Physics-Informed Adaptive Training for 3D Acoustic Wave Propagation

Leonardo Mendonça, Márcio Marques, Pavel Petrov, Lucas Nissenbaum

Keywords: Physics-Informed Neural Networks, 3D wave equation, Adaptive sampling, Neural Tangent Kernel, Implicit representation, Meshless representation

TL;DR: We apply a stable adaptive physics-informed training for learning a meshless representation of a 3D acoustic wavefield in the time domain.

Abstract: Physics-informed neural networks (PINNs) provide an implicit, meshless approach to solving high-dimensional partial differential equations while avoiding the curse of dimensionality. Despite recent progress, their application to three-dimensional wave propagation problems in time domain remains limited. In this study, a novel stable training scheme that combines adaptive sampling, absorbing boundary conditions, and neural tangent kernel (NTK) dynamical loss balancing is proposed. Exploiting strong space–time localization of wavefields allows accurate propagation modeling, while avoiding the exponential growth of the number of collocation points with the dimension that is inherent to classical numerical methods.

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Submission Number: 30