Ensemble weather forecasts based on multiple runs of numerical weather
prediction models typically show systematic errors and require post-processing
to obtain reliable forecasts. Accurately modeling multivariate dependencies is
crucial in many practical applications, and various approaches to multivariate
post-processing have been proposed where ensemble predictions are first
post-processed separately in each margin and multivariate dependencies are then
restored via copulas. These two-step methods share common key limitations, in
particular the difficulty to include additional predictors in modeling the
dependencies. We propose a novel multivariate post-processing method based on
generative machine learning to address these challenges. In this new class of
nonparametric data-driven distributional regression models, samples from the
multivariate forecast distribution are directly obtained as output of a
generative neural network. The generative model is trained by optimizing a
proper scoring rule which measures the discrepancy between the generated and
observed data, conditional on exogenous input variables. Our method does not
require parametric assumptions on univariate distributions or multivariate
dependencies and allows for incorporating arbitrary predictors. In two case
studies on multivariate temperature and wind speed forecasting at weather
stations over Germany, our generative model shows significant improvements over
state-of-the-art methods and particularly improves the representation of
spatial dependencies