发表机构
University of Tennessee, Knoxville; University of Chicago; UChicago Data Science Institute（田纳西大学诺克斯维尔分校; 芝加哥大学; 芝加哥大学数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出结合时间先验、生成校正与多分辨率重建的Iterative Refinement（IR）框架，在多尺度物理系统超分辨数据同化任务中，于Kraichnan湍流基准上取得优于多种对比方法的性能。
AI 中文摘要
从稀疏的低分辨率观测中恢复高分辨率状态是科学机器学习与数据同化领域的核心挑战。经典数据同化通过预报-分析循环利用时间信息，但通常需要反复访问昂贵的高分辨率预报模型；生成式超分辨率可从粗观测中恢复未解析结构，但常被用作单次映射，未充分利用过去状态的约束。我们提出Iterative Refinement（IR，迭代精化），一种结合上述视角的学习型数据同化框架。IR不执行单次从粗到精的重建，而是将任务分解为多分辨率层级上的逐分辨率预报-分析操作：在每个阶段，带有分辨率相关谱模式切片的共享神经算子提供动态先验，而共享条件扩散校正器利用当前较粗分辨率状态，在更精细分辨率生成精化后验。我们在一维随机强迫Burgers动力学与二维Kraichnan湍流上评估IR：在具有挑战性的256×256 Krachnan基准测试中，IR的RMSE为0.184、SSIM为0.836，优于谱上采样、单次扩散超分辨率、增强型深度超分辨率及自回归预报器；在约束更严格的Burgers测试平台上，IR仍与取得最低RMSE的单次扩散方法具有竞争力。这些结果表明，单次生成式重建在简单场景中有效，而分层预报-分析精化在强多尺度与欠定场景中更具优势。总体而言，IR将时间先验、生成校正与多分辨率重建相结合，用于复杂物理系统的学习型数据同化。
英文摘要
Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation. Classical data assimilation exploits temporal information through forecast-analysis cycles, but often requires repeated access to expensive high-resolution forecast models. Generative super-resolution can recover unresolved structure from coarse observations, but is commonly used as a one-shot mapping that does not fully exploit constraints from past states. We introduce Iterative Refinement (IR), a learned data assimilation framework that combines these perspectives. Instead of performing a single coarse-to-fine reconstruction, IR decomposes the task into resolution-wise forecast-analysis operations across a multiresolution hierarchy. At each stage, a shared neural operator with resolution-dependent spectral mode slicing provides a dynamical prior, while a shared conditional diffusion corrector uses the current coarser-resolution state to produce a refined posterior at the next finer resolution. We evaluate IR on one-dimensional stochastically forced Burgers dynamics and two-dimensional Kraichnan turbulence. On the challenging 256x256 Kraichnan benchmark, IR achieves an RMSE of 0.184 and an SSIM of 0.836, outperforming spectral upsampling, one-shot diffusion super-resolution, enhanced deep super-resolution, and an autoregressive forecaster. On the more constrained Burgers testbed, IR remains competitive with one-shot diffusion, which achieves the lowest RMSE. These results show that one-shot generative reconstruction can be effective for simpler settings, while hierarchical forecast-analysis refinement becomes advantageous in strongly multiscale and underdetermined regimes. Overall, IR combines temporal priors, generative correction, and multiresolution reconstruction for learned data assimilation in complex physical systems.
