Fast and precise model calculation for KATRIN using a neural network

We present a fast and precise method to approximate the physics model of the Karlsruhe Tritium Neutrino (KATRIN) experiment using a neural network. KATRIN is designed to measure the effective electron anti-neutrino mass m_ν using the kinematics of β -decay with a sensitivity of 200 meV at 90% confidence level. To achieve this goal, a highly accurate model prediction with relative errors below the 10 ^{- 4}-level is required. Using the regular numerical model for the analysis of the final KATRIN dataset is computationally extremely costly or requires approximations to decrease the computation time. Our solution to reduce the computational requirements is to train a neural network to learn the predicted β -spectrum and its dependence on all relevant input parameters. This results in a speed-up of the calculation by about three orders of magnitude, while meeting the stringent accuracy requirements of KATRIN.