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Heidarnejad, et al.

                 Table 7. Residual analysis of the machine learning models’ outputs
                 Model                     Training phase                                Testing phase
                            Maximum      Minimum      Mean       Sum      Maximum     Minimum       Mean       Sum
                 SVM          0.0549      −0.041      0.006      0.454      0.0327      −0.022      0.004     0.140
                 GEP          0.0485      −0.078      −0.012    −0.862      0.0440      −0.043     −0.004     −0.146
                 MLP          0.0393      −0.052      −0.002    −0.140      0.0235      −0.028      0.002     0.086
                 MARS         0.0743      −0.090      −0.013    −0.902      0.0431      −0.071     −0.005     −0.191
                 Abbreviations: GEP: Gene expression programming; MARS: Multivariate adaptive regression splines; MLP: Multilayer perceptron;
                 SVM: Support vector machine.

                              A


























                              B

























                Figure 5. Residual error variation of the machine learning models’ outcomes. (A) Training phase. (B) Testing
                phase.
                Abbreviations:  GEP:  Gene  expression  programming;  MARS:  Multivariate  adaptive  regression  splines;
                MLP: Multilayer perception; SVM: Support vector machine.






                Volume 22 Issue 6 (2025)                        84                           doi: 10.36922/AJWEP025120081
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