  We discuss an approach to probabilistic forecasting based on two chained
machine-learning steps: a dimensional reduction step that learns a reduction
map of predictor information to a low-dimensional space in a manner designed to
preserve information about forecast quantities; and a density estimation step
that uses the probabilistic machine learning technique of normalizing flows to
compute the joint probability density of reduced predictors and forecast
quantities. This joint density is then renormalized to produce the conditional
forecast distribution. In this method, probabilistic calibration testing plays
the role of a regularization procedure, preventing overfitting in the second
step, while effective dimensional reduction from the first step is the source
of forecast sharpness. We verify the method using a 22-year 1-hour cadence time
series of Weather Research and Forecasting (WRF) simulation data of surface
wind on a grid.
