In the context of generating robust robot motions, it is crucial to consider the effects of parameter uncertainties on the robot model. One approach to address this challenge is to compute ’uncertainty tubes’ that envelop the robot state for any combination of parameters within a given range, and to use these tubes to robustly check for collisions within a motion planning algorithm. However, computing them directly can be computationally expensive due to the need to solve and integrate potentially numerous nonlinear ordinary differential equations (ODEs) associated with robot dynamics. To overcome this limitation, we propose a GRU-based architecture that provides fast and accurate estimation of the uncertainty tubes. We demonstrate that GRUs achieve the best compromise between prediction accuracy, prediction time, and network size compared to RNNs and LSTMs, justifying our choice. Finally, we showcase the efficiency of the learning process within a motion planning framework for an aerial vehicle.