## 4 Discussion  
Our study aimed to advance the understanding of metabolic cost estimation through biomechanical data, focusing on the predictive capabilities of the GRF and joint moments using ANNs. We hypothesized that both the GRF and joint moments could accurately estimate metabolic costs. Our objective was to assess their comparative predictive power, offering insights into the biomechanics of energy efficiency in human locomotion. Our  
Figure 7: Analysis of joint moments’ influences on metabolic cost prediction under net\({}_{\text{moment}}\). (**a**) Depicts the hip joint moment (\(\text{Hig}_{\text{M}}\)) variations across different gait cycle percentages, compiled from all trials (270 in total). (**b**) Illustrates the progression of knee joint moment (\(\text{Knee}_{\text{M}}\)) signals throughout the gait cycle, encompassing all trials. (**c**) Portrays ankle joint moment (\(\text{Ankle}_{\text{M}}\)) fluctuations over the gait cycle and aggregates data from all trials. (**d**) Provides a granular analysis of each gait cycle percentage’s influence on the Root-Mean-Square Error (RMSE) between the model’s predicted and the actual joint moments under net\({}_{\text{moment}}\). This plot, the Partial Dependence Plot (PDP), highlights the critical phases of the gait cycle that significantly affect the model’s accuracy in predicting joint moments. The vertical lines indicate the standard deviation of the RMSE, offering insights into the variability and reliability of the model’s predictions at each gait cycle percentage. The stability of other variables in this analysis implies that these effects are directly linked to changes in the joint moments during the gait cycle. results supported these hypotheses, as the results indicate that both the GRF and moment ANN models can predict metabolic cost. The comparative analysis reveals that the net\({}_{\text{GRF}}\) model, with more neurons in the hidden layer, showed slightly better overall performance and higher R-value of the training component (\(p\)-value \(<\) 0.001) than the net\({}_{\text{Moment}}\) model. However, the net\({}_{\text{Moment}}\) model demonstrated a more robust correlation and significant R-value for the validation component (\(p\)-value \(<\) 0.001), indicating potential differences in generalization capabilities. The net\({}_{\text{GRF}}\) model resulted in a higher test performance error, suggesting possible overfitting compared to the net\({}_{\text{Moment}}\) model, which had a more balanced error distribution across training, validation, and testing phases (Table 1). Determining the 'best' model between net\({}_{\text{GRF}}\) and net\({}_{\text{Moment}}\) depends on specific criteria and application needs. If predictive accuracy and lower training errors are prioritized, the net\({}_{\text{GRF}}\) model might be preferred due to its significant, stronger (\(p\)-value \(<\) 0.001) R-value in training and overall performance. However, for applications valuing generalization to unseen data, the net\({}_{\text{Moment}}\) model, with its stronger, significant validation (\(p\)-value \(<\) 0.001) R-value, could be more suitable, despite its slightly lower overall R-value. The choice ultimately hinges on whether the focus is on training accuracy or validation performance. The GRF model demonstrates higher accuracy and superior performance across the other evaluation metrics (accuracy, recall, precision, F1 score, and k-fold cross-validation) compared to the moment prediction model (Table 1). This indicates that the GRF model provides more reliable and precise predictions, making it a more effective tool for our study's objectives. The regression analysis for the net\({}_{\text{GRF}}\) model across 'validation', 'test', 'training', and 'all' datasets (Figure 2) illustrates a robust linear relationship between the predicted and actual metabolic costs, with the R-values serving as a quantitative measure of this relationship.