  When extreme weather events affect large areas, their regional to
sub-continental spatial scale is important for their impacts. We propose a
novel machine learning (ML) framework that integrates spatial extreme-value
theory to model weather extremes and to quantify probabilities associated with
the occurrence, intensity, and spatial extent of these events. Our approach
employs new loss functions adapted to extreme values, enabling our model to
prioritize the tail rather than the bulk of the data distribution. Applied to a
case study of Western European summertime heat extremes, we use daily 500-hPa
geopotential height fields and local soil moisture as predictors to capture the
complex interplay between local and remote physical processes. Our generative
model reveals the importance of individual circulation features in determining
different facets of heat extremes, thereby enriching our process understanding
from a data-driven perspective. The occurrence, intensity, and spatial extent
of heat extremes are sensitive to the relative position of upper-level ridges
and troughs that are part of a large-scale wave pattern. Our approach is able
to extrapolate beyond the range of the data to make risk-related probabilistic
statements. It applies more generally to other weather extremes and offers an
attractive alternative to traditional physical and ML-based techniques that
focus less on the extremal aspects of weather data.
