# Solving the Discretised Boltzmann Transport Equations using Neural Networks: Applications in Neutron Transport

arXiv: https://arxiv.org/abs/2301.09991 · HTML: https://mlsanity.com/paper/2301.09991/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 5 of 5)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [MultiResUNet : Rethinking the U-Net Architecture for Multimodal Biomedical Image Segmentation](https://mlsanity.com/paper/1902.04049/) (2019)
- [Recurrent Residual Convolutional Neural Network based on U-Net (R2U-Net) for Medical Image Segmentation](https://mlsanity.com/paper/1802.06955/) (2018)
- [An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion](https://mlsanity.com/paper/2008.10532/) (2020)

## Built on by (most cited first, 4 of 4)

- [Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries](https://mlsanity.com/paper/2401.06755/) (2024)
- [Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics](https://mlsanity.com/paper/2402.17913/) (2024)
- [Parameter estimation for land-surface models using Neural Physics](https://mlsanity.com/paper/2505.02979/) (2025)
- [Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2603.24196/) (2026)

## Abstract (arXiv)

In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer architectures and enables one to tap into the vast quantity of community based software that has been developed for AI and ML applications e.g. mixed arithmetic precision or model parallelism. Here we take the first steps towards developing this approach for the Boltzmann transport equation and develop the necessary methods in order to do that effectively. This includes: 1) A space-angle multigrid solution method that can extract the level of parallelism necessary to run efficiently on GPUs or new AI computers. 2) A new Convolutional Finite Element Method (ConvFEM) that greatly simplifies the implementation of high order finite elements (quadratic to quintic, say). 3) A new non-linear Petrov-Galerkin method that introduces dissipation anisotropically.