This article presents an approach for modelling hysteresis in piezoelectric materials, that leverages recent advancements in machine learning, particularly in sparse-regression techniques. While sparse regression has previously been used to model various scientific and engineering phenomena, its application to nonlinear hysteresis modelling in piezoelectric materials has yet to be explored. The study employs the least-squares algorithm with a sequential threshold to model the dynamic system responsible for hysteresis, resulting in a concise model that accurately predicts hysteresis for both simulated and experimental piezoelectric material data. Several numerical experiments are performed, including learning butterfly-shaped hysteresis and modelling real-world hysteresis data for a piezoelectric actuator. The presented approach is compared to traditional regression-based and neural network methods, demonstrating its efficiency and robustness. Source code is available at https://github.com/chandratue/SmartHysteresis

翻译：本文提出了一种利用机器学习最新进展（特别是稀疏回归技术）建立压电材料滞回模型的方法。尽管稀疏回归已被用于模拟各种科学与工程现象，但其在压电材料非线性滞回建模中的应用尚待探索。本研究采用带有顺序阈值的偏最小二乘算法，对产生滞回效应的动态系统进行建模，生成了一个简洁且能准确预测仿真与实验压电材料滞回数据的模型。研究开展了多项数值实验，包括学习蝴蝶形滞回曲线以及建模压电致动器的真实滞回数据。所提方法与传统基于回归及神经网络方法进行了对比，证明了其高效性与鲁棒性。源代码详见https://github.com/chandratue/SmartHysteresis