High Energy Density Radiative Transfer in the Diffusion Regime with Fourier Neural Operators

TL;DR

This paper introduces Fourier Neural Operators to model radiative heat transfer in high energy density physics, significantly improving accuracy and efficiency over traditional methods by learning from analytical and numerical solutions.

Contribution

It develops two FNO-based models for Marshak wave prediction, enhancing accuracy and generalization in modeling radiative transfer in high energy density systems.

Findings

FNO models outperform traditional analytic approximations in accuracy.

The models generalize well across different material properties and conditions.

Significant reduction in computational cost compared to conventional solvers.

Abstract

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.