偏微分方程
人工神经网络
领域(数学分析)
基质(化学分析)
计算机科学
偏导数
应用数学
秩(图论)
数学分析
数学
算法
人工智能
材料科学
组合数学
复合材料
作者
Ruixian Liu,Peter Gerstoft
出处
期刊:Journal of the Acoustical Society of America
[Acoustical Society of America]
日期:2024-06-01
卷期号:155 (6): 3690-3701
摘要
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.
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