Radiative heat transfer is a fundamental process in high energy density
physics and inertial fusion. Accurately predicting the behavior of Marshak
waves across a wide range of material properties and drive conditions is
crucial for design and analysis of these systems. Conventional numerical
solvers and analytical approximations often face challenges in terms of
accuracy and computational efficiency. In this work, we propose a novel
approach to model Marshak waves using Fourier Neural Operators (FNO). We
develop two FNO-based models: (1) a base model that learns the mapping between
the drive condition and material properties to a solution approximation based
on the widely used analytic model by Hammer & Rosen (2003), and (2) a model
that corrects the inaccuracies of the analytic approximation by learning the
mapping to a more accurate numerical solution. Our results demonstrate the
strong generalization capabilities of the FNOs and show significant
improvements in prediction accuracy compared to the base analytic model.

利用 Fourier 神经算子 (FNO) 建立了两个模型，分别通过学习将驱动条件和材料特性映射到基于 Hammer 和 Rosen (2003) 经典解析模型的解精度近似以及更准确的数值解来模拟 Marshak 波，结果表明 FNO 具有很强的泛化能力并显著提高了预测准确性。