Sequential networks for cosmic ray simulations

A hybrid model of generating cosmic ray showers based on neural networks is presented. We show that the neural network learns the solution to the governing cascade equation in one dimension. We then use the neural network to generate the energy spectra at every height slice. Pitfalls of training to generate a single height slice is discussed, and we present a sequential model which can generate the entire shower from an initial table. Errors associated with the model and the potential to generate the full three dimensional distribution of the shower is discussed.