A Unified Physics-Informed Neural Network for Modeling Coupled Electro- and Elastodynamic Wave Propagation Using Three-Stage Loss Optimization

TL;DR

This paper demonstrates that physics-informed neural networks can effectively model coupled electro-elastodynamic wave propagation, achieving low error rates and validating PINNs as mesh-free solvers for complex PDE systems.

Contribution

The study introduces a PINN framework for coupled electro-elastodynamic PDEs, employing a three-stage loss optimization to improve accuracy in modeling piezoelectric wave propagation.

Findings

Achieved 2.34% and 4.87% relative L2 errors for displacement and electric potential.

Validated PINNs as effective mesh-free solvers for coupled PDE systems.

Identified challenges with error accumulation and stiffness in eigenvalue problems.

Abstract

Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the application of PINNs to solve a one dimensional coupled electro-elastodynamic system modeling linear piezoelectricity in stress-charge form, governed by elastodynamic and electrodynamic equations. Our simulation employs a feedforward architecture, mapping space-time coordinates to mechanical displacement and electric potential. Our PINN model achieved global relative L2 errors of 2.34 and 4.87 percent for displacement and electric potential respectively. The results validate PINNs as effective mesh free solvers for coupled time-dependent PDE systems, though challenges remain regarding error accumulation and stiffness in coupled eigenvalue systems.