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

arXiv: https://arxiv.org/abs/2307.14013 · HTML: https://mlsanity.com/paper/2307.14013/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2023.

## Built on by (most cited first, 3 of 3)

- [A Physics-Informed Neural Network-Based Approach for the Spatial Upsampling of Spherical Microphone Arrays](https://mlsanity.com/paper/2407.18732/) (2024)
- [Point Neuron Learning: A New Physics-Informed Neural Network Architecture](https://mlsanity.com/paper/2408.16969/) (2024)
- [SHAMaNS: Sound Localization with Hybrid Alpha-Stable Spatial Measure and Neural Steerer](https://mlsanity.com/paper/2506.18954/) (2025)

## Abstract (arXiv)

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.