Thermo-mesh transformer network for generalizable three-dimensional temperature prediction with mechanism-based representation

The application of artificial intelligence for predicting physical fields holds significant potential in military and manufacturing domains. However, physical phenomenon prediction networks face challenges in accurately modeling physical laws across diverse scenarios while ensuring computational efficiency and generalization. This paper presents a novel Thermo-Mesh Transformer Network (TMTN) for universal three-dimensional (3D) temperature reconstruction from a single two-dimensional (2D) image. To enhance the network's understanding of heat transfer phenomena, a multi-scale feature extraction module is proposed to effectively capture and integrate both local and global features from the mesh and the image of the complex thermodynamic scenario. A mesh-enhanced transformer block (METB) is designed to implicitly represent the energy conservation equation, combining a Graph Convolutional Network (GCN) for modeling the diffusion term and a Transformer for modeling the source term. This innovative mechanism-based representation architecture directly integrates physical laws, enabling TMTN to predict heat transfer phenomena across various shapes and conditions, including untrained models and out-of-range conditions. Additionally, a parameter-efficient design based on an improved Laplacian matrix is proposed, leveraging the PointNet framework and farthest point sampling to efficiently represent global vertex relationships via Transformer with reduced parameters. Experimental results demonstrate that TMTN achieves a 38% reduction in error compared to state-of-art methods and exhibits robust performance under out-of-range and untrained conditions. TMTN offers valuable engineering applications in military infrared reconnaissance and the thermal management of civilian systems like energy storage and heating devices.