## 2 Methodology
### Data Preprocessing and Splitting  
A total of 361 stress-strain curves were generated by means of uniaxial compression simulations (Figure 3a). These curves spanned a wide range of mechanical responses: peak stresses varied from near 5 MPa up to approximately 380 MPa, and maximum strains reached about 0.05.  
For each curve, eight characteristic points were extracted as input features for the AutoML model (Figure 3b). The three primary landmarks, initial point (0,0), peak stress, and terminal point, were first identified. The strain interval was then partitioned into two segments (from start to peak and from peak to end); four equidistant points were sampled on the larger segment and one on the smaller segment. Each extracted point was  
Figure 3: The obtained numerical simulation stress–strain curves: (**a**) all 361 stress–strain curves; (**b**) schematic of eight sampled points per curve used as AutoML inputs.  
represented by its strain (\(x\)) and stress (\(y\)) coordinates, yielding 16 features per simulation. Consequently, the input dataset consisted of 361 samples \(\times\) 16 features, and the outputs comprised the three parallel bond parameters \(E\), \(k_{s}/k_{n}\), and \(E_{d}\).  
Data preprocessing is a very important part in machine learning tasks, especially when dealing with high-dimensional and nonlinear data. In order to improve the training effect and stability of the AutoML model, the input variables were normalized using the Min-Max normalization method [15; 16; 17], which scales data into the range [0, 1] (Equation (3)), preserving the relationships between values while ensuring uniform contribution to model training.  
\[x^{*}=\frac{(x-x_{min})}{(x_{max}-x_{min})} \tag{3}\]  
where \(x\), \(x_{min}\), and \(x_{max}\) denote an original feature value and its observed minimum and maximum, respectively.  
In this study, the preliminary experiments indicated that the multi-objective AutoML model showed higher prediction accuracy when the target output parameters \(E\), \(k_{s}/k_{n}\), and \(E_{d}\) were normalized using the RobustScaler method (Equation (4)) [18]. The RobustScaler method is less sensitive to outliers by centering the data around the median and scaling them according to the interquartile range (IQR), which would improve the stability of the model [18]. Therefore, the RobustScaler normalization method was adopted for output variables in this study.  
\[x^{*}=\frac{x-Q_{2}}{Q_{3}-Q_{1}} \tag{4}\]  
where \(Q_{1}\), \(Q_{2}\), and \(Q_{3}\) are the 25 th percentile, median, and 75 th percentile, respectively.  
Summary statistics for all normalized inputs and outputs (mean, standard deviation, minimum, maximum, and median) are provided in Table 2. Input features are bounded within [0, 1] with consistent distributions; output variables likewise occupy acceptable normalized ranges.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Variable** & **Mean** & **Std. Dev.** & **Min** & **Max** & **Median** \\ \hline \(x_{1}\) & 0.272 & 0.159 & 0 & 1 & 0.257 \\ \(y_{1}\) & 0.400 & 0.224 & 0 & 1 & 0.357 \\ \(x_{2}\) & 0.134 & 0.166 & 0 & 1 & 0.086 \\ \(y_{2}\) & 0.030 & 0  
The dataset was then partitioned at random: 80% of samples were allocated to the training dataset (for model fitting and validation), and the remaining 20% constituted the independent testing dataset. Model selection and hyperparameter tuning proceeded automatically within the AutoML framework, based on performance metrics computed on the validation split.