标题： 通过生成模型进行高维分布匹配的统计降尺度 显示英文标题

标题： Statistical Downscaling via High-Dimensional Distribution Matching with Generative Models

摘要： 统计降尺度是气候建模中用于提高气候模拟分辨率的技术。 高分辨率的气候信息对于各种高影响应用至关重要，包括自然灾害风险评估。 然而，在高分辨率下模拟气候是难以处理的。 因此，通常在粗分辨率下进行气候模拟，然后将其降尺度到所需的分辨率。 现有的降尺度技术要么是计算成本高的基于模拟的方法，要么是准确性或应用特异性有限的统计方法。 我们引入了生成偏差校正和超分辨率（GenBCSR），这是一种两阶段的概率框架，用于统计降尺度，克服了之前方法的局限性。 GenBCSR采用两种变换来匹配不同分辨率下的高维分布：(i) 第一阶段，偏差校正，将粗分辨率下的分布对齐，(ii) 第二阶段，统计超分辨率，通过引入细粒度细节来提升校正后的粗分辨率分布。 每个阶段都由最先进的生成模型实现，从而为广泛研究的分布匹配问题提供了一个高效且有效的计算流程。 通过将降尺度问题表述为分布匹配，GenBCSR放松了监督学习的约束，监督学习要求样本对齐。 尽管不需要这种对应关系，我们证明GenBCSR在关键影响变量的预测准确性方面超过了标准方法，特别是在预测由相互作用变量组成的综合指数的尾部（99%分位数）时，实现了4到5倍的误差减少。 显示英文摘要

摘要： Statistical downscaling is a technique used in climate modeling to increase the resolution of climate simulations. High-resolution climate information is essential for various high-impact applications, including natural hazard risk assessment. However, simulating climate at high resolution is intractable. Thus, climate simulations are often conducted at a coarse scale and then downscaled to the desired resolution. Existing downscaling techniques are either simulation-based methods with high computational costs, or statistical approaches with limitations in accuracy or application specificity. We introduce Generative Bias Correction and Super-Resolution (GenBCSR), a two-stage probabilistic framework for statistical downscaling that overcomes the limitations of previous methods. GenBCSR employs two transformations to match high-dimensional distributions at different resolutions: (i) the first stage, bias correction, aligns the distributions at coarse scale, (ii) the second stage, statistical super-resolution, lifts the corrected coarse distribution by introducing fine-grained details. Each stage is instantiated by a state-of-the-art generative model, resulting in an efficient and effective computational pipeline for the well-studied distribution matching problem. By framing the downscaling problem as distribution matching, GenBCSR relaxes the constraints of supervised learning, which requires samples to be aligned. Despite not requiring such correspondence, we show that GenBCSR surpasses standard approaches in predictive accuracy of critical impact variables, particularly in predicting the tails (99% percentile) of composite indexes composed of interacting variables, achieving up to 4-5 folds of error reduction.