# Physics Informed Neural Networks for Simulating Radiative Transfer

arXiv: https://arxiv.org/abs/2009.13291 · HTML: https://mlsanity.com/paper/2009.13291/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2020.

## Built on by (most cited first, 30 of 35)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [On the approximation of functions by tanh neural networks](https://mlsanity.com/paper/2104.08938/) (2021)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Generic bounds on the approximation error for physics-informed (and) operator learning](https://mlsanity.com/paper/2205.11393/) (2022)
- [Error estimates for physics informed neural networks approximating the Navier-Stokes equations](https://mlsanity.com/paper/2203.09346/) (2022)
- [Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs](https://mlsanity.com/paper/2106.14473/) (2021)
- [Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be?](https://mlsanity.com/paper/2405.04230/) (2024)
- [wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws](https://mlsanity.com/paper/2207.08483/) (2022)
- [An operator preconditioning perspective on training in physics-informed machine learning](https://mlsanity.com/paper/2310.05801/) (2023)
- [Partial Differential Equations Meet Deep Neural Networks: A Survey](https://mlsanity.com/paper/2211.05567/) (2022)
- [Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure](https://mlsanity.com/paper/2105.05690/) (2021)
- [Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem](https://mlsanity.com/paper/2405.12380/) (2024)
- [Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases](https://mlsanity.com/paper/2410.03496/) (2024)
- [Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?](https://mlsanity.com/paper/2204.11231/) (2022)
- [Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance](https://mlsanity.com/paper/2303.03918/) (2023)
- [Deep neural network surrogates for non-smooth quantities of interest in shape uncertainty quantification](https://mlsanity.com/paper/2101.07023/) (2021)
- [Physics-constrained Unsupervised Learning of Partial Differential Equations using Meshes](https://mlsanity.com/paper/2203.16628/) (2022)
- [A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations](https://mlsanity.com/paper/2212.05523/) (2022)
- [Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers](https://mlsanity.com/paper/2505.12556/) (2025)
- [Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time](https://mlsanity.com/paper/2303.12245/) (2023)
- [Maximum-likelihood Estimators in Physics-Informed Neural Networks for High-dimensional Inverse Problems](https://mlsanity.com/paper/2304.05991/) (2023)
- [Understanding Generalization in Physics Informed Models through Affine Variety Dimensions](https://mlsanity.com/paper/2501.18879/) (2025)
- [Machine learning moment closure models for the radiative transfer equation IV: enforcing symmetrizable hyperbolicity in two dimensions](https://mlsanity.com/paper/2604.20143/) (2026)
- [Number Theoretic Accelerated Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.13869/) (2023)
- [Bayesian Reasoning for Physics Informed Neural Networks](https://mlsanity.com/paper/2308.13222/) (2023)
- [Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations](https://mlsanity.com/paper/2403.01820/) (2024)
- [Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks](https://mlsanity.com/paper/2406.06350/) (2024)
- [Feasibility Study of CNNs and MLPs for Radiation Heat Transfer in 2-D Furnaces with Spectrally Participative Gases](https://mlsanity.com/paper/2506.08033/) (2025)
- [Emulating Radiative Transfer in Astrophysical Environments](https://mlsanity.com/paper/2511.08219/) (2025)
- [Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation](https://mlsanity.com/paper/2512.05976/) (2025)

## Abstract (arXiv)

We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative tranfer equations. We present extensive experiments and theoretical error estimates to demonstrate that PINNs provide a very easy to implement, fast, robust and accurate method for simulating radiative transfer. We also present a PINN based algorithm for simulating inverse problems for radiative transfer efficiently.