HergNet: a Fast Neural Surrogate Model for Sound Field Predictions via Superposition of Plane Waves

ABSTRACT We present a novel neural network architecture for the efficient prediction of sound fields in two and three dimensions. The network is designed to automatically satisfy the Helmholtz equation, ensuring that the outputs are physically valid. Therefore, the method can effectively learn solutions to boundary-value problems in various wave phenomena, such as acoustics, optics, and electromagnetism. Numerical experiments show that the proposed strategy can potentially outperform state-of-the-art methods in room acoustics simulation, in particular in the range of mid to high frequencies. Index T erms-- Helmholtz equation, wave fields, room acoustics, physics-informed neural networks 1. INTRODUCTION Several physical phenomena are represented by propagation of waves, especially in fields like acoustics, optics, quantum mechanics, electromagnetism and surface fluid mechanics [1, 2, 3, 4, 5]. Fast and accurate simulations of waves dynamics is therefore of great relevance to the scientific community, in particular in complex scenarios, where high frequencies, broad domains or long time intervals are considered.