Construction of Prediction Models of Mass Ablation Rate for Silicone Rubber-Based Flexible Ablative Composites Based on a Small Dataset

Abstract

The prediction of the ablation rate of silicone rubber-based composites is of great significance to accelerate the development of flexible thermal protection materials. Herein, a method which combines uniform design experimentation, active learning, and virtual sample generation was proposed to establish a prediction model of the mass ablation rate based on a small dataset. Briefly, a small number of sample points were collected using uniform design experimentation, which were marked to construct the initial dataset and primitive model. Then, data points were acquired from the sample pool and iterated using various integrated algorithms through active learning to update the above dataset and model. Finally, a large number of virtual samples were generated based on the optimal model, and a further optimized prediction model was achieved. The results showed that after introducing 300 virtual samples, the average percentage error of the gradient boosting decision tree (GBDT) prediction model on the test set decreased to 3.1%, which demonstrates the effectiveness of the proposed method in building prediction models based on a small dataset.

1. Introduction

Silicone rubber-based flexible ablative materials play a vital role in the field of thermal protection of space vehicles [1]. To optimize their ablative resistance, researchers have carried out numerous investigations on the molecular structure modification of polysiloxanes and the synergistic compounding of ablative-resistant fillers [2,3,4,5,6]. However, traditional experimental methods based on experience and trial-and-error have faced many challenges, such as long research cycles and substantial resource consumption. These issues seriously hinder the development speed of novel flexible ablative materials, lagging behind application requirements. The data-driven approach has gradually become an important method to accelerate material development. Machine learning (ML), as a typical data-driven technique, excels in data analysis, summarization, and rule mining in the field of material research [7]. It can address the long-cycle and high-cost issues of traditional experimental research, circumventing futile trial and error, and effectively driving the development of new materials [8,9,10]. The utilization of machine learning for predicting the performance of silicone rubber-based flexible ablative materials can guide rational material design, which is of great significance for the development of flexible thermal protective materials.

At present, machine learning is widely used in the field of polymer materials. One of the most common applications is the utilization of big data to build predictive models of material properties. Predictive models mostly focus on studying properties that do not involve complex chemical changes, such as dielectric properties, glass transition temperature, and mechanical properties, etc. For example, Mai et al. [11] provide a way to apply machine learning models to discover novel electro-photocatalysts and use the models to elucidate electrocatalytic or photocatalytic reaction mechanisms. Another important application is the design and development of new materials. Related research often involves screening new polymer structures by establishing structure–property relationship models. For example, Wu et al. [12] established a prediction model for the relationship between chemical structure and thermal conductivity, and then prepared high-thermal-conductivity materials with new structures based on this model. It is worth noting that traditional machine learning requires a large amount of data to support it.

However, few applications related to machine learning are carried out in the field of ablation, with applications mainly in the prediction of ablative performance and optimal design of materials. For example, Hao et al. [13] focused on the oxidation reaction of ultra-high-temperature ceramic materials under thermal flow, and they collected 123 samples and calculated their enthalpy change. Using this information, a mass ablation rate prediction model was successfully constructed. An et al. [14] investigated the thermal insulation performance of resin-based coating materials under laser ablation. A model with low prediction errors of thermal insulation performance on the test set was constructed by training a dataset of 190 samples. Xiao et al. [15] used ML algorithms to construct models and provided an in-depth analysis of key factors affecting the ablation performance of ultra-high-temperature ceramic matrix composites (UHTCMCs). Eight ML models were successfully used to predict the linear ablation rate (LAR) of UHTCMCs. Previous studies were able to accurately predict the ablative properties by analyzing a large amount of experimental data, reducing experimental time and cost and promoting the development of new materials. Unfortunately, current flexible ablative materials suffer from many problems such as insufficient data accumulation, high cost, and difficulties in material preparation and characterization, as well as difficulty in quickly generating large amounts of data. 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, Pruksawan 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. Wang 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. Retraining the 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]. Shen 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. The uniform design, active learning, and virtual sample generation technology mentioned above enabled the efficient construction of the ablation performance prediction model with a small number of experimental samples. This technology provides guidance for the development of silicone rubber-based flexible ablative materials.

