In this paper, forward/inverse dynamics of a continuum robotic arm is developed using a data-driven approach, which could tackle uncertainties and extreme nonlinearities to obtain reliable solutions. By establishing a direct mapping between the actuator and task spaces, the unnecessary mappings of actuator-to-configuration then configuration-to-task are eliminated, to reduce extra computational cost. The proposed approach is validated through simulation (based on Cosserat rod theory) and experimental tests on RoboArm. Next, path tracking in the presence/absence of obstacles as well as load carrying maneuver are investigated. Finally, the obtained results concerning repeatability, scalability, and disturbance rejection performance of the approach are discussed.