用物理残差训练图神经网络，无需标签即可高精度模拟流体场。
Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields
- 基于有限体积法残差直接训练注意力图神经网络，不依赖标注数据。
- 稳态场景下全域归一化误差仅2.3%-2.8%，与真实仿真高度一致。
- 适用于参数化瞬态问题，避免昂贵数据生成，适合科研快速建模。
神经代理模型广泛用于科学机器学习中对三维热流场的快速预测。然而，传统数值求解器生成训练数据常带来巨大的计算与存储成本。本文提出通过最小化控制方程的有限体积法（FVM）残差来训练注意力图神经网络，该残差在网格上直接计算，无需标签数据。我们在四个场景下将训练后的代理模型与计算流体力学（CFD）参考解及数据监督基线进行对比。在两个稳态基准测试中，FVM损失模型的全域归一化均方根误差（nRMSE）为2.3%-2.8%，与CFD参考结果高度吻合，包括浮力-能量耦合效应。在两个参数化瞬态案例中，FVM损失模型在精度上优于监督基线，且完全避免了数据生成成本。结果表明，FVM损失可为神经代理模型提供有效训练信号，显著降低模型开发成本。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。