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

2026-07-21 · Source: cs.NE updates on arXiv.org · Field: Science & Research — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, extended

Summary

A Physics-Informed Neural Network (PINN) was developed to model one-dimensional coupled electro-elastodynamic wave propagation in linear piezoelectricity, a challenging multiphysics system. This PINN utilizes a feedforward architecture with 8 hidden layers and 180 neurons per layer, mapping space-time coordinates to mechanical displacement and electric potential. It achieved global relative L2 errors of 2.34% for displacement and 4.87% for electric potential on a 200,000-point evaluation grid. The model incorporates hard-constraint basis functions for boundary and initial conditions and a three-stage optimization strategy (Adam, AdamW, L-BFGS) for training on dual NVIDIA T4 GPUs. While successfully reproducing standing-wave behavior, the study identified limitations, including time-dependent error growth and amplified errors in the electric potential field due to derivative propagation.

Key takeaway

For AI Scientists and Research Scientists developing PINNs for coupled multiphysics problems, you should implement hard-constraint basis functions to ensure boundary accuracy and consider a multi-stage optimization strategy like Adam, AdamW, and L-BFGS for robust convergence. Be prepared for potential error amplification in coupled fields, particularly with derivatives, and explore advanced architectures or domain decomposition for long-time horizon simulations.

Key insights

PINNs can model coupled electro-elastodynamic systems, but face challenges with error propagation and time-dependent accuracy in multiphysics.

Principles

• PINNs integrate physical laws via soft constraints in the loss function.
• Hard constraints for boundary conditions significantly reduce errors.
• Coupled systems can amplify errors across interacting fields.

Method

A three-stage optimization (Adam, AdamW, L-BFGS) trains a feedforward PINN with hard-constrained boundary/initial conditions and physics residuals. Collocation points are sampled for PDE, boundary, and initial losses.

In practice

• Use hard constraints for boundary conditions in PINNs.
• Employ multi-stage optimization for improved PINN convergence.
• Be aware of error amplification in coupled PINN systems.

Topics

• Physics-Informed Neural Networks
• Electro-elastodynamics
• Piezoelectricity
• Partial Differential Equations
• Scientific Machine Learning
• Neural Network Optimization
• Multiphysics Modeling

Best for: AI Scientist, Research Scientist

Related on AIssential

• A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems — PINNs combined with explicit FEA accurately model elastodynamic wave propagation in bimaterial systems.
• Differential Equations V — Physics Informed Neural Networks (PINNs) — Physics Informed Neural Networks embed physical laws into neural networks for fast, accurate, and physically consistent simulations.
• Extended pseudo-spectral physics-informed neural networks for phase-field models — ESPINN accurately infers phase-field model parameters and free-energy structure from limited transient data, even with noise.
• PINN loss functions: why physics-informed networks often fail to train — PINNs struggle to train due to severe gradient imbalance and scale differences among their multi-term loss functions.
• Evolutionary Two-Stage Hyperparameter Optimization Strategies for Physics-Informed Neural Networks — A two-stage evolutionary approach effectively optimizes PINN hyperparameters, improving accuracy and robustness under computational constraints.
• Dual-Network PINNs for Optimal Control: A Reproducible Benchmark on the Mass-Spring-Damper System — A dual-network PINN formulation achieves high accuracy in optimal control by exactly enforcing boundary conditions, offering a clear, reproducible alternative to classical methods.

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.