Supplementary Material S1-ATE-D-24-04532

As for the GMDH model design method, we used 416 sets of simulation data to calculate f and j, and then trained the GMDH model with this data to directly predict f and j. When comparing the performance metrics of the training and test sets between the two models shown in Table 7, we found that the GMDH model performs very well in predicting f, with high R2 values for both the training and test sets, indicating that directly using the GMDH model to predict f is reasonable and efficient. However, in predicting j, the R2 value of the GMDH model is lower. Although slightly worse than the performance for heat transfer Q, it is still at a good prediction level. The RMSE and MAPE values indicate that the model's prediction error is relatively small, especially the MAPE (1.85% on the test set), which shows a relatively low percentage error, better performance than for Q, and strong generalization ability. The clear model network structure and the calculation formulas for each neuron are presented in supplementary material (see Supplementary Material S1). The training data for the GMDH model is provided as supplementary material (see Supplementary Material S2).