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

Source

Source name: arXiv
Source kind: paper
Authors / organization: Tianyu Li, Zhiwei Cao, Qingang Zhang, Ruihang Wang, Binyang Song, Yonggang Wen
Venue: arXiv: physics.flu-dyn
Published: 2026-07-22
Collected: 2026-07-23
URL: http://arxiv.org/abs/2607.20321v1
PDF: https://arxiv.org/pdf/2607.20321v1
DOI: UNKNOWN

Plain-Language Brief

Researchers propose a new method to train Attention Graph Neural Networks for predicting three-dimensional thermo-fluid fields. Instead of using conventional numerical solvers that incur high computational costs, they minimize the finite-volume method (FVM) residuals of the governing equations. This method requires no labeled data and is evaluated against CFD references and a data-supervised baseline across four scenarios.

What the Document Says

Neural surrogates are used for predicting 3D thermo-fluid fields
Traditional numerical solvers can be expensive and time-consuming for generating training data
The proposed method minimizes the FVM residuals of the governing equations to train Attention Graph Neural Networks
No labeled data is required as residuals are evaluated directly on the mesh
The trained surrogates are compared with CFD references and a data-supervised baseline across four scenarios

Key Concepts Mentioned

Neural surrogates
Three-dimensional thermo-fluid fields
Conventional numerical solvers
Finite-volume method (FVM) residuals
Attention Graph Neural Networks
Computational fluid dynamics (CFD)
Data-supervised baseline

Claims Made by the Document

The proposed FVM loss can provide a practical training signal for neural surrogates
The FVM-loss model achieves low error rates on steady-state benchmarks
The FVM-loss model outperforms the supervised baseline in terms of accuracy on transient cases

Evidence Used

Results from four scenarios are provided to support the claims

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

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.