Deep Learning based Spatially Dependent Acoustical Properties Recovery
This work addresses the challenge of recovering acoustical properties in inhomogeneous media for applications like medical imaging or material science, representing an incremental improvement over existing PINN methods by handling spatial dependence.
The authors tackled the problem of recovering spatially dependent coefficients in partial differential equations (PDEs) from physical measurements, proposing a spatially dependent physics-informed neural network (SD-PINN) that eliminates the need for domain-specific expertise and demonstrates robustness to noise.
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.