发表机构
University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究评估流匹配、DDPM、得分SDE和VAE等深度生成模型在非平稳高斯随机场上的表现，提供综合指标评估均值和协方差结构恢复情况，发现不同模型家族表现各异，还通过ERA5温度异常实验支持DGM对复杂时空数据的验证与开发。
AI 中文摘要
深度生成模型（DGM）广泛用于复杂高维数据，越来越多地应用于空间和时空建模。其生成样本隐含表示学习到的数据分布及相关不确定性。但对于现实世界数据，评估DGM是否学习到潜在过程很困难，因为真实情况未知且评估常仅依赖观测。我们在已知非平稳高斯随机场上评估了代表性DGM，包括流匹配（FM）、DDPM、得分SDE和VAE。本文提供综合指标，以已知样本和固定控制为参考评估对真实均值和协方差结构的恢复情况。所有四个模型都能恢复均值表面，但其协方差恢复在不同模型家族中有所不同：DDPM和得分SDE恢复协方差结构较好，FM呈现轻度衰减的非平稳性和轻微方差不足，VAE难以恢复协方差结构。对ERA5温度异常的实验进一步证明了该框架如何支持DGM对复杂现实世界时空数据的验证和开发。
英文摘要
Deep generative models (DGMs) are widely used for complex high-dimensional data and increasingly applied to spatial and spatio-temporal modeling. Their generated samples implicitly represent the learned data distribution and associated uncertainty. However, for real-world data, assessing whether DGMs have learned the underlying process is difficult because the ground truth is unknown and evaluation often relies on observations alone. We evaluate representative DGMs, flow matching (FM), DDPM, score-SDE, and VAE, on a known non-stationary Gaussian random field. This paper provides comprehensive metrics to assess recovery of the ground-truth mean and covariance structures, with oracle samples and a stationary control as references. All four models recover the mean surface, while their covariance recovery differs across model families: DDPM and score-SDE recover the covariance structure reasonably well, FM exhibits mildly attenuated non-stationarity and slight variance under-dispersion, and VAE has difficulty recovering the covariance structure. An experiment on ERA5 temperature anomalies further demonstrates how the framework can support the validation and development of DGMs for complex real-world spatio-temporal data.
Comments9 pages, 4 figures, 2 tables
