# Weak Adversarial Neural Pushforward Method for Boltzmann Equation

arXiv: https://arxiv.org/abs/2608.06823 · HTML: https://mlsanity.com/paper/2608.06823/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 3 of 3)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [A Discontinuous Galerkin Fast Spectral Method for the Full Boltzmann Equation with General Collision Kernels](https://mlsanity.com/paper/1809.10186/) (2018)

## Abstract (arXiv)

In this paper, we extend a weak adversary neural network pushforward method for solving time dependent Boltzmann equation and a weak formulation of the collision operator is proposed where an invertible neural pushforward mapping is used to generating samples given by the distribution governed by the Boltzmann equation. The training of the pushforward mapping is learnt by enforcing the weak form of the Boltzmann equation. Numerical results have demonstrated the effectiveness of the proposed method.