2. Experimental Section

2.1. Materials

Vinyl silicone rubber (XHG-110) was purchased from Zhejiang Xin’an Chemical Group Co., Ltd., Hangzhou, China. Gas-phase SiO₂ (AEROSIL 200) was supplied by the German Degussa Company, Dusseldorf, Germany. Short-cut carbon fiber (length: 3mm) was provided by Shanghai Lishuo Composite Materials Technology Co., Ltd., Shanghai, China. Silicon carbide (particle size: 800) was purchased from Hebei Yangming Metal Materials Co., Ltd., Baoding, China. Dicumyl peroxide (DCP) was provided by Chengdu Cologne Chemical Co., Ltd., Chengdu, China. The microstructures of carbon fiber (CF), silicon dioxide (SiO₂), and silicon carbide (SiC) are shown in Figure 1. It can be seen that the CF has a diameter of approximately 9 μm, and the SiC has a particle size of around 13 μm. However, the particle size of the gas-phase silica is at the nanoscale, about 20 nm.

2.2. Sample Preparation

The preparation and ablation process of the silicone rubber composite is illustrated in Figure 2a. Firstly, the weighted vinyl silicone rubber (100 phr, and phr refers to parts per hundred parts of rubber matrix by weight), silica, and silicon carbide were added to the two-roll mix in sequence and mixed for 15 min. Then, the cross-linking agent DCP (2 phr) was introduced into the mixed system. Carbon fibers were incorporated last to avoid breaking due to prolonged mixing, and the mixing continued for 5 min. Finally, the mixture was transferred into molds and vulcanized at 175 °C for 20 min under a pressure of 10 MPa. After being cold pressed for 5 min, the sheets were unloaded and left at room temperature for 12 h, after which a pneumatic punching machine was used to cut the samples into cylindrical samples with dimension of Φ30 × 10 mm.

2.3. Ablation Test

The oxyacetylene ablation test was performed using a customized experimental platform. All samples were tested according to the standard GJB 323B-2018 [26] under a heat flux of 4 MW/m². The oxyacetylene torch was first ignited and when the flame became stable the sample was moved in front of the nozzle. The nozzle was aimed at the center of the sample, and the ablation process lasted for 30 s. After the ablation test is completed, the mass ablation rate can be calculated as per the following equation.

$$MAR={\displaystyle \frac{m_1{-m}_2}{t}}$$

(1)

where $m_2$ represents the mass of the silicone rubber sample after ablation (g) and $m_1$ represents the mass of the silicone rubber sample before ablation (g). To minimize the error caused by the stripping of the char layer during the ablation process, the mass after removal of the char layer was used for $m_2$, and t denotes the testing time (s).

Figure 2b,c shows the optical images of the oxyacetylene flame under 4 MW/m² and during ablation, respectively. Figure 2d–f presents the surface morphology of the silicone rubber composites before and after ablation.

3. Results and Discussion

3.1. Construction of Datasets

Machine learning models were built using the results of oxyacetylene ablation performed on as-prepared samples. Input variables and the single output variable (mass ablation rate, MAR (g/s)) are given in

Table 1. List of input and output variables for machine learning.

Variables	Description	Type	Unit
SiO2	Content of SiO2 whose values range from 5 to 50	Input	phr
SiC	Content of SiC whose values range from 2 to 20	Input	phr
CF	Content of CF whose values range from 2 to 20	Input	phr
MAR	Mass ablation rate of samples after exposure for 30 s under the heat flux of 4 MW/m2	Output	g/s

. The content of SiO₂, SiC, and CF varies in the range of 5–50 phr, 2–20 phr, and 2–20 phr, respectively. The intervals of the fillers’ content are evenly divided into steps of 2.5, 1, and 1 phr within their respective ranges, which generates 6859 points in the original unlabeled sample pool.

According to the Supplementary Material Tables S1 and S2, ten points evenly distributed in the pool were selected firstly to prepare the corresponding materials, and the MAR of the materials was obtained by an oxyacetylene ablation test. Ten generated samples formed the initial dataset used for modeling. Thus, 10 points are removed from the pool, leaving 6849 unlabeled samples in the pool.

