Neural Network Approaches to 2D Acoustic Wave Modelling for Room Acoustics Simulation

The accurate simulation of wave propagation in enclosed spaces is critical for applications ranging from architectural acoustics and audio system design to the auralisation of digital environments in virtual reality. Numerical solutions to the acoustic wave equation offer one approach, providing sufficient levels of accuracy to wave propagation problems, but they are limited in other ways, for instance when dealing with complex scenarios or environments, in terms of the computational resources they demand, or the numerical errors introduced.

This thesis initially investigates Physics-Informed Neural Networks (PINNs) as a method to solve the 1D and 2D acoustic wave equation. PINNs do not require domain discretization and so predict dispersion-error free solutions compared to traditional Finite Difference Time Domain (FDTD) numerical approaches. The limitations of the PINN architecture and unsupervised training are explored, leading to a Fourier Operator Network (FNO) and supervised training scheme solution. The FNO architecture is shown to solve for various 2D acoustic system parameters of increasing complexity without retraining, including sound source position and domain geometry. To test the subjective quality of the FNO results produced, an ABX listening test is presented using signals auralised from both FNO predictions and ground-truth FDTD numerical simulations.

The PINN networks presented here show issues with convergence and generalisation, whilst the FNO networks discussed address these issues and demonstrate better prediction accuracy. It is also shown that listeners cannot consistently distinguish between FDTD and FNO auralisations when there is a direct path between source and receiver in a reflective domain. Introducing an object that blocks this direct path causes the subjective accuracy of the FNO model to degrade, allowing for aural distinctions to be made by listeners. Additional challenges, such as FNO training times, data preparation and computational constraints are also discussed.