## 3 Results and Discussion
### Active Learning  
Four common integrated learning algorithms, namely RF, GBDT, AdaBoost, and XGB, were employed to train the samples of the initial dataset, and the obtained lowest error of the test set for each algorithm by particle swarm optimization is displayed in Figure 6. The GBDT model performed best on the test set, so it was chosen as the initial sampling model of pure exploration and EI strategies in the sample pool. At the end of each subsequent round for sampling, the training set was updated, and each model thus was retrained with its MAPE on the test set being recalculated. The model with the lowest error will be used as the model for the next round of sampling. The parameters of each model were determined through grid search and particle swarm optimization [45], and the tuning intervals of the main parameters are shown in Table 2.  
Figure 5: (**a**) Effect of filler on mass ablation rate obtained by analyzing the results of homogeneous experiments; (**b**) fitting performance of different algorithms on the initial training set; and (**c**) composition of the initial dataset and test set: the initial dataset is the result of the uniform design experiments, and the test set consists of the results of the validation experiments for uniform design and the pure exploitation experiments. The performance of all the abovementioned algorithms over each round of the two sampling routes is recorded in Figure 7. As the sampling process continued, the errors of the models trained by each algorithm on the test set gradually decreased. After just three rounds of sampling, the MAPE for all models predicting mass ablation performance was found to be less than 10%. Notably, the GBDT model had a much lower MAPE of 4.14%. Under EI sampling, the GBDT model ultimately achieved the lowest prediction MAPE of 3.62% among the two sampling routes. However, during the EI sampling process, the RF and AdaBoost models exhibited an increase in MAPE at the end of the second round of sampling, possibly due to their relatively weaker ability to explain complex nonlinear relationships compared to GBDT. In conclusion, it can be inferred that the goal of building an ML model with good predictive performance based on a small dataset has been successfully achieved. Overall, the GBDT and XGB models showed better predictions of mass ablation rates. This is due to the fact that both models are more amenable to nonlinear problems, whereas the AdaBoost and RF models are more sensitive to noise in the data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithms** & \multicolumn{2}{c}{**Hyperparameters**} \\ \hline \multirow{4}{*}{**AdaBoost**} & n\_estimators & 10–200 \\  & learning\_rate & 0.01–0.2 \\  & max\_depth & 1–5 \\  & n\_estimators & 10–200 \\  & max\_depth & 1–5 \\  & min\_child\_weight & 1–5 \\
**XGB** & learning\_rate & 0.01–0.2 \\  & subsample & 0.2–1 \\  & gamma & [0, 0.0001, 0.001, 0.01, 0.1] \\  & n\_estimators & 10–200 \\  & max\_depth & 1–5 \\
**RF** & min\_samples\_split & 2–5 \\  & min\_samples\_leaf & 1–5 \\  & max\_features & 1–3 \\  & n\_estimators & 10–200 \\  & learning\_rate & 0.01–0.2 \\
**GBDT** & subsample & 0.1–1 \\  & min\_child\_weight & 1–5 \\  & max\_depth & 1–5 \\  & max\_features & 1–3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Adjustment range of model parameters. Figure 6: Error of models based on the initial ablation dataset. However, GBDT and XGB algorithms have numerous hyperparameters which are more difficult to tune, and they take relatively longer to train samples, according to Table S4. In addition, other conventional algorithms were used to train the dataset under both routes, and the validation results of the model are in Table S3. To assess the importance of features for the three kinds of fillers, the Shapley Additive Explanations (SHAP) method was utilized to analyze the dataset generated by the EI strategy, and the results are shown in Figure 8. Among them, silica possesses the highest value, indicating that it has the greatest influence on the ablation rate.