[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119581-en":3,"doc-seo-119581-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119581,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Physics-Informed Machine Learning For Sound Field Estimation - Invited paper","Sound field estimation focuses on reconstructing the spatial distribution of acoustic quantities such as sound pressure, forming a foundation for spatial audio processing technologies. The problem is modeled as function interpolation, yet data-only interpolation methods cannot reliably achieve high accuracy. Physics-informed machine learning (PIML) addresses this limitation by injecting prior physical properties of sound fields into learning and estimation. The paper presents PIML fundamentals for sound field estimation and surveys state-of-the-art PIML-based methods, emphasizing how governing acoustical constraints improve performance and reduce unrealistic artifacts.","arXiv :2408 . 14731v1 [ cs . SD] 27 Aug 2024  \nPhysics-Informed Machine Learning For Sound Field Estimation  \nInvited paper for the IEEE SPM Special Issue on Model-based Data-Driven Audio Signal  \nProcessing  \nShoichi Koyama, Senior Member, IEEE, Juliano G. C. Ribeiro, Member, IEEE, Tomohiko Nakamura, Member, IEEE, Natsuki Ueno, Member, IEEE, and Mirco Pezzoli, Member, IEEE  \nAbstract  \nThe area of study concerning the estimation of spatial sound, i.e., the distribution of a physical quantity of sound such as acoustic pressure, is called sound field estimation, which is the basis for various applied technologies related to spatial audio processing. The sound field estimation problem is formulated as a function interpolation problem in machine learning in a simplified scenario. However, high estimation performance cannot be expected by simply applying general interpolation techniques that rely only on data. The physical properties of sound fields are useful a priori information, and it is considered extremely important to incorporate them into the estimation. In this article, we introduce the fundamentals of physics-informed machine learning (PIML) for sound field estimation and overview current PIML-based sound field estimation methods.  \nIndex Terms  \nSound field estimation, kernel methods, physics-informed machine learning, physics-informed neural networks  \nI. INTRODUCTION  \nSound field estimation, which is also referred to as sound field reconstruction, capturing, and interpolation, is a fundamental problem in acoustic signal processing, which is aimed at reconstructing a  \nThis work was supported by JST FOREST Program, Grant Number JPMJFR216M, JSPS KAKENHI, Grant Number 23K24864, and the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on “Telecommunications of the Future”(PE00000001—program “RESTART”) .  \nManuscript received April xx, 20xx; revised August xx, 20xx.  \nFig. 1. Sound field recording for VR audio. The sound field captured by a microphone array is reproduced by loudspeakers or headphones. The estimated sound field should account for listener movement and rotation within large regions.  \nspatial acoustic field from a discrete set of microphone measurements. This essential technology has a wide variety of applications, such as room acoustic analysis, the visualization/auralization of an acoustic field, spatial audio reproduction using a loudspeaker array or headphones, and active noise cancellation in a spatial region. In particular, virtual/augmented reality (VR/AR) audio would be one of the most remarkable recent applications of this technology, as it requires capturing a sound field in a large region by multiple microphones (see Fig. 1) . The spatial reconstruction of room impulse responses (RIRs) or acoustic transfer functions (ATFs), which is a special case of sound field estimation, can be applied to the estimation of steering vectors for beamforming and also head-related transfer functions (HRTFs) for binaural reproduction.  \nSound field estimation has been studied for a number of years. Estimating a sound field in the inverse direction of wave propagation based on wave domain (or spatial frequency domain) processing, i.e., the basis expansion of a sound field into plane wave or spherical wave functions, has been particularly applied to acoustic imaging tasks [1] . This technique has been introduced in the signal-processing field in recent decades. In particular, spherical harmonic domain processing using a spherical microphone array has been intensively investigated because its isotropic nature is suitable for spatial sound processing [2] . Wave domain processing has been applied to, for instance, spatial audio recording, source localization, source separation, and spatial active noise control.  \nThe theoretical foundation of wave domain processing is derived from expansion representations by the solutions of the governing partial differentia","cbCaimOf5XE08YF7","https://ap.wps.com/l/cbCaimOf5XE08YF7","pdf",5903353,1,23,"English","en",105,"# Introduction\n## Sound field estimation problem and applications\n## Wave domain processing and theoretical foundations\n## Physics-informed approaches (PIML/PINNs)\n# Physics-informed machine learning for sound field estimation","[{\"question\":\"What problem does sound field estimation aim to solve?\",\"answer\":\"It reconstructs the spatial distribution of acoustic quantities, such as acoustic pressure or related fields, from discrete microphone measurements.\"},{\"question\":\"Why are general data-driven interpolation methods insufficient for this task?\",\"answer\":\"They rely only on data and cannot enforce the physical constraints that sound fields must satisfy, which limits achievable estimation accuracy.\"},{\"question\":\"How does physics-informed machine learning improve sound field estimation?\",\"answer\":\"It incorporates prior physical properties—often by enforcing governing equations through physics-informed losses—so the learned estimate better satisfies acoustical wave/Helmholtz constraints.\"}]","Physics-Informed Machine Learning For Sound Field Estimation - 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