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

Jul 16, 2026

Upload by Ezra

A learning-based physics-constrained neural kernel is proposed for sound field estimation, reconstructing the spatial acoustic pressure distribution from discrete microphone measurements used across spatial audio and acoustic analysis. Kernel-regression methods provide a principled way to enforce governing-equation constraints via linear inference. To avoid overfitting from snapshot-only optimization, a source-position-dependent implicit neural representation is introduced for the directional weighting function, improving generalization to unseen source positions and matching target sound-field directivity.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages5

Reading Time13 min

Abstract

Introduction

Problem Formulation

# LEARNING-BASED PHYSICS-CONSTRAINED NEURAL KERNELFOR SOUND FIELD ESTIMATION WITH SOURCE-POSITION-DEPENDENT DIRECTIONAL WEIGHTING Mattia Marella₁,2* and Shoichi Koyama¹ ¹National Institute of Informatics,Tokyo,Japan,²University of Ferrara,Ferrara,Italy arXiv:2607.06274v1[cs.SD]7 Jul 2026 ## ABSTRACT A learning-based physics-constrained neural kernel for sound fieldestimation is proposed.Sound field estimation aims to estimate thespatial distribution of an acoustic field from a discrete set of mi-crophone 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 incor-porating physical constraints and allow inference through linear op-eration.It is also possible to adapt the kernel function to the tar-get acoustic environment by representing the directional weightingfunction as an implicit neural representation(INR)and optimizinghyperparameters using measurements.However,the kernel func-tion is generally optimized for single snapshot measurements of themicrophones,which can lead to strong overfitting and poor gener-alization.We propose a source-position-dependent INR for the di-rectional weighting function,enabling the kernel function to cap-ture common directional patterns and to generalize to unseen sourcepositions in the target acoustic environment.Experimental resultsindicate that our proposed method outperforms the snapshot-basedmethod by estimating a directional weighting function that matchesthe directivity of the target sound field. Index Terms—kernel regression,neural networks,physics-informed machine learning,sound field reconstruction,spatial audio ## 1.INTRODUCTION Sound field estimation/reconstruction/interpolation is a fundamentaltask in audio signal processing and machine learning,aiming to esti-mate the spatial distribution of an acoustic field from a discrete set ofsensor(microphone)observations.It can be applied to a wide varietyof downstream tasks,for example,acoustic imaging,room acous-tic analysis 2,and spatial audio reproduction and control 34. There have been many studies on sound fied estimation 5].One of the most widely used techniques is the basis-expansion-basedmethod,which is based on the representation of the sound field asa linear combination of predefined basis functions,such as planewaves,spherical wave functions,and equivalent point sources 36].The expansion coefficients are then estimated from the microphonemeasurements using the least squares method.Sparse regulariza-tion techniques have also been applied to promote sparsity in thecoefficient space to improve reconstruction accuracy忆-9].Kernel-regression-based methods generalize the (finite-dimensional)basis-expansion-based method to an infinite-dimensional basis expansion, thereby enabling the estimates to be constrained to the solution ofthe governng equation(wave and Helmholtz equations)11. In recent years,neural network (NN)-based methods have at-tracted attention because of their high representational power andinterpolation capabilities [12-16].Physics-informed (penalized andconstrained)approaches have also been investigated in the NN-basedmethods to avoid overfitting and increase the interpretability[17- 21. Among these current sound field estimation methods,thekernel-regression-based methods are particularly practical for ap-plications requiring real-time processing,as they satisfy physicalconstraints while enabling inference through linear operation.Todesign physics-constrained kernel functions,the Herglotz wavefunction [22,which is equivalent to a plane wave expansion,is used.To incorporate prior information regarding the directivity of the tar-get sound field,a directional weighting function can be introducedinto the Herglotz wave function [10.Although a fixed unimodalfunction or its linear combination has been used as the directionalweighting function,they are unable to fully capture the ch

FAQs

What problem does the proposed method address in sound field estimation?

It addresses overfitting and poor generalization caused by optimizing the kernel function using only single-snapshot microphone measurements.

How does the method improve generalization to unseen source positions?

It models the directional weighting function with a source-position-dependent implicit neural representation, trained from data so common directional patterns are captured and adapted without fine-tuning.

What inputs and constraints does the approach rely on?

The method reconstructs the acoustic field in a Helmholtz-governed, source-free region and uses acoustic transfer function data from known source positions, incorporating physical constraints through physics-constrained kernel regression.

Jul 16, 2026

Upload by Ezra