Physics-informed graph neural network based on the finite volume method for steady incompressible laminar convective heat transfer

The rapid development of deep learning has significantly influenced computational studies in convective heat transfer. To facilitate broader applications of deep learning models in convective heat transfer, this paper proposes a physics-informed graph neural network based on the finite volume method (FVGP-Net) for unsupervised training and prediction of steady incompressible laminar convective heat transfer problems. In this model, mesh data generated by the finite volume method (FVM) are converted into graph data, preserving the mesh's topological properties. This conversion allows FVGP-Net to utilize a graph convolutional network for information aggregation, capturing both local and global flow features and enhancing the model's geometric adaptability and predictive performance. The model incorporates physical laws directly into its loss function, ensuring compliance to these laws without reliance on training data. Unlike traditional physics-informed neural networks (PINNs), FVGP-Net replaces automatic differentiation with FVM-based numerical differentiation, balancing training efficiency with prediction accuracy. Boundary conditions are handled in accordance with the FVM, ensuring that the model strictly satisfies these constraints. We validated FVGP-Net using representative test cases, also examining the effects of different initialization methods on model training. The results demonstrate that FVGP-Net achieves high accuracy in predicting incompressible laminar steady convective heat transfer. Compared to traditional PINNs, this model inherits the conservation properties of the FVM, enhancing velocity prediction accuracy in convective heat transfer problems by 70.03%. Furthermore, the application of transfer learning markedly accelerates training, achieving approximately 70% faster results compared to Xavier initialization.