Spatial acoustic properties recovery with deep learning

The physics-informed neural network (PINN) can recover partial differential equation (PDE) coefficients that remain constant throughout the spatial domain directly from measurements. We propose a spatially dependent physics-informed neural network (SD-PINN), which enables recovering coefficients in spatially dependent PDEs using one neural network, eliminating the requirement for domain-specific physical expertise. The network is trained by minimizing a combination of loss functions involving data-fitting and physical constraints, in which the requirement for satisfying the assumed governing PDE is encoded. For the recovery of spatially two-dimensional (2D) PDEs, we store the PDE coefficients at all locations in the 2D region of interest into a matrix and incorporate a low-rank assumption for this matrix to recover the coefficients at locations without measurements. We apply the SD-PINN to recovering spatially dependent coefficients of the wave equation to reveal the spatial distribution of acoustic properties in the inhomogeneous medium.