switching operator presents challenges in parameter identification due to the nonconvex optimization involved. This paper introduces a physics‐informed hybrid neural network, namely hysteretic neural network‐long short‐term memory (HNN‐LSTM), for identifying Duhem model parameters and modeling the hysteresis nonlinearity. First, a LSTM network with an expanded input is constructed to describe the nonlinear hysteresis between input and output. The resulting LSTM sub‐model achieves universal approximation of the Duhem hysteresis and accurate estimation of the internal state. Second, a physics‐informed sub‐model, HNN, is then introduced to impose physical constraints on LSTM training by embedding Duhem model parameters into network weights. Then, by minimizing a composite loss combining numerical and physical errors, the model achieves both numerical accuracy and physical consistency. Thus, parameter identification is thereby accomplished by solving the inverse problem of the HNN‐LSTM while ensuring consistency with the original differential model. Finally, simulation and experimental results confirm the effectiveness of the proposed method. This approach offers a promising solution for modeling non‐smooth systems and estimating their parameters accurately.