# Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learning

arXiv: https://arxiv.org/abs/2504.14422 · HTML: https://mlsanity.com/paper/2504.14422/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 72 references that are in the map.
- First posted on arXiv 19 Apr 2025.

## Builds on (most cited first, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Tianshou: a Highly Modularized Deep Reinforcement Learning Library](https://mlsanity.com/paper/2107.14171/) (2021)
- [Efficient collective swimming by harnessing vortices through deep reinforcement learning](https://mlsanity.com/paper/1802.02674/) (2018)
- [A review on Deep Reinforcement Learning for Fluid Mechanics](https://mlsanity.com/paper/1908.04127/) (2019)
- [Scientific multi-agent reinforcement learning for wall-models of turbulent flows](https://mlsanity.com/paper/2106.11144/) (2021)
- [Deep Neural Networks for Data-Driven Turbulence Models](https://mlsanity.com/paper/1806.04482/) (2018)
- [Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations](https://mlsanity.com/paper/2206.11038/) (2022)
- [XLB: A differentiable massively parallel lattice Boltzmann library in Python](https://mlsanity.com/paper/2311.16080/) (2023)
- [Lettuce: PyTorch-based Lattice Boltzmann Framework](https://mlsanity.com/paper/2106.12929/) (2021)
- [Closure Discovery for Coarse-Grained Partial Differential Equations Using Grid-based Reinforcement Learning](https://mlsanity.com/paper/2402.00972/) (2024)
- [Fokker-Planck Central Moment Lattice Boltzmann Method for Effective Simulations of Fluid Dynamics](https://mlsanity.com/paper/2410.09739/) (2024)

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

- [Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows](https://mlsanity.com/paper/2602.15592/) (2026)
- [A fully GPU-based workflow for building physics emulators of hypersonic flows](https://mlsanity.com/paper/2606.13742/) (2026)

## Abstract (arXiv)

The Lattice Boltzmann method (LBM) offers a powerful and versatile approach to simulating diverse hydrodynamic phenomena, spanning microfluidics to aerodynamics. The vast range of spatiotemporal scales inherent in these systems currently renders full resolution impractical, necessitating the development of effective closure models for under-resolved simulations. Under-resolved LBMs are unstable, and while there is a number of important efforts to stabilize them, they often face limitations in generalizing across scales and physical systems. We present a novel, data-driven, multiagent reinforcement learning (MARL) approach that drastically improves stability and accuracy of coarse-grained LBM simulations. The proposed method uses a convolutional neural network to dynamically control the local relaxation parameter for the LB across the simulation grid. The LB-MARL framework is showcased in turbulent Kolmogorov flows. We find that the MARL closures stabilize the simulations and recover the energy spectra of significantly more expensive fully resolved simulations while maintaining computational efficiency. The learned closure model can be transferred to flow scenarios unseen during training and has improved robustness and spectral accuracy compared to traditional LBM models. We believe that MARL closures open new frontiers for efficient and accurate simulations of a multitude of complex problems not accessible to present-day LB methods alone.