Sound Field Estimation around a Rigid Sphere with Physics-informed Neural Network

TL;DR

This paper introduces a physics-informed neural network for estimating sound fields around a rigid sphere, effectively integrating physical laws to improve accuracy with limited data.

Contribution

It presents a novel neural network architecture that incorporates Helmholtz equation constraints, enabling accurate sound field estimation without extensive data or spherical harmonic truncation issues.

Findings

Outperforms spherical harmonic and plane-wave methods in accuracy

Requires fewer measurements for reliable estimation

Provides physically feasible sound field reconstructions

Abstract

Accurate estimation of the sound field around a rigid sphere necessitates adequate sampling on the sphere, which may not always be possible. To overcome this challenge, this paper proposes a method for sound field estimation based on a physics-informed neural network. This approach integrates physical knowledge into the architecture and training process of the network. In contrast to other learning-based methods, the proposed method incorporates additional constraints derived from the Helmholtz equation and the zero radial velocity condition on the rigid sphere. Consequently, it can generate physically feasible estimations without requiring a large dataset. In contrast to the spherical harmonic-based method, the proposed approach has better fitting abilities and circumvents the ill condition caused by truncation. Simulation results demonstrate the effectiveness of the proposed method in achieving accurate sound field estimations from limited measurements, outperforming the spherical harmonic method and plane-wave decomposition method.