Spatial acoustic properties recovery with deep learning.

Area of Science:

• Computational physics
• Machine learning applications
• Inverse problems in physics

Background:

• Traditional physics-informed neural networks (PINNs) excel at recovering constant partial differential equation (PDE) coefficients.
• Recovering spatially varying coefficients often requires domain-specific expertise or multiple models.
• A gap exists in efficiently identifying spatially heterogeneous material properties from limited data.

Purpose of the Study:

• To introduce a novel Spatially Dependent Physics-Informed Neural Network (SD-PINN) for recovering spatially varying PDE coefficients.
• To demonstrate the SD-PINN's ability to function without prior domain-specific physical knowledge.
• To apply the SD-PINN to characterizing acoustic properties in inhomogeneous media using the wave equation.

Main Methods:

• Developed an SD-PINN architecture capable of inferring coefficients that change across the spatial domain.
• Trained the network by minimizing a combined loss function incorporating data-fitting and physical constraints derived from the governing PDE.
• Employed a low-rank matrix assumption for PDE coefficients in two-dimensional (2D) regions to enable recovery at unmeasured locations.

Main Results:

• The SD-PINN successfully recovered spatially dependent coefficients of the wave equation.
• The method demonstrated effective coefficient recovery even in regions with sparse or no direct measurements.
• The spatial distribution of acoustic properties in an inhomogeneous medium was successfully revealed.

Conclusions:

• SD-PINNs offer a powerful, unified approach for identifying spatially varying PDE coefficients.
• This method significantly reduces the reliance on specialized physical expertise for inverse problems.
• The SD-PINN framework shows promise for material characterization and understanding complex physical phenomena.