Based on the regression analysis of the results of the uniform design and exploitation strategy, an additional 10 samples were selected from the sample pool to be labeled to form the validation set for the subsequent model. The remaining 6839 unlabeled samples became candidates for subsequent active learning.

3.2. Active Learning

There are usually a few labeled samples and many unlabeled samples with known features when faced with an ML task. Labeling all unlabeled samples for modeling is resource-intensive and time-consuming. Instead, choosing and labeling just the samples that significantly contribute to the building of a model that meets the requirements is a more efficient approach [27,28,29]. Based on this concept, the pool-based active learning process is illustrated in Figure 3. Initially, a basic model is built with a few labeled samples to predict the MAR. The model is then employed to choose candidates from the pool consisting of unlabeled samples. These candidates are subsequently labeled and added to the training set, then utilized to update the model. This process is repeated until a satisfactory model is obtained. In this paper, the final mean absolute percentage error (MAPE) of the model on the validation set needs to be less than 10%.

In the above process, the key is in the selection of the appropriate samples to be prepared. The selection criterion is usually based on the uncertainty of the unlabeled samples. Typically, the higher the uncertainty of a sample, the more information it might encompass [30,31,32]. There are two main directions for uncertainty-based sampling: exploitation and exploration. Exploitation involves using the established model to predict samples in the pool and selecting the sample with the highest predicted value for the next round of labeling. The exploration strategy samples by choosing the sample with the highest prediction error from the current model.

In this work, sampling based on uncertainty was carried out as follows [33]. During each round of sampling, the currently labeled dataset is resampled by a bootstrap method several times, equal to the number of labeled samples, forming a sample subset. This subset is then trained, and the resulting model is used to predict the MAR of all unlabeled samples in the pool. Repeating the above steps 1000 times will result in 1000 subsets and then produce 1000 models by training these subsets. Every model predicts for all unlabeled samples and 1000 values are assigned to each unlabeled sample. Hence, each sample has 1000 predicted MARs, and the averaged MAR μ and standard deviation σ of these 1000 predictions are calculated. The exploitation strategy chooses the one with the maximum μ, but it is used in this paper to select the samples composing the validation set because of its defect in local optimization. The exploration strategy acquires the sample with the largest σ. Expected improvement (EI), a strategy balancing exploitation and exploration, is introduced as another sampling method, whose acquisition is based on the biggest U:

$$U=\mathsf{\sigma }\left[\phi \left(z\right)+z\Phi \left(z\right)\right]$$

(2)

$$z={\displaystyle \frac{{\mu }_{max}-\mu }{\mathsf{\sigma }}}$$

(3)

where φ(z) and Φ(z) are the probability density function and the cumulative distribution function of the standard normal distribution, respectively, while μ_max is the maximum value among 1000 predictions for each sample.

Two sampling strategies of exploration and expected improvement were carried out in parallel, with each iteration adding two new samples to the initial dataset. The prediction model of the MAR was updated until the MAPE of the verification samples was less than 10%. Because the pure exploration strategy often encounters the problem of local optimization, it is only employed to prepare a sample of the validation set in this paper.

3.3. Virtual Sample Generation

Although the performance of a mass ablation rate prediction model based on a small number of ablative samples may be unreliable, it uncovers some information concealed in the data of the ablative samples. When the model can fully reflect the relationship between the obtained small sample features and labels (the general standard is that the MAPE on the test set must be less than 10%), the hyperplane of input and output values deduced by the model is considered to be closer to the hyperplane of the real sample population. According to the distribution of the model and real data, virtual samples can be generated, and these virtual samples will have the same feature distribution as real small samples [34]. By mixing them with real small samples, the retrained prediction model will further approximate the real feature-label hyperplane compared with the initial estimate, thus improving the performance of the model. Therefore, the application of virtual sample generation technology after active learning is expected to further improve the prediction model of ablation performance.

