Solving the inhomogeneous wave equation using physics-informed neural networks

Physics-informed neural networks (PINNs) have emerged as an effective framework for solving forward and inverse problems involving the wave equation. Current PINN formulations primarily address the homogeneous wave equation, where the forcing term is null. Consequently, the absorption or injection of acoustic energy is either unaccounted for or implicitly introduced as boundary conditions. In this work, we explore the use of PINNs to explicitly solve the inhomogeneous wave equation. By incorporating a forcing term in the wave equation residual, our PINN formulation can readily account for time-dependent sources and sinks of acoustic energy. This approach facilitates the inclusion of moving sources or sources with time-dependent output power. As an example, we solve a sound field reconstruction problem involving dynamic sources moving through a medium.