Biomechanical analysis and predictions of human movement increasingly depend on computational optimal control methods with musculoskeletal (MSK) models. Several state-of-the-art software frameworks, including OpenSim Moco, PredSim, and the BioMAC-Sim-Toolbox, now enable complex three-dimensional movements to be simulated. However, these existing toolboxes are limited in their compability with GPUs and machine learning frameworks. In the age of AI, we expect to see increased integration of optimal control frameworks and deep learning methods. Examples include learned priors as objectives in optimal control simulations or integrating dynamics constraints from optimal control simulations into physics-informed machine learning frameworks. To meet the evolving demands of MSK optimal control in the era of AI, we introduce biosym, a symbolic optimal control framework based on JAX. The framework exploits vectorized operations or GPU acceleration to perform parallel computations, yielding substantial speedups relative to conventional CPU-based implementations. To test the speed of biosym’s multibody dynamics function, we benchmark it versus the efficient C code implementations in BioMAC-Sim-Toolbox for the constraint function of a 100-node optimal control problem. Here, biosym offers a 2.5x speedup when using a three-dimensional MSK model compared to BioMAC-Sim-Toolbox, while being on par when using a two-dimensional MSK model. A 50-node two-dimensional predictive gait simulation solved in 47 s. The biosym framework has a modular structure that allows for easy modification or replacement of, for example, ground contact or muscle models. Furthermore, biosym’s multibody dynamics functions are differentiable with regard to the MSK model parameters, making it suitable for system identification. Overall, biosym provides a fast, fully differentiable, and modular framework for MSK optimal control. Through easy model customization and seamless integration with machine learning methods, we support emerging hybrid workflows in simulation, system identification, and physics-informed modeling.