  Many real-world processes have complex tail dependence structures that cannot
be characterized using classical Gaussian processes. More flexible spatial
extremes models exhibit appealing extremal dependence properties but are often
exceedingly prohibitive to fit and simulate from in high dimensions. In this
paper, we aim to push the boundaries on computation and modeling of
high-dimensional spatial extremes via integrating a new spatial extremes model
that has flexible and non-stationary dependence properties in the
encoding-decoding structure of a variational autoencoder called the XVAE. The
XVAE can emulate spatial observations and produce outputs that have the same
statistical properties as the inputs, especially in the tail. Our approach also
provides a novel way of making fast inference with complex extreme-value
processes. Through extensive simulation studies, we show that our XVAE is
substantially more time-efficient than traditional Bayesian inference while
outperforming many spatial extremes models with a stationary dependence
structure. Lastly, we analyze a high-resolution satellite-derived dataset of
sea surface temperature in the Red Sea, which includes 30 years of daily
measurements at 16703 grid cells. We demonstrate how to use XVAE to identify
regions susceptible to marine heatwaves under climate change and examine the
spatial and temporal variability of the extremal dependence structure.
