Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields

2026-07-22

AI Summary

This work addresses the high cost of generating three-dimensional thermal flow field data in traditional computational fluid dynamics (CFD), which hinders the development of neural surrogate models. The authors propose an unsupervised physics-informed training framework that, for the first time, leverages the residual of finite volume method discretized governing equations as an unlabeled training signal to drive an attention-based graph neural network in learning buoyancy–energy coupling effects—eliminating reliance on expensive labeled data. The method achieves normalized root-mean-square errors of 2.3–2.8% across the entire domain in steady-state cases and outperforms supervised baselines in transient parametric tasks, substantially reducing both data generation and model development costs.

Abstract

Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, the FVM-loss model achieves an all-field normalized root-mean-square error (nRMSE) of 2.3-2.8%. It demonstrates close agreement with the CFD references, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model outperforms the supervised baseline in terms of accuracy, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.

Problem

• neural surrogates
• thermo-fluid fields
• training data cost
• computational fluid dynamics
• scientific machine learning

Innovation

• label-free training
• finite-volume residuals
• attention graph neural networks
• thermo-fluid surrogate modeling
• physics-informed machine learning