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

<title>Abstract</title> <p>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.</p>