## 2 Materials and Methods
### Statistical Analyses  
In our investigation of the effectiveness of nonlinear measures (LyE\({}_{\text{R}}\), DFA, ApEn, CD, SpEn, LyE\({}_{\text{W}}\)) for predicting the metabolic cost, we constructed six unique ANNs. These ANNs underwent a thorough evaluation to determine their capacity as predictors of metabolic expenditure, comparing their performance against traditional multiple linear regression (MLR) models for each nonlinear metric. The assessment of the ANNs encompass an analysis of the error distribution, response correlation, and predictive accuracy during various data phases, including training, validation, and testing. Additionally, we scrutinized the patterns in prediction errors and their association with input variables to identify the models' strengths and areas requiring enhancement. We expanded our assessment metrics to include 5-fold cross-validation (k = 5) for a comprehensive evaluation of the ANN models, which provided more reliable metrics and minimized overfitting, particularly given the small dataset [14; 42]. Regression analysis was employed to measure \begin{table}
\begin{tabular}{c c c} \hline
**Signal Type** & **Measurement** & **Normalization Process** \\ \hline Joint Angle & Hip, Knee, Ankle & N/A \\ Joint Velocity & Hip, Knee, Ankle & N/A \\ Joint Moment & Hip, Knee, Ankle & Normalized to body mass (N-m/kg) \\ Center of Mass & Position, Velocity & N/A \\ Ground Reaction Force & Anterior-Posterior and Vertical Components & Normalized to body mass (N/kg) \\ Metabolic Cost & Indirect Calorimetry & Normalized to body mass (W/kg) \\ \hline \end{tabular}
\end{table} 
Table 1: Listing all measured signals and their corresponding normalization processes. This table presents signals and their corresponding normalization processes. Joint moments and the GRF were normalized to each participant’s body mass (N-m/kg for moments and N/kg for the GRF), while the metabolic cost was expressed in watts per kilogram (W/kg) to allow for meaningful cross-trial and cross-condition comparisons, minimizing individual variability and facilitating the analysis. “N/A” indicates that the value is not applicable or could not be calculated for the corresponding metric. the alignment of the model outputs with the actual target values, providing a detailed understanding of the model's predictive capabilities. In addition, the regression analyses underscore the complexity of predicting the metabolic cost from gait variables. The differences in the \(\text{R}^{2}_{\text{ANN}}\) and \(\text{R}^{2}_{\text{MLR}}\) values and the significance of various predictors across the nonlinear measures highlight the nuanced relationship between gait dynamics and the metabolic cost. These insights are crucial for developing more accurate models for metabolic cost prediction. To provide a more detailed evaluation of model performance, we conducted supplementary analyses, including error histograms and scatter plots comparing predicted and actual values and confidence intervals across nonlinearity measures. These Supplementary Figures and Table are included in the Supplementary Materials and offer additional insights into the distribution of errors and the prediction accuracy. We encourage readers to refer to these figures to understand the model's performance across different gait conditions comprehensively. This comprehensive approach enabled us to leverage sophisticated nonlinear analyses to dissect the complex biomechanical data from hip exoskeleton-assisted walking. We aimed to derive profound insights into assisted gait dynamics and formulate an improved and precise predictive framework for assessing the metabolic implications of hip exoskeleton use by contrasting the predictive abilities of ANNs with MLR models. All statistical procedures were conducted using MATLAB, with a set significance threshold of 0.05 for all tests. Model performances were compared using the MSE and R-squared values.