Blind source separation (BSS) algorithms, such as gradient convolution kernel compensation (gCKC), can efficiently and accurately decompose high-density surface electromyography (HD-sEMG) signals into constituent motor unit (MU) action potential trains. Once the separation matrix is blindly estimated on a signal interval, it is also possible to apply the same matrix to subsequent signal segments. Nonetheless, the trained separation matrices are sub-optimal in noisy conditions and require that incoming data undergo computationally expensive whitening. One unexplored alternative is to instead use the paired HD-sEMG signal and BSS output to train a model to predict MU activations within a supervised learning framework. A gated recurrent unit (GRU) network was trained to decompose both simulated and experimental unwhitened HD-sEMG signal using the output of the gCKC algorithm. The results on the experimental data were validated by comparison with the decomposition of concurrently recorded intramuscular EMG signals. The GRU network outperformed gCKC at low signal-to-noise ratios, proving superior performance in generalising to new data. Using 12 seconds of experimental data per recording, the GRU performed similarly to gCKC, at rates of agreement of 92.5% (84.5%-97.5%) and 94.9% (88.8%-100.0%) respectively for GRU and gCKC against matched intramuscular sources.