## 4 Discussion
These errors highlight the intricate biomechanical interactions these variables represent, as well as the modeling challenges involved. Additionally, the GRF\({}_{\text{Ver}}\) exhibits a high prediction error in DFA, highlighting its importance in capturing the complex gait dynamics. The ankle moment also shows a substantial prediction error in the CD, indicating its significant role in the nonlinear dynamics associated with the metabolic cost. The high prediction error for the GRF\({}_{\text{Ver}}\) in DFA suggests that the vertical ground reaction force plays a key role in capturing long-term dependencies in gait patterns, as it directly impacts each step's stability and energy requirements, especially in maintaining a balance against gravitational forces. Similarly, the substantial prediction error for the ankle moment in the CD highlights the complexity of the ankle torque in contributing to the multidimensional aspects of gait dynamics. Ankle moments are critical for propulsion and stabilization, and their variability reflects the intricate control required for efficient energy use, which is closely tied to the metabolic cost. These findings suggest that the ankle velocity, COM velocity, GRF\({}_{\text{Ver}}\), and ankle moment are key factors in the ANN models' predictive capabilities, especially in the context of the nonlinear characteristics of gait and their impact on metabolic efficiency. Table 5 shows that the highest mean error of the nets comes from the GRF, and the lowest comes from the knee. It also shows that, across the gait parameters, the COM velocity, GRF\({}_{\text{ver}}\), knee velocity, ankle moment, and hip angle influence the ANN-based metabolic cost predictions the most. Consistent with existing research [51; 52], it is indicated that factors such as the GRF, COM dynamics, moments at various joints, and how mechanical work is shared among the hip, knee, and ankle joints play crucial roles in influencing the metabolic cost of movement. In summary, the tables and figure analysis suggest that the LyE\({}_{\text{R}}\) and DFA show the highest explanatory power for the metabolic cost among the nonlinear gait measures, which is aligned with the literature [53; 54; 55; 56; 57; 58]. Specifically, the R\({}^{2}\) MLR values from the multiple linear regression analyses indicate that DFA and the LyE\({}_{\text{R}}\) can explain 63% and 72% of the variance in the metabolic cost, respectively. Among the ANN models, models created based on the LyE\({}_{\text{R}}\), DFA, and ApEn showed better performance, as indicated by their low MSE and high R\({}^{2}\)ANN values. This suggests that these measures capture variations in gait that are more closely related to the metabolic cost than others. The coefficients (estimates) reflect the change in the metabolic cost associated with a one-unit change in the variable and help elucidate the most influential variables within the MLR and ANN models. Variables with significant \(p\)-values are considered strong predictors of the metabolic cost. Although the specifics of these variables are not quoted directly here, the high \(\text{R}^{2}_{\text{ANN}}\) values for the DFA and \(\text{LyE}_{\text{R}}\) models suggest that the variables included in these models are substantial connectors to the predicted metabolic cost. Based on the \(\text{R}^{2}_{\text{ANN}}\) values, DFA and the \(\text{LyE}_{\text{R}}\) appear to predict the greatest proportion of the metabolic costs. Within the ANN and MLR models, the specific variables that most effectively change the metabolic cost would be those with significant coefficients in the models using DFA and \(\text{LyE}_{\text{R}}\) measures. It is recommended that these variables be focused on optimizing gait parameters for metabolic cost reduction in assistive devices such as hip exoskeletons. The integration of AI in healthcare introduces critical ethical considerations, such as data privacy, algorithmic biases, and the transparency of AI decision-making.