  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 using the
kinematics of beta-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 1e-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 beta-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.
