Physics-Informed Neural Networks for Real-Time Muscle-Tendon Force Estimation From Wearable Sensors

Clinicians currently lack practical tools to quantify muscle-tendon forces outside of research laboratories, limiting load-management decisions during rehabilitation to symptom-based progression. This article presents a physics-informed neural network (PINN) framework that estimates individual muscle-tendon forces from wearable inertial measurement units (IMUs) and pressure-sensitive insoles, without requiring labeled force data or electromyography. The framework combines deep neural networks with differentiable rigid-body and Hill-type muscle models, enforcing torque equilibrium and minimizing activation effort to handle muscle redundancy. Validated on 16 subjects during walking, the framework estimated Achilles tendon forces with nRMSE $= 8.8\pm 1.5\%$ , ${R}^{{2}} = 0.92\pm 0.03$ , matching the performance of supervised methods trained on labeled forces despite using none. Inference times of approximately 7 ms support potential closed-loop biofeedback applications. We further show that the framework can adapt to altered musculoskeletal parameters representing post-rupture Achilles pathology using only physics-based constraints, predicting compensatory recruitment patterns consistent with clinical observations. The proposed approach establishes a computational foundation for translating laboratory-grade biomechanical analysis to wearable systems for continuous rehabilitation monitoring.