Reconstruction of nearshore wave fields based on physics-informed neural networks

This paper focuses on utilizing physics-informed neural networks (PINNs) to model nearshore wave transformation. The nearshore wave nets (NWnets), which integrate the prior knowledge of wave mechanics (i.e., the wave energy balance equation and dispersion relation) and fully connected neural networks, are developed to reconstruct nearshore wave fields with scarce wave measurements. The performance of the NWnets is examined by comparing the PINN outputs with numerical solutions from XBeach and experimental data over a twodimensional alongshore uniform barred beach and a three-dimensional circular shoal, respectively. It is found that the test errors are reasonably small with wave height measurements at only three locations applied as the training data for the alongshore uniform barred beach. Moreover, the NWnets are able to reconstruct the entire wave field and capture the focusing and defocusing of wave energy with sufficient accuracy over the circular shoal when a small amount of wave height measurements from the laboratory experiment are employed as the training data. The influence of network sizes, collocation points, training points, and the resolution of wave directional spreading on the performance of the NWnets is investigated. The adaptive learning rate annealing algorithm is utilized to calculate weighting coefficients for balancing the interplay between different loss terms in the total loss functions. Several illustrative examples of transfer learning are also provided, which can accelerate the training of NWnets for modeling waves under different boundary and bathymetric conditions. Our results show that the physics-guided deep learning method is a promising tool for studying nearshore processes.

Automated summary

This paper focuses on utilizing physics-informed neural networks (PINNs) to model nearshore wave transformation. The performance of the developed nearshore wave nets (NWnets) is examined by comparing the results with numerical solutions and experimental data. The study shows that the physics-guided deep learning method is a promising tool for studying nearshore processes.