  This work presents a multi-resolution physics-informed recurrent neural
network (MR PI-RNN), for simultaneous prediction of musculoskeletal (MSK)
motion and parameter identification of the MSK systems. The MSK application was
selected as the model problem due to its challenging nature in mapping the
high-frequency surface electromyography (sEMG) signals to the low-frequency
body joint motion controlled by the MSK and muscle contraction dynamics. The
proposed method utilizes the fast wavelet transform to decompose the mixed
frequency input sEMG and output joint motion signals into nested
multi-resolution signals. The prediction model is subsequently trained on
coarser-scale input-output signals using a gated recurrent unit (GRU), and then
the trained parameters are transferred to the next level of training with
finer-scale signals. These training processes are repeated recursively under a
transfer-learning fashion until the full-scale training (i.e., with unfiltered
signals) is achieved, while satisfying the underlying dynamic equilibrium.
Numerical examples on recorded subject data demonstrate the effectiveness of
the proposed framework in generating a physics-informed forward-dynamics
surrogate, which yields higher accuracy in motion predictions of elbow
flexion-extension of an MSK system compared to the case with single-scale
training. The framework is also capable of identifying muscle parameters that
are physiologically consistent with the subject's kinematics data.
