A Variational Physics‐Informed Neural Network Framework for Simulating Nonlinear Elastic Wave Propagation

ABSTRACT This work employs Variational Physics‐Informed Neural Networks (VPINNs) to solve the forward problem of one‐dimensional wave propagation in nonlinear elastic solids. A first‐order elastodynamic formulation is adopted, where particle velocity and strain serve as the primary field variables. In particular, an elementwise hp‐VPINN formulation is considered, enabling the incorporation of finite element concepts such as local approximation spaces, numerical quadrature, and domain decomposition into the VPINN framework. The weak first‐order formulation shifts all derivatives to the test functions, such that the residual evaluation only requires first‐order gradients and avoids higher‐order automatic differentiation. This improves numerical efficiency and stability, which is particularly beneficial for nonlinear wave propagation problems involving steep gradients and harmonic generation. Furthermore, the proposed framework naturally exhibits absorbing boundary behavior without requiring special boundary treatments or damping layers.