## 1 Introduction
Thus, there is a \"small sample problem\" when applying machine learning technology to study the ablation performance of flexible ablative materials. The main issue of the small sample problem [16] is the insufficient sample size for model training and the challenge of labeling new samples. Therefore, it is essential to strategically incorporate new samples within a reasonable cost range. Furthermore, maximizing the information extracted from existing samples is crucial. When adding new samples, the ideal situation is to perform as few experiments as possible and obtain samples that are as important as possible for improving the generalization performance of the model. Active learning strategies [17; 18; 19] can intelligently select samples for labeling by human experts. The benefit is that it can improve model performance and minimize the requirements for a big data size, thus saving time and cost. For instance, [PERSON] et al. [20] collected an initial dataset containing 32 samples of epoxy adhesive, and then selected the top five samples with the highest predicted adhesion strength based on a gradient boosting algorithm. After three rounds of iteration, the average coefficient of determination (R2) increased from 0.68 to 0.85, while the root mean square error (RMSE) and mean absolute error (MAE) consistently decreased. This demonstrates that sampling by artificial intelligence can efficiently and rapidly enhance generalization performance. [PERSON] et al. [21] used a graph convolutional neural network to select samples iteratively in a chemical space with 155,610 structures, starting from an initial dataset containing 309 polyimide (PI) structures and their properties. Through eight cycles of active learning and multi-label screening, they identified PI structures with an excellent gas separation performance. These structures' performance was further validated through molecular dynamics simulations. In addition, there are currently three main solution strategies for fully mining and utilizing small datasets: (i) performing feature selection on high-dimensional samples and extracting features that are beneficial for improving model performance; (ii) establishing a gray prediction model [22] through differential equations; (iii) generating a large number of virtual samples to build the model. In contrast to the other two approaches, the virtual sample generation technique [23] may completely utilize the effective information concealed in a limited number of samples and generate a huge number of virtual samples. Retrainingthe dataset containing real and virtual samples enables a more accurate interpretation of the data and improves the performance of the associated model. So, this would be an effective way to deal with small sample sizes [24]. [PERSON] et al. [25] proposed a virtual sample generation algorithm based on the Gaussian Mixture Model (GMM-VSG). By generating a large number of virtual samples, they effectively addressed the issue of insufficient training samples and predicted the abrasion resistance of rubber materials. Experimental results showed that the R2 of the prediction model reached 0.95, and the prediction accuracy increased by 41% compared to when not introducing virtual samples. In this paper, we aim to predict the mass ablation rate based on a small dataset. Based on the two ideas of labeling new samples and fully mining the dataset, the sample preparation and corresponding ablation experiments were carried out under the framework of uniform design and active learning. A representative small dataset was constructed and an effective mass ablation rate prediction model was developed using this small dataset. The model was further optimized using the virtual sample generation method, which demonstrated the feasibility of training small samples to develop an ablation performance prediction model.