CGFFT Iterative Solver of Integral Equations Launched on a Neural Network Platform

Recent studies on neural networks in solving Maxwell's equations inquire about the explainability of neural networks. Most neural networks are constructed by multiple neural layers, which are in a similar architecture as numerical iterative solvers for Maxwell's equations. This paper demonstrates the work that launches a fast iterative solver for integral equations as a neural network on a neural network platform, PyTorch. The fast iterative solver is the Conjugate-Gradient Fast-Fourier-Transform (CGFFT) solver, considering its fast convergence, small computation cost, and good scalability. A 1D single-slab scattering problem and a 2D cylinder scattering problem are solved through the CGFFT neural network implemented on PyTorch. With PyTorch's optimized computation scheme for matrix computation and GPU parallelization, the solver takes much less time compared to its traditional implementation.