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To diagnose, plan, and treat musculoskeletal pathologies, understanding and reproducing muscle recruitment for complex movements is essential. With muscle activations for movements often being highly redundant, nonlinear, and time dependent, machine learning can provide a solution for their modeling and control for anatomy-specific musculoskeletal simulations. Sophisticated biomechanical simulations often require specialized computational environments, being numerically complex and slow, hindering their integration with typical deep learning frameworks. In this work, a deep reinforcement learning (DRL) based inverse dynamics controller is trained to control muscle activations of a biomechanical model of the human shoulder. In a generalizable end-to-end fashion, muscle activations are learned given current and desired position-velocity pairs. A customized reward functions for trajectory control is introduced, enabling straightforward extension to additional muscles and higher degrees of freedom. Using the biomechanical model, multiple episodes are simulated on a cluster simultaneously using the evolving neural models of the DRL being trained. Results are presented for a single-axis motion control of shoulder abduction for the task of following randomly generated angular trajectories.