The accurate prediction of rainfall, and in particular rainfall
extremes, remains challenging for numerical weather prediction models.
This can be attributed to subgrid-scale parameterizations of processes
that play a crucial role in the multi-scale dynamics, as well as the
strongly intermittent nature and the highly skewed, non-Gaussian
distribution of rainfall. Here we show that a specific type of deep
neural networks can learn rainfall extremes from a numerical weather
prediction ensemble. A frequency-based weighting of the loss function is
proposed to enable the learning of extreme values in the distributions'
tails. We apply our framework in a post-processing step to correct for
errors in the model-predicted rainfall. Our method yields a much more
accurate representation of relative rainfall frequencies and improves
the forecast skill of extremes by factors ranging from two to above six,
depending on the event magnitude.