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 sequential threshold least-squares algorithm 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. Additionally, insights are provided on sparse white-box modelling of hysteresis for magnetic materials taking non-oriented electrical steel as an example. The presented approach is compared to traditional regression-based and neural network methods, demonstrating its efficiency and robustness.

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）对压电材料中的迟滞现象进行建模的方法。尽管稀疏回归此前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迟滞建模中的应用尚未得到探索。本研究采用序贯阈值最小二乘算法来构建导致迟滞的动态系统模型，最终得到一个简洁的模型，该模型能够准确预测模拟数据与实验压电材料数据的迟滞行为。此外，本文还以无取向电工钢为例，为磁性材料的稀疏白箱迟滞建模提供了见解。所提出的方法与传统的基于回归的方法及神经网络方法进行了比较，证明了其高效性与鲁棒性。