Modeling the Wave Equation Using Physics-Informed Neural Networks Enhanced with Attention to Loss Weights

Modeling Partial differential equations (PDEs) is a well-known challenge in the field of scientific computing. In particular, the linear acoustic wave PDE forms a significant problem in modeling due to its oscillatory behavior and multi-scale tendency. With the recently introduced class of deep neural networks, the physics-informed neural networks (PINNs), a mesh-free approach can now be utilized to model the wave PDE without the need for a previously known solution for training. Other training challenges remain such as the selection of hyperparameters and loss convergence. In this paper, we propose an enhancement that focuses on the assigned weights for the PINN loss function terms in order to more accurately model the wave PDE in a homogeneous, inhomogeneous domain, and with a higher frequency wave source function. The proposed enhancement reflected reduced residual and relative error values compared to the baseline architecture.