## 3 Results  
Six unique ANN models were constructed, each focusing on a different gait nonlinearity measure (LyE\({}_{\text{R}}\), DFA, ApEn, CD, SpEn, LyE\({}_{\text{W}}\)) derived from the kinematic and kinetic features calculated across the 120-trial dataset to estimate metabolic costs. Table 2 and Supplementary Figures show the performance of six different ANN models, each tailored to a specific gait nonlinearity measure (LyE\({}_{\text{R}}\), DFA, ApEn, CD, SpEn, LyE\({}_{\text{W}}\)). The varied number of neurons in the hidden layer across models suggests that differing levels of complexity are required to capture best the relationship between each nonlinearity measure and the metabolic cost. Models with the highest number of neurons reflected the greatest complexity, while those with the fewest neurons reflected the least complexity. Performance was evaluated using the mean squared error (MSE) and R\({}^{2}\)ANN with lower MSE and higher R\({}^{2}\)ANN values indicating better model performance. The \(p\)-values assessed the statistical significance of the model's predictions. Supplementary Table represents the confidence intervals for the MLR and ANN models to provide a more robust assessment of the model reliability. Tables 3 and 4 present the results of multiple linear regression analyses for various nonlinear gait measures: the LyE\({}_{\text{R}}\), DFA, ApEn, CD, SpEn, and LyE\({}_{\text{W}}\). The R\({}^{2}\)MLR values indicate the proportion of variance in the metabolic cost explained by each model, with the LyE\({}_{\text{R}}\) and DFA showing the highest explanatory power at 0.72 and 0.63, respectively. Every row in the tables corresponds to a distinct gait parameter, including the angles, velocities, and moments of the hip, knee, and ankle joints, along with the velocity and position of the COM and the anterior-posterior and vertical components of the GRF. The coefficients (estimates) reflect the change in the metabolic cost associated with a one-unit change in the variable, holding other variables constant. The Standard Error (SE) measures the variability in the estimate, and the \(p\)-value indicates the statistical significance of the coefficients. This study employed Partial Dependence Plots (PDPs) to delve into the influence of specific gait variables--such as joint angles, velocities, moments, the center of mass position and velocity in the sagittal plane, and the GRF in vertical and anterior-posterior directions--across different nonlinear analyses on metabolic cost estimation [39; 40; 41]. PDPs were utilized for each nonlinear measure to identify variables that significantly impact the model's predictive accuracy, as reflected by the RMSE. For each model, individual variable signals were adjusted through the entire range of their observed values during the gait cycle while keeping everything else constant. Changes in the RMSE arising from the manipulation of each variable enabled the determination of the gait parameters that are most crucial for precise metabolic cost predictions. Figure 2 represents the graphical analysis of gait nonlinearity measures and their prediction errors. Table 5 represents the summary of nonlinear gait parameters and ANN prediction errors.