Physics-informed Deep Learning for Muscle Force Prediction with Unlabeled sEMG Signals

TL;DR

This work introduces a physics-informed neural network (PINN) that predicts muscle forces from unlabeled sEMG while simultaneously identifying subject-specific Hill muscle parameters. The approach embeds Hill-based forward dynamics into a residual loss and adds an implicit loss aligning neural outputs with Hill-model forces, enabling training without labeled EMG. Across a wrist-extension dataset of six subjects, the method achieves RMSE and $R^{2}$ comparable to or better than supervised baselines and demonstrates robust parameter identification within physiological ranges. The contributions offer real-time-capable, label-free muscle force estimation with personalized muscle-tendon parameter identification, leveraging OpenSim-derived dynamics for physical plausibility and practical biomechanical insight.

Abstract

Computational biomechanical analysis plays a pivotal role in understanding and improving human movements and physical functions. Although physics-based modeling methods can interpret the dynamic interaction between the neural drive to muscle dynamics and joint kinematics, they suffer from high computational latency. In recent years, data-driven methods have emerged as a promising alternative due to their fast execution speed, but label information is still required during training, which is not easy to acquire in practice. To tackle these issues, this paper presents a novel physics-informed deep learning method to predict muscle forces without any label information during model training. In addition, the proposed method could also identify personalized muscle-tendon parameters. To achieve this, the Hill muscle model-based forward dynamics is embedded into the deep neural network as the additional loss to further regulate the behavior of the deep neural network. Experimental validations on the wrist joint from six healthy subjects are performed, and a fully connected neural network (FNN) is selected to implement the proposed method. The predicted results of muscle forces show comparable or even lower root mean square error (RMSE) and higher coefficient of determination compared with baseline methods, which have to use the labeled surface electromyography (sEMG) signals, and it can also identify muscle-tendon parameters accurately, demonstrating the effectiveness of the proposed physics-informed deep learning method.

Figures (8)

• Figure 1: Main framework of the proposed method. Inputs to the $\lambda$-parameterized deep neural network are sEMG measurements $e_t = (e_{t,1}, e_{t,2},\cdots, e_{t, N})$ and time $t$, while outputs are joint movements $q_t$ and muscle forces $F_t = (F_{t,1}, F_{t,2},\cdots, F_{t, N})$, where $N$ is the total number of muscles at the joint of interest. For the subject-specific Hill-muscle-based forward dynamics model, $\kappa = (A, \kappa_1, \kappa_2,\cdots, \kappa_N)$, where $n = (1,2,\cdots, N)$, $\kappa_n$ is the muscle-tendon parameters of the $n$th muscle, and $A$ is the EMG-to-activation coefficient.
• Figure 2: Illustration of different loss terms over the number of iterations.
• Figure 3: Evolution of the maximum isometric muscle force $F_0^m$ and the optimal muscle fiber length $l_0^m$ identified of the specific subject during the training of the proposed method. The estimations are all within the physiological range and possess physiological consistency.
• Figure 4: Representative results of the wrist case through the proposed method. The predicted outputs include FCR muscle force, FCU muscle force, ECRL muscle force, ECRB muscle force, and ECU muscle force.
• Figure 5: Average RMSEs of the included muscle forces across all the subjects (wrist case).