# Multi-Stage Graph Neural Networks for Data-Driven Prediction of Natural Convection in Enclosed Cavities

arXiv: https://arxiv.org/abs/2509.06041 · HTML: https://mlsanity.com/paper/2509.06041/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 7 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Deep learning observables in computational fluid dynamics](https://mlsanity.com/paper/1903.03040/) (2019)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations](https://mlsanity.com/paper/2211.00713/) (2022)
- [DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks](https://mlsanity.com/paper/2004.08826/) (2020)
- [Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2205.02637/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learning Transient Convective Heat Transfer with Geometry Aware World Models](https://mlsanity.com/paper/2601.22086/) (2026)

## Abstract (arXiv)

Buoyancy-driven heat transfer in closed cavities serves as a canonical testbed for thermal design High-fidelity CFD modelling yields accurate thermal field solutions, yet its reliance on expert-crafted physics models, fine meshes, and intensive computation limits rapid iteration. Recent developments in data-driven modeling, especially Graph Neural Networks (GNNs), offer new alternatives for learning thermal-fluid behavior directly from simulation data, particularly on irregular mesh structures. However, conventional GNNs often struggle to capture long-range dependencies in high-resolution graph structures. To overcome this limitation, we propose a novel multi-stage GNN architecture that leverages hierarchical pooling and unpooling operations to progressively model global-to-local interactions across multiple spatial scales. We evaluate the proposed model on our newly developed CFD dataset simulating natural convection within a rectangular cavities with varying aspect ratios where the bottom wall is isothermal hot, the top wall is isothermal cold, and the two vertical walls are adiabatic. Experimental results demonstrate that the proposed model achieves higher predictive accuracy, improved training efficiency, and reduced long-term error accumulation compared to state-of-the-art (SOTA) GNN baselines. These findings underscore the potential of the proposed multi-stage GNN approach for modeling complex heat transfer in mesh-based fluid dynamics simulations.