The interpretation of indirect detection experiments searching for dark matter annihilations requires computationally expensive simulations of cosmic-ray propagation. We present a new method based on Recurrent Neural Networks (RNNs) that significantly accelerates simulations of secondary and dark matter cosmic ray antiprotons. This approach allows for an efficient marginalization over the nuisance parameters of a cosmic ray propagation model in order to perform parameter scans for a wide range of dark matter models. We present resulting constraints using the most recent AMS-02 antiproton data on dark matter WIMP models. The speed-up achieved with our method results in a runtime two orders of magnitude below a conventional MCMC approach, once the neural network has been trained.