Deep Learning based Spatially Dependent Acoustical Properties Recovery

• URL: http://arxiv.org/abs/2310.10970v2
• Date: Thu, 23 Nov 2023 00:02:55 GMT
• Title: Deep Learning based Spatially Dependent Acoustical Properties Recovery
• Abstract summary: The physics-informed neural network (PINN) is capable of recovering partial differential equation (PDE) coefficients that remain constant throughout the spatial domain directly from physical measurements. We apply the SD-PINN to spatially-dependent wave equation coefficients recovery to reveal the spatial distribution of acoustical properties in the inhomogeneous medium. The proposed method exhibits to noise owing to the robustness of a loss function for the physical constraint that the assumed PDE must be satisfied.
• Score: 24.038657275311373
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The physics-informed neural network (PINN) is capable of recovering partial differential equation (PDE) coefficients that remain constant throughout the spatial domain directly from physical measurements. In this work, we propose a spatially dependent physics-informed neural network (SD-PINN), which enables the recovery of coefficients in spatially-dependent PDEs using a single neural network, eliminating the requirement for domain-specific physical expertise. We apply the SD-PINN to spatially-dependent wave equation coefficients recovery to reveal the spatial distribution of acoustical properties in the inhomogeneous medium. The proposed method exhibits robustness to noise owing to the incorporation of a loss function for the physical constraint that the assumed PDE must be satisfied. For the coefficients recovery of spatially two-dimensional PDEs, we store the PDE coefficients at all locations in the 2D region of interest into a matrix and incorporate the low-rank assumption for such a matrix to recover the coefficients at locations without available measurements.

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