Load-Decomposition Learning Enhances Ground Reaction Force Estimation Using IMUs

Accurate estimation of ground reaction forces (GRFs) is fundamental to gait analysis and supports functional gait assessment, surgical planning, and rehabilitation. We propose a physics-learning hybrid framework that combines linked-segment dynamics with a bidirectional long short-term memory network to estimate vertical GRFs (vGRFs) from seven inertial measurement units (IMUs). The learning module produces an unconstrained allocation variable that decomposes the physics-derived net force into limb-specific vGRFs. The framework was systematically evaluated against machine learning-based baselines, including MLP, LSTM, BiLSTM, and Transformer variants, using three datasets: two self-collected datasets comprising healthy individuals and individuals with unilateral transtibial amputation, and an independent public biomechanics dataset covering multiple walking speeds, ramps, and stairs. Evaluation included intra-subject, intersubject, cross-population, and between-day evaluations, as well as cross-task transfer. The proposed framework achieved an RMSE of 0.034 BW in intra-subject evaluation and 0.065 BW in inter-subject evaluation, both below the 0.10 BW high-accuracy reference, while maintaining high coefficients of determination (R² = 0.994 and R² = 0.978, respectively). These findings demonstrate that integrating biomechanical structure with data-driven learning can improve vGRF estimation performance in both intra- and inter-subject settings, while showing potential for transfer across populations, measurement sessions, and locomotor tasks. The framework therefore supports further development toward quantitative gait assessment and broader clinical applications.