A physics-informed machine learning approach to piezoelectric plate modelling

Abstract

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.

Publication DOI: https://doi.org/10.1016/j.engappai.2025.111847
Divisions: College of Engineering & Physical Sciences > School of Engineering and Technology > Mechanical, Biomedical & Design
College of Engineering & Physical Sciences > Aston Fluids Group
College of Engineering & Physical Sciences > School of Engineering and Technology
Funding Information: Emad Tandis gratefully acknowledges the start-up funding provided by Aston University and the use of the TAURUS High-Performance Computing facility at Aston University.
Additional Information: Copyright © 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Uncontrolled Keywords: Physics-informed neural network,Piezoelectricity,Coupled partial differential equations,Nondimensionalisation,Plate deformation,Loss function
Publication ISSN: 1873-6769
Data Access Statement: The code supporting the findings of this study is available on GitHub. A link to the repository is provided within the manuscript.
Last Modified: 08 Aug 2025 07:28
Date Deposited: 07 Aug 2025 11:35
Full Text Link:
Related URLs: https://linking ... 952197625018494 (Publisher URL)
PURE Output Type: Article
Published Date: 2025-11-23
Published Online Date: 2025-08-07
Accepted Date: 2025-07-19
Authors: Tandis, Narges
Tandis, Emad (ORCID Profile 0000-0002-3352-0171)

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