Taking the labeled dataset finally generated by the pure exploration route as an example [34,35], the generation of virtual samples first requires the extension of the range of features and labeled values of real samples using the global trend diffusion method. Then, the virtual sample generates eigenvalues in the expanded region according to the distribution of real data. The mass ablation rate of the virtual sample is assigned by the model obtained by the previous active learning process. The assigned value should be within the extended range of the label value, and the required virtual sample is finally obtained. However, it can be seen from Figure 4 that the lower bound of each feature and label is extended to a region less than zero. The contents of filler and the mass ablation rate cannot be negative, so the lower bound is 0 in this case. Virtual samples are then mixed with real samples to form a hybrid dataset. The reconstructed dataset is trained by each algorithm, and the prediction performance of each generated model is evaluated and compared by using the samples from the validation set.

3.4. Machine Learning Algorithm and Model Verification Method

Machine learning algorithms are extensively utilized for model construction across the stages of active learning and virtual sample generation. Since the MAR of silicone rubber-based composites is the result of complex physicochemical reactions, the function for predicting MAR is supposed to be nonlinear. Decision trees are often used to construct performance prediction models of materials because of their interpretability, simplicity, and capacity to handle nonlinear connections. However, they are prone to overfitting. As a result, several common ensemble tree algorithms are employed in this work, including random forest [36,37] (RF), Gradient Boosting Decision Tree [38,39] (GBDT), adaptive boosting [40] (AdaBoost), and Extreme Gradient Boosting [41] (XGB). These ensemble tree algorithms combine multiple decision trees and can build more robust models through averaging or iterative adjustments, improving prediction accuracy [42]. The main evaluation methods in the process are R2, root mean square error [43] (RMSE), and mean absolute percentage error [44] (MAPE). They can be calculated as follows:

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^m{(y_i-{\hat{\mathrm{y}}}_i)}^2}{{\sum }_{i=1}^m{\left(y_i-{\overline{\mathrm{y}}}_i\right)}^2}}$$

(4)

$$RMSE=\sqrt{ {\displaystyle \frac{1}{m}}\sum _{i=1}^m{(y_i-{\hat{\mathrm{y}}}_i)}^2}$$

(5)

$$MAE={\displaystyle \frac{1}{m}}\sum _{i=1}^m\left|{\displaystyle \frac{y_i-{\hat{\mathrm{y}}}_i}{y_i}}\right|\times 100\%$$

(6)

where $y_i$ and ${\hat{\mathrm{y}}}_i$ are, respectively, the test value and predicted value of MAR, and m is the number of samples of the validation set.

3.5. Construction of Initial Dataset and Verification Set

The results of uniform design experiments are analyzed by regression. According to the regression equation, the effects of the various contents of each filler on the mass ablation rate are shown in Figure 5a. There is a complex nonlinear relationship between the ablation rate and the amount of filler. Algorithms such as RF, GBDT, and AdaBoost were used to train the samples in the initial dataset. The fitting of the real samples is shown in Figure 5b; GBDT interprets the training set slightly better than AdaBoost. RF has the worst fit, but its R2 is close to 0.9. Therefore, GBDT was chosen as the first algorithm to train the initial dataset, and active learning of the pure exploitation strategies was further performed based on this model. Through four rounds of sampling in the sample pool, a total of eight groups of samples were selected and labeled in the exploitation strategy. Finally, experimental results of uniform design, verification experiment, and exploitation can be obtained, as shown in Figure 5c. It can be noted that the mass ablation rate of the verification samples selected from the regression analysis based on the results of uniform experimentation is significantly lower than that of the samples of uniform experimental designs. It indicates that the sample points chosen through uniform design are indeed representative, and the regression result effectively captures the relationship between the filler contents and the ablation rate.

In comparison, the overall mass ablation rate for the samples selected by the pure exploitation strategy is significantly lower. It can be argued that the exploitation strategy can indeed find advantageous samples relatively quickly. However, the essence of such a strategy is to find the sample with the minimum prediction value of the MAR, so the collected samples may not improve the performance of prediction greatly, and it is often easy to fall into the local optimal situation. Therefore, it can be seen that although the training samples increase, the MAR of the new samples selected by the GBDT model gradually increases as well, implying a decline in the predictive capacity of the GBDT model. Finally, the samples selected by pure exploitation were combined with the two samples selected by regression analysis to form a dataset with a sample size of ten, which served as a test set for subsequent exploration and EI sampling methods.

