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 develop a new spatial extremes model that has flexible and non-stationary dependence properties, and we integrate it in the encoding-decoding structure of a variational autoencoder (XVAE), whose parameters are estimated via variational Bayes combined with deep learning. The XVAE can be used as a spatio-temporal emulator that characterizes the distribution of potential mechanistic model output states and produces outputs that have the same statistical properties as the inputs, especially in the tail. As an aside, 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 also outperforming many spatial extremes models with a stationary dependence structure. To further demonstrate the computational power of the XVAE, 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 find that the extremal dependence strength is weaker in the interior of Red Sea and it has decreased slightly over time.

翻译：许多真实世界过程具有复杂的尾部依赖结构，无法用经典高斯过程刻画。更灵活的空间极值模型展现出吸引人的极值依赖特性，但在高维情况下通常难以拟合与模拟。本文提出一种具有灵活非平稳依赖特性的新型空间极值模型，并将其整合进变分自编码器（XVAE）的编码-解码结构中，模型参数通过变分贝叶斯与深度学习联合估计。XVAE可作为时空模拟器，刻画潜在机理模型输出状态分布，并生成与输入具有相同统计特性（尤其是尾部特性）的输出。此外，我们的方法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在时间效率上显著优于传统贝叶斯推断，同时超越众多具有平稳依赖结构的空间极值模型。为进一步展示XVAE的计算能力，我们分析了红海海表温度的高分辨率卫星遥感数据集（包含30年、16703个网格点的日观测数据），发现红海内部极值依赖强度较弱，且随时间略有下降。