Learning-based Physics-Constrained Neural Kernel for Sound Field Estimation With Source-Position-Dependent Directional Weighting

2026-07-07

AI Summary

This work addresses the poor generalization of single-snapshot acoustic field estimation methods to unseen source locations, a limitation often caused by overfitting. To overcome this, the authors propose a neural kernel approach that integrates physical constraints with learning-based mechanisms. The key innovation lies in modeling directional weighting functions as implicit neural representations (INRs) conditioned on source position, enabling the kernel to capture shared directional patterns and generalize effectively to novel locations. By combining physics-informed kernel regression with a multi-position measurement optimization strategy, the proposed method significantly outperforms conventional single-snapshot techniques in experiments, achieving more accurate reconstruction of the target sound field’s directional characteristics and superior estimation performance at previously unobserved source positions.

Abstract

A learning-based physics-constrained neural kernel for sound field estimation is proposed. Sound field estimation aims to estimate the spatial distribution of an acoustic field from a discrete set of microphone measurements, which have a wide range of applications. Among existing sound field estimation methods, kernel-regression-based methods offer a flexible and principled framework for incorporating physical constraints and allow inference through linear operation. It is also possible to adapt the kernel function to the target acoustic environment by representing the directional weighting function as an implicit neural representation (INR) and optimizing hyperparameters using measurements. However, the kernel function is generally optimized for single snapshot measurements of the microphones, which can lead to strong overfitting and poor generalization. We propose a source-position-dependent INR for the directional weighting function, enabling the kernel function to capture common directional patterns and to generalize to unseen source positions in the target acoustic environment. Experimental results indicate that our proposed method outperforms the snapshot-based method by estimating a directional weighting function that matches the directivity of the target sound field.

Problem

• sound field estimation
• kernel regression
• overfitting
• generalization
• source position

Innovation

• physics-constrained neural kernel
• implicit neural representation
• sound field estimation
• source-position-dependent weighting
• directional pattern generalization