A physics-informed machine learning approach to piezoelectric plate modelling

This paper develops the physics-informed neural network (PINN) framework for solving steady-state piezoelectric equations in plates of various geometries without requiring labelled data. The neural network loss function is designed to capture five dependent variables, including deformation, electric potential, and carrier concentration change, while ensuring the satisfaction of a coupled system of partial differential equations (PDEs). This system comprises five conservation equations, nine constitutive equations, and five relevant boundary conditions. To address the significant disparities in magnitudes among the dependent variables, the governing PDEs are reformulated using dimensionless variables. The performance of the proposed PINN method is benchmarked against traditional numerical approaches implemented in COMSOL Multiphysics, demonstrating comparable accuracy. The spatial average relative errors, with respect to the COMSOL results, for the predicted quantities across the three cases range from 0.36% to 1.23%, with larger errors observed in the electrical quantities. Furthermore, this study investigates the impact of the complexity of neural networks, the number of random training points, and the weight of the boundary loss on the accuracy of the predictions to provide insights into the optimisation of the PINN loss function for piezoelectric problems.