Knowledge-Based Deep Learning for Time-Efficient Inverse Dynamics

TL;DR

This work tackles the challenge of time-consuming inverse dynamics for estimating muscle activations and forces from joint kinematics by proposing a knowledge-based deep learning framework. It uses a BiGRU backbone to map $(q_t,\dot{q}_t,\ddot{q}_t)$ to $(\hat{a}_t,\hat{F}_t)$ while training with a physics-informed loss $L_{total}=L_m+L_f+\omega\,(L_p+L_b)$, eliminating the need for labeled data. On knee bending and elbow FE benchmarks, the method achieves average $R^2$ values around $0.945$ for activation and $0.941$ for force, with BiGRU outperforming other backbones and attaining competitive performance to supervised approaches but with improved stability. The approach enables fast, non-invasive estimation suitable for neuro-rehabilitation and assistive device applications, by tightly integrating forward dynamics and inverse dynamics criteria into learning.

Abstract

Accurate understanding of muscle activation and muscle forces plays an essential role in neuro-rehabilitation and musculoskeletal disorder treatments. Computational musculoskeletal modeling has been widely used as a powerful non-invasive tool to estimate them through inverse dynamics using static optimization, but the inherent computational complexity results in time-consuming analysis. In this paper, we propose a knowledge-based deep learning framework for time-efficient inverse dynamic analysis, which can predict muscle activation and muscle forces from joint kinematic data directly while not requiring any label information during model training. The Bidirectional Gated Recurrent Unit (BiGRU) neural network is selected as the backbone of our model due to its proficient handling of time-series data. Prior physical knowledge from forward dynamics and pre-selected inverse dynamics based physiological criteria are integrated into the loss function to guide the training of neural networks. Experimental validations on two datasets, including one benchmark upper limb movement dataset and one self-collected lower limb movement dataset from six healthy subjects, are performed. The experimental results have shown that the selected BiGRU architecture outperforms other neural network models when trained using our specifically designed loss function, which illustrates the effectiveness and robustness of the proposed framework.

Figures (8)

• Figure 1: The main framework of the proposed knowledge-based deep learning framework. Inputs to the neural network comprise joint kinematic data (angles, angular velocities, and angular accelerations), while outputs are muscle activations and forces for the modeled muscles. The total loss, incorporating prior knowledge from MSK modeling, guides the network training to ensure physiologically consistent predictions.
• Figure 2: Representative results of the knee bending case through the proposed method. The predicted outputs include the muscle activations and muscle forces of the five main Muscles (BFS, BFL, SEMT, MG, LG).
• Figure 3: Representative results of the elbow FE case through the proposed method. The predicted outputs include the muscle activations and muscle forces of the five main Muscles (TRIl, TRIm, TRIlat, BICl, BICs).
• Figure 4: Comparative analysis of average $R^2$ values across subjects using different neural network architectures for two datasets (Knee and Elbow). Results are presented for knee dataset (a-b) and elbow dataset (c-d), showing muscle activation prediction (a,c) and force prediction (b,d). "$\triangledown$" denotes the mean $R^2$ across six subjects, while "$\bullet$" represents individual $R^2$ values for each subject (rounded to two decimal places).
• Figure 5: Comparative analysis of average RMSEs across subjects using different neural network architectures for two datasets (Knee and Elbow). Results from knee dataset (a-b) and elbow dataset (c-d) show muscle activation prediction (a,c) and force prediction (b,d).