Taking into account the effects of parameter uncertainties in the robot model is crucial to the robustness of motion generation. One approach to address this issue is to compute ‘uncertainty tubes’ enveloping 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 these tubes for complex dynamical systems can be too 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 these uncertainty tubes. We demonstrate that GRUs achieve the best compromise between prediction accuracy, prediction time, and network size compared to basic RNNs and LSTMs, justifying our choice. Finally, we showcase the efficiency of the learning process within a motion planning framework for an aerial vehicle.