Acoustic wave behaviour is described by the acoustic wave equation, which is a partial differential equation (PDE). PDEs are difficult to solve except for in the simplest cases, which necessitate the use of simplified models (such as geometric approaches) or numerical methods (such as Finite Element) for real-world applications like room acoustics and loudspeaker radiation. Neural Operators are an emerging class of deep learning architectures that learn to approximate a solution to a PDE. Fourier Neural Operators (FNOs) project input functions onto Fourier modes, and parametrise the kernel operator in Fourier space. Learning the underlying acoustic physics should make models more generalisable and accurate, compared to a traditional datato-data approach. However, a large amount of data is still required, and the training process can be challenging. In this paper, a U-shaped Fourier Neural Operator (U-NO or FNO) is used to solve the 3D Helmholtz Equation in air with pairs of simplified loudspeakers (radiating solid cubes). The network is able to learn wave behaviour with varying accuracy across a range of frequencies, ranging from 0.87 dB Mean Absolute Error (MAE) at 500 Hz to 5.35dB at 4 kHz. Once trained, inference is 15 to 3000 times faster than the Boundary Element Method (BEM). Although still at an early stage of development, Neural Operators show significant potential for a wide range of simulation applications.
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