## 2 Methodology
### Sampling
The algorithm then selects the candidate with the largest \"minimum distance\" to be added to the sample set, ensuring that the newly added point is as far as possible from the current samples and thereby guaranteeing that all types of data have an opportunity to be sampled. All the features are standardized before the calculation to avoid errors caused by significant differences in scale between features (Equation (14)). \[x_{\text{next}}=\underset{x\in\delta_{\ell_{x}}\backslash C}{\text{argmax}} \bigg{(}\underset{c\in C}{\min}\|x-c\|\bigg{)} \tag{12}\]  
\[\|x-c\|=\sqrt{\sum_{i=1}^{d}(x_{i}-c_{i})^{2}} \tag{13}\]  
\[x_{i,Scaled}=\frac{x_{i}-mean}{std} \tag{14}\]  
where \(\delta_{\ell_{x}}\), \(C\), \(x\), and \(c\) in Equation (12) stand for candidate set, current sample set, a candidate, and a sample in the current sample set, respectively. In Equation (13), \(d\), \(x_{i}\), and \(c_{i}\) represent the number of dimensions (features) in the feature space, the \(i\)-th feature of  
Figure 3: Schematic illustration of the stratified and greedy sampling process. The differently colored particles simply represent distinct individuals within the population. a candidate (the value of the candidate in the \(i\)-th dimension of the feature space), and the \(i\)-th feature of a sample in the current sample set, respectively. In Equation (14). _mean_ corresponds to the mean value of the \(i\)-th feature, and \(std\) stands for the standard deviation of the \(i\)-th feature. Finally, the genetic algorithm (GA) is applied to optimize the number of stratified layers and the total sampling size. Each individual in the algorithm represents a combination of the optimized number of layers and the total sampling size. The average of the variance ratio and mean ratio of all 48 features, referred to as the Global Ratio (Equation (15)), is used as the evaluation criterion. To prevent division by zero, a small positive constant is added to the denominator. The stopping condition for the algorithm is met when the Global Ratio for all the features falls within the range of 0.85 to 1.15, indicating that the distribution of the sampled data is sufficiently similar to that of the total particles. \[ \begin{array}{l}\text{Var Ratio}(f)=\frac{\text{Var}_{\text{sample}}(f)}{ \text{Var}_{\text{orig}}(f)+\varepsilon}\\ \text{Mean Ratio}(f)=\frac{\mu_{\text{sample}}(f)}{\mu_{\text{orig}}(f)+\varepsilon }\\ \text{Global Var Ratio}=\frac{1}{N}\sum\limits_{k=1}^{N}\text{VarRatio}(f_{k})\\ \text{Global Mean Ratio}=\frac{1}{N}\sum\limits_{k=1}^{N}\text{MeanRatio}(f_{k}) \end{array}  \tag{15}\]  
where \(\text{Var}(f)\) is the variance of the feature \(f\), \(\mu(f)\) is the mean of the feature \(f\), \(\text{Var}_{\text{sample}}(f)\) is the variance of the sampled data for feature \(f\), \(\text{Var}_{\text{orig}}(f)\) is the variance of the original data for feature \(f\), \(N\) is the number of datasets, and \(\varepsilon\) is a small positive value to avoid division by zero. The workflow of the GA is illustrated in Figure 4 and its corresponding hyperparameters are in Table 1. The optimized stratification resulted in dividing both the y- and z-coordinates into 70 intervals each, yielding a total of 4900 layers when combined. A total of 4902 samples were selected. The Global Ratio for each feature is presented in Table 2, demonstrating the effectiveness of the optimization process. Overall, to ensure the representative coverage of both dense and sparse particle regions, we use a two-stage sampling process: stratified sampling followed by greedy diversity \begin{table}
\begin{tabular}{c|c} \hline _Hyperparameter_ & _Value_ \\ \hline _Max generations_ & 20 \\ _Population size_ & 30 \\ _Mutation rate_ & 0.1 \\ \hline \end{tabular}
\end{table} 
Table 1: Genetic algorithm hyperparameters.