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.

翻译：许多现实世界过程具有复杂的尾部依赖结构，无法通过经典高斯过程进行刻画。更具灵活性的空间极值模型展现出吸引人的极值依赖特性，但在高维情形下的拟合与模拟往往计算代价极高。本文旨在通过将一种具有灵活非平稳依赖特性的新型空间极值模型——XVAE——整合到变分自编码器的编码-解码结构中，以突破高维空间极值计算与建模的边界。XVAE能够模拟空间观测数据，并生成与输入数据具有相同统计特性（尤其是尾部特性）的输出。该方法还为复杂极值过程的快速推断提供了新途径。通过大量模拟研究，我们证明XVAE在显著优于许多具有平稳依赖结构的空间极值模型的同时，其计算时效性远高于传统贝叶斯推断方法。最后，我们分析了红海区域一个包含16703个网格点、历时30年的日尺度海表温度高分辨率卫星数据集，展示了如何利用XVAE识别气候变化下易受海洋热浪影响的区域，并检验极值依赖结构的时空变异性。