3.6. 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. Adjustment range of model parameters.

Algorithms	Hyperparameters
AdaBoost	n_estimators learning_rate max_depth	10–200 0.01–0.2 1–5
XGB	n_estimators max_depth min_child_weight learning_rate subsample gamma	10–200 1–5 1–5 0.01–0.2 0.2–1 [0, 0.0001, 0.001, 0.01, 0.1]
RF	n_estimators max_depth min_samples_split min_samples_leaf max_features	10–200 1–5 2–5 1–5 1–3
GBDT	n_estimators learning_rate subsample min_child_weight max_depth max_features	10–200 0.01–0.2 0.1–1 1–5 1–5 1–3

.

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. 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. It is worth pointing out that, unlike traditional machine learning where the number of features is high, the number of features in this study is only three, all of which are crucial for model prediction performance. In addition, the optimal model under the EI route was used to predict the mass ablation rate for all samples in the sample pool, and the results in Figure 8c demonstrate the effect of the amount of silica on the mass ablation rate. It can be seen that the composite exhibits a relatively lower mass ablation rate when the amount of silica is between 25 and 40 phr. Based on the above results, it is clear that the predictions can be used to optimize the ablation resistance of the present composites, avoiding the need to carry out extensive experiments. This makes the design and development of ablative composites more efficient.

Actually, the method of combining uniform design and active learning to form the training set is more targeted and efficient than the random sample selection approach. However, the final training set still contains very few samples and does not capture the details of the filler ablation rate interval. It is noted that the current dataset focuses on a system containing three fillers, and it is clear that the constructed models are not applicable to other filler systems. However, the method of constructing this dataset can be adapted to achieve specific research objectives.

3.7. Virtual Sample Generation Technology

In the previous study on active learning, two small datasets and various ML models with MAPE values less than 10% were obtained. Then, virtual samples were generated based on the sample feature distributions in the two updated small datasets to further enhance the precision of these models. The GBDT models trained under two sampling routes both demonstrated the lowest MAPE within their respective active learning processes, so they were used to predict the mass ablation rate of the generated virtual samples in their respective routes. The labeled virtual samples were then mixed with the real samples to form mixed datasets. The reconstructed datasets were trained by each algorithm, and the predictive ability of the new model was still verified by samples in the test set. After training a model with sufficiently high prediction accuracy, using the contents of fillers as inputs, reliable predictions of the mass ablation rate of new samples can be obtained.

At present, there is no conclusion on the optimal number of virtual samples or the influence of the number of samples on the performance. Therefore, it is necessary to discuss the effect of introducing different numbers of virtual samples. Hence, 50 to 500 virtual samples at 50 intervals for each route were generated, and the performance of models trained on mixed datasets with different sample sizes was evaluated. The MAPE of the models’ test sets in these cases is shown in Figure 9.

For the small dataset resulting from the exploration strategy, it can be observed that after the introduction of 300 virtual samples, the MAPE of the GBDT model has significantly reduced, with the percentage error on the test set decreasing by approximately 25% to 3.1%. The AdaBoost model also achieves certain performance improvements in most cases when virtual samples are introduced, although the improvement is not significant. However, the performance of the RF model decreases after the introduction of a certain number of virtual samples, which may be attributed to the fact that the MAR value of virtual samples is generated by the GBDT model. The understanding of the data by RF differs from that of the boosting model, leading to a decrease in performance. By comparison, the influence of introducing virtual samples is more pronounced in enhancing the performance of models trained on the small dataset generated through EI sampling, as depicted in Figure 9e–h. After the introduction of 400 virtual samples, the averaged MAPE of repeating modeling by the XGB algorithm decreased to 2.48%. In general, the introduction of virtual samples can indeed further optimize the predictive ability of ML models.

It is worth noting that the labelled values of the generated virtual samples are calculated by the resulting model of active learning. The model itself is in error in its prediction of ablation rates, so the generated virtual samples may suffer from the model’s misinterpretation of the filler content–mass ablation rate relationship. They eventually deviate from the true sample distribution and become noise in the training set, which may affect the predictive ability of the mass ablation rate prediction model.

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 SiO₂, 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.