## 4 Discussion
The superior performance of our net\({}_{\text{CRF}}\) model, demonstrated by stronger R-values and lower MSEs, resonates with the understanding that the GRF, due to its direct relationship with the external forces during locomotion, can provide a more reliable estimate of metabolic cost compared to joint moments. This is further exemplified in our study, where the net\({}_{\text{CRF}}\) model showed a slightly better consistency across various performance metrics, highlighting its robustness and potential as a versatile tool for biomechanical analysis and intervention design to optimize human movement efficiency. In the current study, the RMSE across the gait cycle for both the GRF and joint moment models reveals the prediction accuracy at various gait cycle phases. This illustrates the variability in predicted metabolic cost based on biomechanical parameters at different stages of gait. The variability and consistency of these predictions are illustrated through the standard deviation of the RMSE, depicted as vertical lines in Figures 6 and 7. Our models analyze data from various gait cycle phases, enhancing prediction accuracy and providing a complete view of energy efficiency in movement. This approach ensures the models' effectiveness in real-world scenarios, capturing the full complexity of the gait cycle for precise metabolic cost estimations. A study by [PERSON] et al. [5] presents the stride average metabolic rate and the time profile of the metabolic rate during different walking conditions. They focused on estimating the stride average metabolic rate and creating a time profile of the metabolic rate during different walking conditions using two methods: musculoskeletal estimation and joint-space estimation. Our study and the previous research found that the push-off phase in the gait cycle generates the largest peaks for both the metabolic cost time profile and the RMSEs. Additionally, a notable peak occurs at approximately 17% of the gait cycle in Figures 6c and 7d, corresponding to the peak in the joint-space model's metabolic cost time profile in [PERSON] et al. 's study [5]. Moreover, using the musculoskeletal method, the single support phase had the highest metabolic cost. In contrast, the joint-space method estimated the highest metabolic cost during the second double-support phase [5]. Our results are within this range, corresponding to 38% and 50% of the gait cycle (Figures 6c and 7d). Our method can have practical applications, including identifying and characterizing gait disabilities by pinpointing the most energy-intensive phase of the stride cycle in patients, devising targeted rehabilitation exercises, such as treadmill walking, with robotic resistance during the least metabolically efficient phase of the stride cycle, and contributing to the engineering of efficient assistive devices, like designing an exoskeleton that aids the least economically efficient phase of the stride cycle. It may pose a challenge to characterize the time profile of metabolic cost in individual patients due to limited walking endurance. Therefore, a future challenge involves developing methods that enable the characterization of the time profile of metabolic cost with shorter experimental protocols for patients, potentially by integrating our method with other approaches, such as simulation [5,7,8] or blood flow measurements [33,34]. To address the stability and reliability of our ANN model,we suggest continuous performance monitoring, periodic re-evaluation, and retraining using new data. This study faces limitations beyond its potential overfitting due to its small sample and potential biases, including the specific design of the ANN models for particular datasets, which may limit their use in broader populations or different biomechanical contexts. The models might also simplify the complex nature of movements, focusing mainly on vertical and parallel GRF signals and lower body joints, potentially neglecting essential elements, like lateral movements and upper body contributions.