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This preprint has been withdrawn due to critical flaws in the simulation code that invalidate its conclusions regarding Physics-Informed Neural Networks for coupled electro-elastodynamic systems. The retraction highlights significant challenges with error accumulation and stiffness in PINNs when applied to complex, time-dependent partial differential equations without a mesh-free solver guaranteeing accuracy. For researchers relying on SciML methods, this case serves as a cautionary reminder that integrating physical laws into loss functions does not automatically ensure robustness against underlying code defects or numerical instability.
A Unified Physics-Informed Neural Network for Modeling Coupled Electro- and Elastodynamic Wave Propagation Using Three-Stage Loss Optimization
arXiv:2602.13811v2 Announce Type: replace-cross 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.
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.
Neural and Evolutionary Computing (cs.NE); Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
arXiv:2602.13811 [cs.NE]
(or arXiv:2602.13811v2 [cs.NE] for this version)
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