首页|AMWNN: Auxiliary Multiresolution Wavelet-based Neural Networks for Solving Radiative Transfer Problems
AMWNN: Auxiliary Multiresolution Wavelet-based Neural Networks for Solving Radiative Transfer Problems
Feng Han
AMWNN: Auxiliary Multiresolution Wavelet-based Neural Networks for Solving Radiative Transfer Problems
AMWNN: Auxiliary Multiresolution Wavelet-based Neural Networks for Solving Radiative Transfer Problems
摘要
In this paper, we propose an auxiliary multiresolution wavelet neural network (AMWNN)method for solving integro-differential problems arising in radiative transfer theory. TheAMWNN reformulates the integro-differential equation into a system of differential equationsthrough an auxiliary function and approximates the unknown functions with a multiresolutionwavelet neural network (MWNN). Substituting these approximations into the governingequations yields a linear least-squares system, which is solved by direct matrix inversionwithout iterative training. The method is applied to a free-space radiation problem, steadyand unsteady absorbing-scattering radiative transfer problems, and a Schwarzschild–Milneintegral equation. Numerical results demonstrate that the AMWNN method delivers superioraccuracy and computational speed compared with the auxiliary physics-informed neural network(APINN) method. The proposed method extends physics-informed multiresolution waveletneural networks to a class of integro-differential radiative transfer problems and provides apromising numerical tool for modeling complex scattering media.