Neural Network Architectures for Simulating Time-Varying Room Acoustics

The application of neural networks to learning physical systems has seen tremendous growth. This is due in part to the ability of neural networks to act as finite or even infinite dimension solution operators. One recent and interesting application is using neural networks to learn room acoustics. This neural network would be a low latency method for assessing the sound quality of any enclosed space. Good sound quality is essential for maintaining an attentive audience in places such as lecture halls, cathedrals, offices, and theaters. Unfortunately, the research in this area is still lacking. Many publications in this field focus on creating neural networks that can learn time-varying acoustic waves on simple square grids with open boundaries, meaning that wave reflection off of arbitrarily-shaped boundaries are ignored. One paper that successfully incorporated the effect of arbitrarily-shaped boundaries, presented at a recent NeurIPS, applied only to time-invariant acoustic fields where the acoustic source was an impulse. Therefore, we have found a hole in the literature with regards to a neural network that can learn time-varying acoustic waves, with reflections, in grids of arbitrary geometry, where the acoustic source is a sinusoidal point source. To create such a neural network, we tried three architectures: physics informed neural networks (PINNs), spatial neural oper-ators (NOs), and Fourier Neural Operators (FNOs). We found that PINNs and NOs worked well, with the PINN having the extra benefit of being able to incorporate any number of input parameters, including the time dimension and frequency.