Physical Modelling of Stiff Membrane Vibration using Neural Networks with Spectral Convolution Layers

Abstract

Physical modelling synthesis is currently limited in its ap- plications due to the high computational cost of some of the algorithms. Typically, these models are obtained by discretizing a mathematical model described by ordinary or partial differential equations, using well-established methods like finite differences or modal decomposition. Recent advances in machine-learning have sought to model these systems of differential equations using spe- cialised architectures such as the Fourier Neural Opera- tor (FNO), enabling extremely fast inference times and resolution-independent computational cost. Building on recent work extending the FNO approach for its applica- tion to acoustics problems, we examine the performance and robustness of these methods in the case of a stiff and lossy membrane. We show that the FNO approach is only able to accurately model the behaviour of the membrane within the range of timesteps used for training, becoming unstable or decaying rapidly beyond that.