Multi-Joint Physics-Informed Deep Learning Framework for Time-Efficient Inverse Dynamics

TL;DR

This work tackles the problem of fast, physiologically consistent estimation of muscle activations and forces across multi-joint systems from kinematics. It introduces PI-MJCA-BiGRU, a physics-informed deep learning framework with a novel Multi-Joint Cross-Attention (MJCA) module and Bidirectional GRUs to capture inter-joint coordination and temporal dynamics, while embedding MSK dynamics, performance criteria, and boundary constraints into the loss function to enable label-free training. Across two datasets, the method achieves performance comparable to supervised baselines, demonstrating strong activation and force tracking with real-time inference, and ablation studies confirm the MJCA module and loss components are critical for performance. The approach offers a practical, scalable alternative to traditional dynamic optimization, with potential applications in clinical gait analysis, rehabilitation, and real-time assistive-device control, especially in resource-limited settings where labeled MSK data are scarce.

Abstract

Time-efficient estimation of muscle activations and forces across multi-joint systems is critical for clinical assessment and assistive device control. However, conventional approaches are computationally expensive and lack a high-quality labeled dataset for multi-joint applications. To address these challenges, we propose a physics-informed deep learning framework that estimates muscle activations and forces directly from kinematics. The framework employs a novel Multi-Joint Cross-Attention (MJCA) module with Bidirectional Gated Recurrent Unit (BiGRU) layers to capture inter-joint coordination, enabling each joint to adaptively integrate motion information from others. By embedding multi-joint dynamics, inter-joint coupling, and external force interactions into the loss function, our Physics-Informed MJCA-BiGRU (PI-MJCA-BiGRU) delivers physiologically consistent predictions without labeled data while enabling time-efficient inference. Experimental validation on two datasets demonstrates that PI-MJCA-BiGRU achieves performance comparable to conventional supervised methods without requiring ground-truth labels, while the MJCA module significantly enhances inter-joint coordination modeling compared to other baseline architectures.

Figures (9)

• Figure 1: Overview of the proposed PI-MJCA-BiGRU framework.
• Figure 2: Planar model of the lower limb during the stance and swing phases of gait with 3 joints (Hip, knee, ankle).
• Figure 3: Subject walking on an instrumented platform with reflective markers for motion capture and ground reaction force measurement.
• Figure 4: Representative results of the gait cycle case through our method. The predicted outputs include the muscle activations and muscle forces of the ten muscles. The results show that PI-MJCA-BiGRU achieves comparable tracking accuracy to supervised MJCA-BiGRU, closely matching the ground truth.
• Figure 5: Performance comparison of physics-informed (PI-MJCA-BiGRU) and supervised (MJCA-BiGRU) training approaches for muscle activations and forces prediction on the benchmark dataset. Results are presented for activation R$^2$ (A), force R$^2$ (B), activation NRMSE (C), and force NRMSE (D) across ten muscles. "$\blacktriangle$" indicates outliers in the distribution. Overall, PI-MJCA-BiGRU achieves accuracy comparable to supervised MJCA-BiGRU training.