粗略去偏，条件采样：通过最优传输与概率扩散模型进行统计降尺度
Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models
AI总结：
本文提出一种基于最优传输去偏与概率扩散模型条件采样的两阶段非配对统计降尺度框架，在8倍和16倍上采样下从有偏低分辨率数据中准确恢复物理统计量，解决了天气与气候模拟中的关键难题。
摘要：
我们引入了一个使用非配对数据的两阶段概率框架，用于统计降尺度。统计降尺度旨在寻找一个概率映射，将来自有偏粗粒度数值方案的低分辨率数据转换为与高保真方案一致的高分辨率数据。我们的框架通过组合两个变换来解决该问题：（i）通过最优传输映射实现的去偏步骤，以及（ii）通过具有后验条件采样的概率扩散模型实现的上采样步骤。该方法在无需配对数据的情况下刻画了条件分布，并忠实地从有偏样本中恢复相关的物理统计量。我们在一维和二维流体流动问题上展示了所提方法的实用性，这些问题代表了天气和气候数值模拟中存在的核心困难。我们的方法通过将分辨率上采样8倍和16倍，从低分辨率输入生成逼真的高分辨率输出。此外，即使输入和输出的低频内容不匹配，我们的流程也能正确匹配物理量的统计量，而这一关键但难以满足的假设正是当前最先进的替代方法所需要的。本工作的代码可在以下地址获取：https://github.com/google-research/swirl-dynamics/tree/main/swirl_dynamics/projects/probabilistic_diffusion。
英文摘要：
We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to high-resolution data that is consistent with a high-fidelity scheme. Our framework tackles the problem by composing two transformations: (i) a debiasing step via an optimal transport map, and (ii) an upsampling step achieved by a probabilistic diffusion model with a posteriori conditional sampling. This approach characterizes a conditional distribution without needing paired data, and faithfully recovers relevant physical statistics from biased samples. We demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems, which are representative of the core difficulties present in numerical simulations of weather and climate. Our method produces realistic high-resolution outputs from low-resolution inputs, by upsampling resolutions of 8x and 16x. Moreover, our procedure correctly matches the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives. Code for this work is available at: https://github.com/google-research/swirl-dynamics/tree/main/swirl_dynamics/projects/probabilistic_diffusion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
