## 4 Discussion  
This study successfully constructed a high-precision PCHE heat transfer coefficient prediction model by systematically comparing traditional machine learning and deep learning models and integrating attention mechanisms and explainability analysis methods, providing a new methodological framework for complex heat exchanger performance modeling. The research results show that the deep learning model based on the attention mechanism has a significantly higher prediction accuracy (R\({}^{2}\geq\) 0.999) in hexagonal channels than traditional empirical correlations, verifying the potential of deep learning in capturing nonlinear thermohydraulic relationships. Additionally, SHAP analysis revealed the dynamic contribution differences of key features under different channel types, providing an explainable physical basis for engineering optimization. Compared with existing studies, the innovation of this work lies in the following: (1) the first introduction of self-attention mechanisms and Transformer into PCHE performance prediction, breaking the traditional model's reliance on local sequence features; (2) the construction of a high-frequency dataset through the distance micro-element analysis method, solving the limitations of traditional averaging methods in complex channels; (3) a systematic evaluation of the impact of feature selection on model generalization ability, providing a standardized process reference for data-driven heat exchanger design. Finally, the numerical simulation stage took about 12 h, and the training and verification of each set of parameters in deep learning was counted in minutes, and we used NVIDIA GeForce RTX 4060. It can also be observed from the results in Tables 5 and 6 that when the same model is applied to predict the PCHE heat transfer coefficient, the prediction performance for the DC channels and hexagonal channels differs significantly. On hexagonal flow channels, even the least effective XGBOOST model achieves high accuracy (R\({}^{2}\geq\) 0.96), while the best-performing Transformer-LA model attains an accuracy exceeding 0.999. In contrast, for DC channels, the prediction accuracy is generally below 0.9. The explanation provided in this study is that hexagonal channels exhibit relatively complex flow patterns and temperature field changes, such as the formation of local vortices and enhanced thermal convection, which increases data diversity and complexity, enabling models to fully leverage the features within the flow channel. For DC channels, the flow pattern is overly simplistic, and the data exhibit strong linearity, leading to model overfitting and reduced prediction accuracy [35]. Additionally, we found that SE performed better on straight flow channels, whereas LA demonstrated superior performance on hexagonal flow channels when attention mechanisms were incorporated. This indicates that the SE mechanism effectively enhances feature representation by explicitly modeling inter-channel dependencies, while LA focuses on local information in the complex variations in hexagonal flow channels, resulting in differing performances. According to SHAP analysis, two independent variables--wall heat flux density (Qw) and Prandtl number (PR)--make significant contributions to the heat transfer characteristics of both flow channel shapes. Qw serves as a quantitative measure of energy transport in PCHE, and variations in its value directly influence the steepness of the temperature gradient in the boundary layer and the enhancement effect of turbulent pulsation on heat transport in the near-wall region [36]. For PR, it reflects the relative strengths of momentum and heat diffusion. When PR is large, momentum diffusion dominates, leading to a relatively thick flow boundary layer and slower heat transfer. Conversely, when PR is small, heat diffusion prevails, resulting in a relatively thick thermal boundary layer and slower momentum transfer [37].