---
title: "Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.20321v1"
permalink: "https://feed.astralor.com/items/itm_8230ec0578f7434c7917fa0f"
published: "2026-07-22T16:07:09.000Z"
score: 77
channel: "ai"
tags: ["Graph Neural Network","Unsupervised Learning","Finite Volume Method","Thermo-Fluid Simulation","Scientific machine learning"]
---

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

## AI commentary

> 这篇论文让我眼前一亮，它巧妙地将传统CFD中的有限体积法残差作为神经网络的损失函数，实现了真正的无监督学习，避免了昂贵的数据生成。对在工业界做仿真代理模型的工程师尤其重要，因为很多场景根本拿不到大量高保真标签数据。

## At a glance

This paper proposes a label-free training method for attention graph neural networks using finite-volume method (FVM) residuals as the loss function, evaluated directly on the mesh for physical conservation equations. On steady-state and transient thermo-fluid simulation tasks, the method achieves 2.3-2.8% all-field normalized RMSE, closely matching CFD references, and eliminates the substantial data generation cost required by supervised baselines. The results demonstrate that FVM loss can serve as a practical training signal for neural surrogates.

## Key points

- Trains graph neural networks using FVM residuals as loss without labeled data.
- Achieves 2.3-2.8% all-field normalized RMSE on steady-state benchmarks.
- Outperforms supervised baseline on parametric transient cases while eliminating data generation cost.

## Full text

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.

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