## 4 Discussion
To provide additional insights into the practical significance of the results, we have classified the strength of the correlations observed in this study using [PERSON]'s guidelines [45; 46; 47; 48; 49] for effect size magnitudes: trivial (<0.10), small to medium (0.10-0.30), medium to large (0.30-0.50), and large to very large (>0.50) [45; 46; 47; 48; 49]. These classifications, combined with Pearson's R-values and \(\text{R}^{2}\) values reported in Tables 2-4, offer a comprehensive understanding of the strength and relevance of the relationships modeled. This approach highlights both statistical significance and practical importance within the context of our study. The varied hidden layer sizes (individual neurons within a single hidden layer) across models reflect the individual complexities of each nonlinear measure; the selection of specific neuron counts was based on iterative testing during the model optimization process. For instance, the \(\text{LyE}_{\text{w}}\) and CD with minimal hidden layer sizes of two and three neurons indicate a more straightforward model structure. The CD and \(\text{LyE}_{\text{w}}\) capture key aspects of system dynamics. The CD reflects dimensionality or complexity (degrees of freedom) [31], while the \(\text{LyE}_{\text{w}}\) measures sensitivity to initial conditions, indicating stability [16; 17; 18; 19]. These metrics provide relatively direct information on complexity and stability, likely requiring fewer individual neurons within a single hidden layer in the neural network to model accurately. Their consistency across variables shown in Figure 2 also introduces less noise, allowing for reliable predictions with simpler architectures. In contrast, DFA, with 19 neurons, indicates a need for a more complex model, as it captures long-range correlations and intricate, nonlinear relationships within the data [21; 22; 23; 24; 25; 26]. This added complexity reflects the raw variability in values shown in Figure 2, requiring more neurons to capture subtle patterns in gait variability effectively. DFA with 19 neurons suggests a more complex model is needed to map the measure to the metabolic cost accurately. Overall, the ANN models demonstrated a substantial capacity for predicting the metabolic cost from nonlinear gait measures. However, differences in performance metrics such as MSE and \(\text{R}^{2}_{\text{ANN}}\) values underscore the importance of model selection based on the specific nonlinear feature being analyzed. These insights are crucial for further refining predictive models and potentially translating these findings into developing advanced assistive technologies. Supplementary Figures display the error histograms with 20 bins, which graphically represent the distribution of errors in the set of all six nonlinear ANN and MLR model predictions. The \(x\)-axis shows the error magnitude, with negative values representing underpredictions and positive values representing overpredictions relative to the actual nonlinear ANN model values. The \(y\)-axis shows the number of instances (frequency) of each error magnitude in the dataset. The error histograms in Supplementary Figures provide a comprehensive overview of the performance of six different nonlinear ANN and MLR models. These models, namely \(\text{net}_{\text{LyER}}\), \(\text{net}_{\text{DFA}}\), \(\text{net}_{\text{ApEn}}\), \(\text{net}_{\text{CD}}\), \(\text{net}_{\text{SpEn}}\), and \(\text{net}_{\text{yEw}}\) for the ANN models and \(\text{MLR}_{\text{LyER}}\), \(\text{MLR}_{\text{DFA}}\), \(\text{MLR}_{\text{ApEn}}\), \(\text{MLR}_{\text{CD}}\), \(\text{MLR}_{\text{SpEn}}\), and \(\text{MLR}_{\text{LyEw}}\) for the MLR models, are evaluated based on their prediction errors relative to actual metabolic costs. The histograms collectively demonstrate a spectrum of accuracy and bias across models. The \(\text{net}_{\text{SpEn}}\) model displays a bell-shaped distribution peaking near zero error, reinforcing its predictive precision.