This article presents an approach for modelling hysteresis in smart materials, specifically 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. 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. Source code is available at https://github.com/chandratue/SmartHysteresis.

翻译：本文提出了一种方法来模拟智能材料中的滞后效应，特别是压电材料，并利用机器学习的最新进展，特别是稀疏回归技术。虽然稀疏回归先前已经被用于模拟各种科学和工程现象，但其在压电材料中非线性滞后建模方面的应用尚未得到研究。该研究采用最小二乘算法和顺序阈值来建模导致滞后的动态系统，从而得到一个简明的模型，可以准确地预测模拟和实验压电材料数据的滞后。进行了几个数值实验，包括学习蝴蝶形滞后和对压电驱动器的实际滞后数据建模。此外，针对非定向电工钢，提供了大致白盒子的稀疏建模方法。该方法与传统的回归和神经网络方法进行了比较，证明其效率和鲁棒性。源代码可在https://github.com/chandratue/SmartHysteresis上获得。