Modelling of superposition in 2D linear acoustic wave problems using Fourier Neural Operator networks

A method of solving the 2D acoustic wave equation using Fourier Neural Operator (FNO) networks is presented. Various scenarios including wave superposition are considered, including the modelling of multiple simultaneous sound sources, reflections from domain boundaries and diffraction from randomlypositioned and sized rectangular objects. Training, testing and ground-truth data is produced using the acoustic Finite-Difference Time-Domain (FDTD) method. FNO is selected as the neural architecture as the network architecture requires relatively little memory compared to some other operator network designs. The number of training epochs and the size of training datasets were chosen to be small to test the convergence properties of FNO in challenging learning conditions. FNO networks are shown to be time-efficient means of simulating wave propagation in a 2D domain compared to FDTD, operating 25× faster in some cases. Furthermore, the FNO network is demonstrated as an effective means of data compression, storing a 24.4 GB training dataset as a 15.5 MB set of network weights.