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

2025-10-28

AI Summary

This work addresses the low computational efficiency and physical inconsistency of existing methods for indoor acoustic field prediction in the mid-to-high-frequency range (1–5 kHz). We propose HergNet, a physics-informed neural network that intrinsically embeds the plane-wave superposition principle into its architecture, ensuring that outputs rigorously satisfy the Helmholtz equation without post-hoc correction. A boundary-aware loss function is introduced to explicitly enforce acoustic boundary conditions. Compared with state-of-the-art data-driven or conventional numerical methods, HergNet achieves superior accuracy and significantly accelerated inference—particularly in 2D and 3D acoustic modeling within the 1–5 kHz band. To our knowledge, this is the first framework enabling end-to-end differentiable coupling of plane-wave bases with deep neural networks. HergNet establishes a general, efficient, and physically self-consistent paradigm for solving wave-based boundary value problems, with broad applicability across acoustics, optics, and electromagnetics.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Low Level & Physics-based Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Predicts sound fields efficiently in 2D and 3D
• Automatically satisfies the Helmholtz equation physically
• Learns boundary-value solutions for wave phenomena

Innovation

• Neural network architecture for sound field prediction
• Automatically satisfies Helmholtz equation physically
• Outperforms state-of-the-art room acoustics simulation methods