Pre-trained physics-informed neural networks for one-dimensional wave propagation in coastal engineering

Modeling wave propagation over variable coastal topographies remains challenging due to the interplay of nonlinear shallow‑water dynamics and dispersive effects. Here, we introduce a Pre‑Trained Physics‑Informed Neural Network (PT‑PINN) framework that couples a physics‑guided pre‑training phase with rigorous cross‑validation to solve the Saint‑Venant and Boussinesq equations. During pre‑training, the network generates a physics‑informed initial approximation, constructs auxiliary supervised data, and yields optimized parameter seeds, all of which accelerate and stabilize subsequent formal training. Cross‑validation on the pre‑training–derived dataset then guides hyperparameter selection, ensuring an effective balance between physics‑driven and data‑driven loss components.

We demonstrate the PT‑PINN approach across four benchmark scenarios: (1) dam‑break flow in a wet domain, (2) non‑breaking wave propagation on inclined slopes, (3) periodic tidal waves in an inclined open channel, and (4) shoaling waves over a submerged breakwater. In each case, PT‑PINNs faithfully capture both bulk wave evolution and fine‑scale dispersive details. Comparative studies against analytical and finite‑difference solutions reveal that PT‑PINNs match their accuracy while offering enhanced stability in representing high‑frequency microscale features. These results underscore the promise of pre‑trained, physics‑informed networks as a versatile and robust tool for coastal wave modeling in complex bathymetric settings.