Abstract: Systems and methods related to incorporating uncertain inputs into a neural network are described herein. A distribution is obtained and processed by a Reproducing Kernel Hilbert Space (RKHS) module to generate an embedding that represents the distribution. The features of the embedding may correspond to a number of Random Fourier Features (RFFs). The embedding can be added to additional features to form an aggregate input for the neural network. The neural network then processes the aggregate input to generate an output based on, at least in part, the embedding of the distribution. In some embodiments, a simulation can be run to generate a distribution for a feature, where each simulator instance generates a different sample for the feature over a plurality of time steps of the simulation. In some embodiments, the output neural network can be used to control robotic systems, vehicles, or other systems.