## 3 Results  
The net\({}_{\text{GRF}}\), with a hidden layer size of six and input delays set to two, achieved significant (\(p\)-value < 0.001) strong R-values across training, validation, and testing datasets, with the R-value of the training at 0.962, the R-value of the validation at 0.937, and the R-value of the test at 0.883 (Figure 2 and Table 1). These values indicate a robust correlation between the predicted and actual metabolic costs, underscoring the model's efficacy. The MSEs were notably low, with training performance at 0.0036, validation performance at 0.0064, and test performance at 0.0140 in (W/kg)\({}^{2}\), further affirming the model's precision (Table 1). Figure 2: Comprehensive regression analysis of the net\({}_{\text{CRF}}\) model. This figure delineates the regression plots for the net\({}_{\text{CRF}}\) model across (**a**) ‘validation’, (**b**) ‘test’, (**c**) ‘training’, and (**d**) ‘all’ datasets, illustrating the model’s predictive accuracy and generalization capability. The plots compare the predicted metabolic costs against actual values, with each subset providing insights into the model’s performance in different phases of data handling, from learning to generalization on unseen data. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**ANN Parameters and Performance**} & \(\mathbf{Net_{\text{CRF}}}\) & \(\mathbf{Net_{\text{Moment}}}\) \\ \hline \multirow{4}{*}{**Settings**} & **Training ratio (\%)** & 70 & 70 \\  & **Validation ratio (\%)** & 15 & 15 \\  & **Test ratio (\%)** & 15 & 15 \\  & **Hidden layer size (neurons)** & 6 & 3 \\  & **Delays (count of time steps)** & 2 & 1 \\ \hline \multirow{4}{*}{MSE (W/kg)\({}^{2}\)} & **Training** & 0.0036 & 0.0071 \\  & **Validation** & 0.0064 & 0.0046 \\  & **Test** & 0.0140 & 0.0121 \\  & **Total trials** & 0.0056 & 0.0075 \\  & **K-fold cross-validation test (k = 5)** & 0.0157 \(\pm\) 0.0019 & 0.0123 \(\pm\) 0.0013 \\ \hline \multirow{4}{*}{R-value} & **Training** & 0.963 & 0.920 \\  & **Validation** & 0.927 & 0.956 \\ \cline{1-1}  & **Test** & 0.882 & 0.874 \\ \cline{1-1}  & **Total trials** & 0.942 & 0.918 \\ \cline{1-1}  & **K-fold cross-validation test (k = 5)** & 0.842 \(\pm\) 0.016 & 0.850 \(\pm\) 0.024  
The joint moments ANN model (net\({}_{\text{Moment}}\)), with a more streamlined architecture featuring a hidden layer size of three and input delays of one, likewise exhibited solid predictive capabilities. The R-values for this model were similarly solid and significant (\(p\)-value \(<\) 0.001), with the R-value of the training reaching 0.920, the R-value of the validation at 0.956, and the R-value of the test at 0.874 (Figure 3 and Table 1). These results highlight the model's ability to estimate metabolic cost from joint moments data accurately. The net\({}_{\text{Moment}}\) model showed strong performance, achieving training, validation, and test scores of 0.0071, 0.0046, and 0.0121 in (W/kg)\({}^{2}\), respectively, underscoring its accuracy (Figure 4b and Table 1). An 'epoch' in machine learning, specif \begin{table}
\begin{tabular}{c l c c} \hline \multicolumn{2}{c}{**ANN Parameters and Performance**} & \(\mathbf{Net_{\text{GRF}}}\) & \(\mathbf{Net_{\text{Moment}}}\) \\ \hline \multirow{4}{*}{\(p\)-value} & Training & \textless{}0.001 & \textless{}0.001 \\  & Validation & \textless{}0.001 & \textless{}0.001 \\  & Test & \textless{}0.001 & \textless{}0.001 \\  & Total trials & \textless{}0.001 & \textless{}0.001 \\  & K-fold cross-validation test (k = 5) & \textless{}0.001 & \textless{}0.001 \\ \hline \multirow{4}{*}{**Performance Metrics**} & Accuracy (\%) & 81.72 & 77.32 \\  & Recall (\%) & 83.27 & 77.32 \\ \cline{1-1}  & Precision (\%) & 81.72 & 77.32 \\ \cline{1-1}  & F1 score & 0.82 & 0.77 \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 3: Comprehensive regression analysis of the net\({}_{\text{Moment}}\) model.