Physics-Informed Machine Learning for Sound Field Estimation: Fundamentals, state of the art, and challenges

The 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">physics-informed machine learning (PIML)</i> for sound field estimation and overview current PIML-based sound field estimation methods.