## 3 Materials and Methods
### Data Collection and Pre-Processing  
The dataset utilized for the calibration and validation of the M5P models, sourced from [PERSON] et al. (2016), comprises 610 shear capacity tests on RC flat slabs without shear reinforcement collected from 55 experimental studies conducted between 1956 and 2016. These tests provide valuable information about various factors that influence the punching shear capacity of a RC flat slab, such as concrete strength, the reinforcement ratio, and the shear-span-to-depth ratio. This design choice aimed to focus the study on the punching shear capacity of flat slabs without shear reinforcement, thus isolating the behavior of the primary material components. Only flat slabs with failures primarily occurring due to punching shear (482 points) rather than flexure were considered in this study. This criterion ensured that the dataset accurately represented the performance of RC flat slabs under punching-shear-dominated failure modes, enabling a more targeted investigation of the factors affecting the punching shear capacity of RC flat slabs. The available data were randomly divided into two sets: a training set for model calibration, which was used to develop and optimize the predictive models, and an independent validation set for model verification, which allowed for the assessment of each model performance and generalizability on previously unseen data. This division strategy ensured a thorough evaluation of the models' capabilities in accurately predicting the punching shear capacity of RC flat slabs across a wide range of scenarios. A stratified sampling technique was employed to ensure that both subsets were representative of the entire dataset in terms of the distribution of key variables. This approach enabled a more robust evaluation of each model performance and generalizability. Typically, the dataset was split into a 80:20 ratio, with the larger portion reserved for training and the smaller portion for testing. Table 1 offers a comprehensive overview of the distribution and range of values for each parameter in both sets, allowing for a better understanding of the dataset characteristics. For enhanced visualization and a deeper understanding of the relationships between input and output parameters, a matrix-plot is provided in Figure 3. This plot presents \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Data Category** & **Statistics** & \(b\) **(mm) \({}^{*}\)** & \(d\) **(mm) \({}^{*}\)** & \(f_{c}\) **(MPa) \({}^{*}\)** & \(f_{y}\) **(MPa) \({}^{*}\)** & \(\rho\) \({}^{*}\)** & \(\lambda\) \({}^{*}\) & \(V_{u}\) **(kN) \({}^{*}\)** \\ \hline Training data & Median & 196.350 & 112.500 & 31.900 & 468.000 & 0.012 & 5.952 & 324.000 \\  & Mean & 192.689 & 117.989 & 35.696 & 475.082 & 0.013 & 5.972 & 441.046 \\  & Minimum & 40.055 & 29.970 & 9.401 & 250.000 & 0.003 & 0.612 & 24.000 \\  & Maximum & 707.644 & 668.500 & 130.100 & 749.000 & 0.050 & 32.507 & 4915.000 \\  & Standard & 99.133 & 62.842 & 19.641 & 112.799 & 0.007 & 3.170 & 456.952 \\  & deviation & & & & & & & \\ \hline Testing data & Median & 200.000 & 100.000 & 29.546 & 453.600 & 0.013 & 5.685 & 330.000 \\  & Mean & 193.885 & 111.895 & 33.209 & 453.680 & 0.015 & 5.910 & 406.104 \\  & Minimum & 51.000 & 33.166 & 11.771 & 250.000 & 0.003 & 1.000 & 44.000 \\  & Maximum & 520.000 & 400.000 & 98.000 & 749.000 & 0.073 & 13.551 & 2224.000 \\  & Standard & & & & & & & \\ deviation & & & & & & & & \\ \hline \end{tabular} \({}^{*}\)\(b\) = equivalent column width; \(d\) = slab effective depth; \(f\) = concrete strength; \(f\) = yield strength of reinforcement, \(\rho\) = longitudinal reinforcement ratio; \(\lambda\) = span–depth ratio; \(V_{u}\) = punching shear capacity.  
\end{table} 
Table 1: Summary of the key input parameters utilized in the model development and based on the experimental datasets. a series of scatterplots showcasing the pairwise relationships among the input variables and their correlation with the output parameter, which in this case is the punching shear capacity of the RC flat slab.