## 4 Conclusions  
In summary, a strategy combining uniform design, active learning, and virtual sample generation was proposed to construct a prediction model of mass ablation rate using a small dataset. Silicone rubber composites containing SiO\({}_{2}\), SiC, and CF were used as a model of flexible ablative materials, and ablation samples were prepared by regulating the content of the three kinds of fillers based on uniform design experimentation. Oxyacetylene ablation experiments were performed to obtain a batch of data on the mass ablation rate, which served as the initial dataset. Then, the initial prediction model was obtained by training the initial dataset through the integrated algorithm including GBDT, RF, AdaBoost, and XGB. Two active learning strategies, pure exploration and expected improvement, were used to iteratively screen the unlabeled samples. The selected samples were subjected to ablation tests, and the obtained data on the mass ablation rate were used to update the dataset and continuously retrain the models until the prediction error of each model on the test set samples was less than 10%. After three rounds of sampling, the prediction errors of the retrained models for mass ablation rate decreased significantly. Among them, the GBDT model under the exploration route showed a MAPE of just 4.14% on the test set. Different numbers of virtual samples were further generated based on the prediction model with the smallest error and the real sample distribution. The results showed that when a certain number of virtual samples were introduced, the errors of the models of different algorithms on the test set were significantly reduced. After the introduction of 300 virtual samples, the percentage error of predictions on the test set decreased by 25% to just 3.1%, proving the feasibility of developing flexible ablative materials based on data-driven methods.  
The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app14178007/s1](https://www.mdpi.com/article/10.3390/app14178007/s1)]([https://www.mdpi.com/article/10.3390/app14178007/s1](https://www.mdpi.com/article/10.3390/app14178007/s1)). Table S1: Uniform design table of U10(103).  
Table S2: Distribution of initial sample features. Table S3: Models constructed by common algorithms and their MAPE on the test set. Table S4: Comparison of the strengths and weaknesses of models. Table S5: Test set for prediction models. Table S6: Training set generated by expected improvement.  
Table S7: Training set generated by pure exploration strategy.  
Conceptualization, W.C. and Y.C.; Methodology, W.C., C.Z., Y.C. and Z.H.; Software, C.Z.; Validation, C.Z. and H.Z. ([PERSON]); Formal analysis, H.Z. ([PERSON]); Investigation, H.Z. ([PERSON]); Resources, M.L.; Data curation, M.L.; Writing--original draft, W.C., S.Z., C.Z. and [PERSON]; Writing--review & editing, W.C., C.Z. and L.Y.; Visualization, L.Y., S.Z. and Z.H.; Supervision, L.Y., S.Z., H.Z. ([PERSON]) and M.L.; Project administration, H.Z. ([PERSON]) and M.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author/s.  
The authors acknowledge some resource support from [PERSON] from China Bluestar Chengrand (Chengdu) Testing Technology Co., Ltd. We also appreciate [PERSON] from the Analytical & Testing Center of Sichuan University for her help with SEM characterization.  
The authors declare no conflict of interest.