PINNs for Learning High-Frequency Elastic Waves in Complex Layered Media

Accurately modelling high-frequency elastic waves in heterogeneous media is central to problems spanning geotechnical engineering, seismic hazard assessment, subsurface energy exploration, and planetary interior studies. Yet traditional numerical solvers are computationally intensive and often struggle with small-scale heterogeneity. Here, we show that physics-informed neural networks (PINNs) can efficiently learn the two-dimensional elastic wave equation without labelled data, using only physical residuals as constraints. We benchmark three architectures—a standard PINN, a Fourier-feature PINN, and the adaptive PirateNet—across homogeneous and multi-layered velocity models. Only PirateNet reproduces complex reflections, transmissions, and mode conversions in six-layered media, achieving stable high-frequency predictions where conventional PINNs fail. Applied examples include subsurface imaging for geothermal and nuclear-energy systems and elastic-wave analysis of planetary crusts. These results highlight the capacity of adaptive PINNs to integrate physical laws and neural representations, offering a unified framework for next-generation simulation and inversion across the Earth and planetary sciences.