Toward Robust and Efficient Musculoskeletal Modeling Using Distributed Physics-Informed Deep Learning

This article develops a novel distributed framework based on physics-informed deep learning for robust and efficient musculoskeletal modeling in nonstationary scenarios, which could simultaneously strengthen the robustness and generalization, and reduce the time cost of model training. Without loss of generality, we utilize surface electromyogram (sEMG)-based muscle forces and joint angle prediction as an example to demonstrate the proposed distributed framework. Specifically, the whole collected sEMG data are first divided into several subdomains, and then a corresponding number of physics-informed deep-learning-based local models is built using these grouped data. Finally, all the local models are integrated into a global model to obtain the final predictions. Moreover, weights inversely proportional to the training errors of local models are added to the corresponding local models to reduce and control the negative effects of unknown factors. Different from existing distributed modeling methods, the proposed distributed framework embeds the prior physics knowledge, i.e., the equation of motion, into local models to regularize loss functions of deep neural networks, it thus could overcome limitations of the conventional data-driven and physics-based musculoskeletal models while preserving their advantages. The local-global distributed modeling mechanism could locally achieve better representation for subdomains while preserving the global performance and reducing the computational cost and memory requirements. In addition, the embedded prior physics knowledge enables local models to reflect physical or physiological mechanisms during the training process, which could alleviate the overfitting problem and reduce the need for the number of training data, thus the global model is more robust and better generalizes to the unseen data. Comprehensive experiments on six healthy subjects demonstrate the feasibility and effectiveness of the proposed distributed framework.