## 2 Research Data and Methods  
### Description of Used Data and Variables  
[PERSON] [1] and [PERSON] and [PERSON] [11] used cementitious materials to stabilize four base aggregates--Meridian limestone with 97% of CaCO\({}_{3}\), Richard Spur limestone with 87% of CaCO\({}_{3}\), Sawyer sandstone with 94% of SiO\({}_{2}\), and Rhyolite--which were subjected to W-D cycles, and then tested for M\({}_{\rm r}\). M\({}_{\rm r}\) samples were cured for 28 days in a control room after compaction at optimum moisture content and maximum dry density. Then, cured samples were subjected to 8, 16, and 30 W-D cycles. More details for test stress states and data are presented in [1; 4; 10; 11]. [PERSON] [1] and [PERSON] [11] developed a regression model (M\({}_{\rm r}\) = \(f\) (W-D, CSAFR, DMR, \(\sigma_{3}\), \(\sigma_{d}\))) that correlated the resilient modulus M\({}_{\rm r}\) with five parameters: W-D, CSAFR, DMR, \(\sigma_{3}\) and \(\sigma_{d}\). The sensitivity of the input variables for predicting M\({}_{\rm r}\) was studied by [PERSON] et al. [4]. They used least square (LS) and SVR methods to study the effectiveness of the input variables at predicting M\({}_{\rm r}\). Based on their results, the five input variables improved the predicted values of M\({}_{\rm r}\) significantly, given that the values of \(r^{2}\) for the LS and SVR methods were 0.69 and 0.97, respectively, while the r\({}^{2}\) values for predicting M\({}_{\rm r}\) using only three or four input variables were within the range of 0.65-0.68 and 0.90-0.96 for the LS and SVR methods, respectively. Thus, five input variables (W-D, CSAFR, DMR, \(\sigma_{3}\) and \(\sigma_{d}\)) were adopted in this study. These input variables, and M\({}_{\rm r}\) as the output variable, were employed to design the PSO-ELM model and to compare it with the PSO-ANN and KELM models. A total of 704 experimentally conducted M\({}_{\rm r}\) tests were used, and these were divided into training (70%) and testing (30%) datasets, as presented in the Supplementary Materials. Table 1 shows the statistical evaluation of the training and testing stages. In Table 1, the terms mean, median, min, max, SD, SK and KU indicate the mean, median, minimum, maximum, standard deviation, skewness, and kurtosis coefficients, respectively. It can be seen from the table that for the whole dataset, the minimum and maximum of W-D were 0 and 30 cycles, respectively. The minimum and maximum of the ratio of oxide compounds in the cementitious materials (CSAFR) were 0.11 and 0.51%, respectively. The minimum and maximum of the ratio of maximum dry density to the optimum moister content (DMR) were 2.34 and 4.63% kN/m\({}^{3}\). The maximum and minimum values of \(\sigma_{3}\) and \(\sigma_{d}\) for the whole dataset were 138, and 0.00 kPa; and 277 and 69 kPa, respectively. In addition, the correlation coefficient between the input variables and M\({}_{\rm r}\) was calculated. The correlation between M\({}_{\rm r}\) and W-D was \(-\)0.29, and between M\({}_{\rm r}\) and CSAFR was 0.46. Moreover, the correlations between M\({}_{\rm r}\) and DMR, \(\sigma_{3}\), and \(\sigma_{d}\) were 0.71, 0.08, and 0.14, respectively. In summary, inverse correlation was yielded with W-D, whereas high correlation was observed with DMR. M\({}_{\rm r}\) had the greatest kurtosis and positive skewness. All data were skewed distributions, and were not normal distributions, since they had considerably high skewness values.