# Transport based particle methods for the Fokker-Planck-Landau equation

arXiv: https://arxiv.org/abs/2405.10392 · HTML: https://mlsanity.com/paper/2405.10392/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 10 of 10)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [Probability flow solution of the Fokker-Planck equation](https://mlsanity.com/paper/2206.04642/) (2022)
- [Self-Consistency of the Fokker-Planck Equation](https://mlsanity.com/paper/2206.00860/) (2022)
- [Score-based Transport Modeling for Mean-Field Fokker-Planck Equations](https://mlsanity.com/paper/2305.03729/) (2023)
- [A score-based particle method for homogeneous Landau equation](https://mlsanity.com/paper/2405.05187/) (2024)
- [Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs](https://mlsanity.com/paper/2303.11205/) (2023)

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

- [DiScoFormer: Plug-In Density and Score Estimation with Transformers](https://mlsanity.com/paper/2511.05924/) (2025)
- [Score-based deterministic density sampling](https://mlsanity.com/paper/2504.18130/) (2025)
- [JKO for Landau: a variational particle method for homogeneous Landau equation](https://mlsanity.com/paper/2409.12296/) (2024)
- [A Neural Score-Based Particle Method for the Vlasov-Maxwell-Landau System](https://mlsanity.com/paper/2603.25832/) (2026)

## Abstract (arXiv)

We propose a particle method for numerically solving the Landau equation, inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation. This method can preserve some important physical properties of the Landau equation, such as the conservation of mass, momentum, and energy, and decay of estimated entropy. We prove that matching the gradient of the logarithm of the approximate solution is enough to recover the true solution to the Landau equation with Maxwellian molecules. Several numerical experiments in low and moderately high dimensions are performed, with particular emphasis on comparing the proposed method with the traditional particle or blob method.