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

arXiv: https://arxiv.org/abs/2405.04003 · HTML: https://mlsanity.com/paper/2405.04003/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 7 May 2024.

## Builds on (most cited first, 6 of 6)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Wavelet neural operator: a neural operator for parametric partial differential equations](https://mlsanity.com/paper/2205.02191/) (2022)
- [Data-Driven Deep Learning of Partial Differential Equations in Modal Space](https://mlsanity.com/paper/1910.06948/) (2019)
- [Koopman operator for time-dependent reliability analysis](https://mlsanity.com/paper/2203.02658/) (2022)

## Built on by (most cited first, 2 of 2)

- [Generative Monte Carlo Sampling for Constant-Cost Particle Transport](https://mlsanity.com/paper/2512.13965/) (2025)
- [Surrogate Modeling for Neutron Transport: A Neural Operator Approach](https://mlsanity.com/paper/2602.15890/) (2026)

## Abstract (arXiv)

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.