Abstract
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.