HergNet: a Fast Neural Surrogate Model for Sound Field Predictions via Superposition of Plane Waves
Matteo Calafà, Yuanxin Xia, Cheol-Ho Jeong
TL;DR
The paper tackles efficient high-frequency sound-field prediction by introducing HergNet, a physics-consistent neural surrogate that enforces the Helmholtz equation through a Herglotz plane-wave representation $p(\mathbf{x}) = \frac{1}{N_{quad}} \sum_{j=1}^{N_{quad}} e^{ik(\mathbf{x}\cdot \mathbf{s}_j + d_j)} \tilde{h}(\mathbf{s}_j)$. A complex-valued neural network learns the Herglotz density $\tilde{h}$, while a boundary-only loss $ \mathcal{L} = \mathbb{E}_{\mathbf{x}\in \partial\Omega}[(p - Z v_{\mathbf{n}})^2]$ enforces impedance conditions, enabling efficient 2D/3D predictions without interior PDE sampling. The approach scales $N_{quad}$ with frequency as $N_{quad} = f^2/2000$ and demonstrates high fidelity against analytic solutions (e.g., Green’s function) for mid-to-high frequencies with substantially lower computational cost than volumetric solvers like FEM or PINNs. Limitations arise at low frequencies due to the intrinsic plane-wave representation, which is better suited to oscillatory regimes, but the method provides a practical, accurate surrogate for room acoustics and potentially other wave phenomena.
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.