## 5 Results and Discussion
### Performance of Data-Driven Models under Study  
In this subsection, the performance of the considered AI models is discussed. In the case of M5 MT, we will refer to the more complete equations marked with #1 in the Table 11, Table 12, and Table 13. Table 13 shows training and testing results for prediction of \(V_{H}^{*}\). By a quick glance, the values of statistical benchmarks illustrate that the EPR model predicted non-dimensionless \(V_{H}^{*}\) parameters with the highest accuracy (IOA = 0.9799, SSE = 0.0030, and MAE = 0.0550) in the training stage compared to the other AI models, followed by MARS (IOA = 0.9468, SSE = 0.0068, and MAE = 0.0826), M5 MT (IOA = 0.9468, SSE = 0.0612, and MAE = 0.0886), and GEP (IOA = 0.9244, SSE = 0.0111, and MAE = 0.1056). Furthermore, values of SI (0.0599) and ADR (1.0026) given by the EPR model displayed this trend. All the ADR values, which were approximately close to 1, indicated highly satisfying performance for AI models. In the case of the testing stage, it is surprising that the EPR model was found to fail in the prediction of \(V_{H}^{*}\) even though it had the best performance in the training stage. Hence, the assessment of statistical benchmarks indicated that MARS had highest most accuracy level (IOA = 0.9506, SSE = 0.1156, and MAE = 0.0912), followed by M5 MT (IOA = 0.9430, SSE = 0.1323, and MAE = 0.0644), GEP (IOA = 0.9084, SSE = 0.2143, and MAE = 0.0893), and EPR (IOA = 0.8237, SSE = 0.4124, and MAE = 0.1254). According to Table 2, SI values demonstrated the superiority of the M5 MT technique. From ADR values, all AI models showed relatively marginal under prediction (ADR \(<1\)) in the testing phase. The performance of AI models for the estimation of \(V_{H}^{*}\) in training and testing stages is illustrated in Figure 5. In Figure 5, data are fitted to \(\pm\)25% error lines. Most values of \(V_{H}^{*}\) predicted by the AI models in the training stage were in the range of an acceptable error bound. Similarly, Figure 5b shows well-matched predictions versus experimental observations, though a relatively significant under prediction is seen in the observed value of \(V_{H}^{*}\) = 3.8 for MSMT, GEP, and EPR models. In Table 3, statistical assessments of training and testing results in the prediction of \(V_{L}^{*}\) are given. It is inferred that the MARS technique (i.e., Equation (A9)) estimated \(V_{L}^{*}\) with the highest level of precision (IOA = 0.9950, SSE = 0.0157, and MAE = 0.0374) in the training phase in comparison with M5 MT (IOA = 0.9877, SSE = 0.0387, and MAE = 0.0672), EPR (IOA = 0.9883, SSE = 0.0369, and MAE = 0.0754), and GEP (IOA = 0.9680, SSE = 0.1001, and MAE = 0.1027). SI (0.0504) and ADR (0.9993) obtained by the MARS model were also indicative of its superiority when compared to the other AI models. Table 3 also indicates that M5 MT and EPR models had approximately the same performance in the prediction of \(V_{L}^{*}\) according to the statistical benchmarks (i.e., IOA, SSE, and SI). Moreover, it can be inferred from the ADR values that all AI models had convincing efficiency; specifically, the MARS model experienced a very marginal under prediction whereas the other AI approaches showed insignificant over predictions. Results of the testing stage demonstrated that the GEP-based formulation (i.e., Equation (A2)) had the best performance (IOA = 0.9911, SSE = 0.0384, and MAE = 0.0544) in the prediction of \(V_{L}^{*}\). M5 MT