## 3 Results
This figure delineates the regression plots for the net\({}_{\text{Moment}}\) 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. refers to one complete pass of the entire training dataset through the network [15,16]. The green circle in Figure 4a,b symbolizes the epoch at which the model's validation performance is at its peak. Figure 5 demonstrates the GRF and joint moment model error histograms (Figures 5a and 5b, respectively). Comparing the two models, both demonstrated exceptional predictive abilities, as evidenced by their high R-values and low MSEs. The GRF model, despite its more complex network structure, did not significantly outperform the joint moments model in terms of R-values, suggesting that both the GRF and joint moments are valuable predictors of metabolic cost. However, the GRF model showed slightly better consistency across different performance metrics (MSEs and R-values), potentially offering a more versatile tool for estimating metabolic cost in varied applications. Figure 4: Performance of the ANN models for the GRF and joint moments. Panel (**a**) illustrates the training and validation performance over epochs for the netGRF model, while Panel (**b**) does the same for the netMoment model. These plots showcase the models’ learning progress, highlighting moments of optimal learning and potential overfitting through changes in error rates and performance metrics. The green circle highlights optimal learning epochs and signs of overfitting. Figure 5: Error histograms for the GRF and joint moment models. Panel (**a**) presents the error distribution for netGRF model, and Panel (**b**), for the netMoment model, illustrates the variance between predicted and actual metabolic costs. The histograms elucidate the frequency of error magnitudes, aiding in identifying consistent prediction deviations and outlier errors for model refinement. A concentration of errors closer to zero for the netGRF model indicates a tighter clustering of predicted values around the actual metabolic costs and, consequently, a higher accuracy. In contrast, there is a broader spread of errors for the netMoment model, implying a greater variance in the accuracy of predictions. To further our understanding of how specific phases within the gait cycle influence metabolic cost predictions, we employed the PDPs [26; 27; 28]. This analysis was applied to GRF-based and moment-based networks to discern which gait cycle phases exert a more pronounced effect on the models' predictive accuracy, as quantified by the RMSE. For the GRF-based network, we systematically varied the GRF vertical and anterior-posterior signals across different gait cycle percentages from zero to their maximum observed values. By isolating one percentage at a time and observing the resultant changes in the RMSE, we could pinpoint phases of the gait cycle that are critical for accurate metabolic cost estimation. The first two plots focus on the GRF vertical and AP directions, respectively (Figure 6). Similarly, an analogous approach was undertaken for the moment-based network (Figure 7). Figure 6: Analysis of ground reaction force influences on metabolic cost prediction under net\({}_{\text{GRF}}\). (**a**) Displays the vertical ground reaction force (GRF\({}_{\text{View}}\)) signals throughout various percentages of the gait cycle, aggregated across all trials (270 in total). (**b**) Shows the progression of anterior–posterior ground reaction force (GRF\({}_{\text{AP}}\)) signals over the gait cycle and across all trials. (**c**) Presents a detailed view of how each percentage of the gait cycle impacts the Root-Mean-Square Error (RMSE) between the predicted and actual metabolic costs under net\({}_{\text{GRF}}\).