Abstract
By a News Reporter-Staff News Editor at Network Daily News - Researchers detailnew data in networks. According to news reporting out of Hubei, People’s Republic of China, by NewsRxeditors, research stated, “Physics-informed neural networks (PINNs) have been used by researchers to solvepartial differential equation (PDE)-constrained problems. We evaluate PINNs to solve for frequency-domainacoustic wavefields.”The news correspondents obtained a quote from the research from China University of Geosciences:“PINNs can solely use PDEs to define the loss function for optimization without the need for labels. Partialderivatives of PDEs are calculated by mesh-free automatic differentiations. Thus, PINNs are free ofnumerical dispersion artifacts. It has been applied to the scattered acoustic wave equation, which reliedon boundary conditions (BCs) provided by the background analytical wavefield. For a more direct implementation,we solve the nonscattered acoustic wave equation, avoiding limitations related to relying onthe background homogeneous medium for BCs. Experiments support our following insights. Althoughsolving time-domain wave equations using PINNs does not require absorbing boundary conditions (ABCs),ABCs are required to ensure a unique solution for PINNs that solve frequency-domain wave equations,because the single-frequency wavefield is not localized and contains wavefield information over the fulldomain. However, it is not trivial to include the ABC in the PINN implementation, so we develop an adaptiveamplitude-scaled and phase-shifted sine activation function, which performs better than the previousimplementations. Because there are only two outputs for the fully connected neural network (FCNN),we validate a linearly shrinking FCNN that can achieve a comparable and even better accuracy with acheaper computational cost. However, there is a spectral bias problem, that is, PINNs learn low-frequencywavefields far more easily than higher frequencies, and the accuracy of higher frequency wavefields is oftenpoor.”
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