Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations

arXiv:2403.01820v1 Announce Type: cross
Abstract: We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. To achieve this, we utilize the Physics-Informed Neural Networks (PINNs) framework and design a new adaptive exponentially weighted Asymptotic-Preserving (AP) loss function, which incorporates the macroscopic auxiliary equation that is derived from the original transfer equation directly and explicitly contains the information of the diffusion limit equation. Thus, …

abstract arxiv cs.lg cs.na design dimensionality framework linear math.na nature network networks neural network neural networks physics physics-informed scale solve transfer type