## 4 Discussion
Strong R-values across all subsets suggest that the net\({}_{\text{GRF}}\) model has learned the underlying patterns effectively and can generalize well to new data. The closeness of data points to the line where predicted values match actual values in the plots signifies the model's precision. This is particularly evident in the validation subset, where a close alignment highlights the model's accuracy with validation data. Similarly, the regression analysis for the net\({}_{\text{Moment}}\) model (Figure 3) demonstrates that while the overall trend of the data points suggests a reasonable fit, the spread of the points around the line of unity is more pronounced than in the net\({}_{\text{GRF}}\) model, especially in the 'test' subset, as indicated by the lower R-value. This suggests that while the net\({}_{\text{Moment}}\) model has learned to an extent, its predictive performance may not be as robust as the net\({}_{\text{GRF}}\) model when applied to new data. Figures 2 and 3 underscore the nuanced differences in the performance of the two models. The net\({}_{\text{CRF}}\) model's stronger R-values imply a more reliable predictive model for estimating metabolic costs from biomechanical data. The data points' distribution to the fit line and the line of unity across all plots serves as a graphical testament to the net\({}_{\text{GRF}}\) model's superior ability to capture the essential patterns of the underlying biomechanical processes. In Figure 4, the training and validation performance plots for the net\({}_{\text{GRF}}\) and net\({}_{\text{Moment}}\) models offer critical insights into the learning dynamics of each network. Figure 4a demonstrates a consistent decrease in the MSE for the net\({}_{\text{GRF}}\) model as the number of epochs increases, with the best validation performance occurring at epoch 9. This suggests that the net\({}_{\text{GRF}}\) model is effectively learning the underlying patterns in the data without signs of significant overfitting, as indicated by the convergence of training and validation error rates. Figure 4b, on the other hand, illustrates the net\({}_{\text{Moment}}\) model's learning progression, with the best validation performance achieved at an earlier epoch, epoch 6. The green circle indicates a key moment where the validation error minimizes before the test error rises, which may signal the onset of overfitting. This point is crucial for model tuning, as it identifies the epoch after which the model may start to learn noise from the training data rather than underlying trends, reducing its generalization performance on new data. The comparative analysis of these learning curves informs the model selection process, guiding the implementation of early stopping or other regularization techniques to optimize model performance. The error histograms presented in Figure 5 for both the net\({}_{\text{CRF}}\) and net\({}_{\text{Moment}}\) models visually represent the variance between predicted and actual metabolic costs. Figure 5a shows a concentration of errors closer to zero for the net\({}_{\text{CRF}}\) model, indicating a tighter clustering of predicted values around the actual metabolic costs and, consequently, a higher accuracy. In contrast, Figure 5b shows a broader spread of errors for the net\({}_{\text{Moment}}\) model, implying a greater variance in the accuracy of predictions. The histograms assist in pinpointing areas where predictions consistently deviate from actual values and identifying outlier errors, which can be pivotal for subsequent model refinements. This graphical analysis of error distribution is instrumental in assessing the predictive performance of the models, guiding efforts to optimize them for enhanced accuracy in estimating metabolic costs. Our findings, demonstrating a solid predictive relationship between the GRF, biomechanical measurements, and metabolic costs in human walking, align with other studies ([1,32]).