# LBM-GNN: Graph Neural Network Enhanced Lattice Boltzmann Method

arXiv: https://arxiv.org/abs/2504.14494 · HTML: https://mlsanity.com/paper/2504.14494/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 20 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Deep Dynamical Modeling and Control of Unsteady Fluid Flows](https://mlsanity.com/paper/1805.07472/) (2018)
- [Adaptive Optimization for Enhanced Efficiency in Large-Scale Language Model Training](https://mlsanity.com/paper/2412.04718/) (2024)
- [Physics-Informed Neural Networks for Enhanced Interface Preservation in Lattice Boltzmann Multiphase Simulations](https://mlsanity.com/paper/2504.10539/) (2025)
- [Federated Learning with Layer Skipping: Efficient Training of Large Language Models for Healthcare NLP](https://mlsanity.com/paper/2504.10536/) (2025)

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

- [Does Bigger Mean Better? Comparitive Analysis of CNNs and Biomedical Vision Language Modles in Medical Diagnosis](https://mlsanity.com/paper/2510.00411/) (2025)
- [Dynamic Graph Neural Networks for Physiological Based Pharmacokinetic Modeling: A Novel Data Driven Approach to Drug Concentration Prediction](https://mlsanity.com/paper/2510.22096/) (2025)

## Abstract (arXiv)

In this paper, we present LBM-GNN, a novel approach that enhances the traditional Lattice Boltzmann Method (LBM) with Graph Neural Networks (GNNs). We apply this method to fluid dynamics simulations, demonstrating improved stability and accuracy compared to standard LBM implementations. The method is validated using benchmark problems such as the Taylor-Green vortex, focusing on accuracy, conservation properties, and performance across different Reynolds numbers and grid resolutions. Our results indicate that GNN-enhanced LBM can maintain better conservation properties while improving numerical stability at higher Reynolds numbers.