发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对湍流粗粒化建模中未解析尺度反馈难以表示的问题，提出基于分数的随机降阶模型，其平稳分布与数据一致，动力学校准可再现波数壳能量相关性，且校准无需前向积分。
AI 中文摘要
在许多湍流中，关注的量是粗粒化变量，这要么是因为解析细尺度在计算上不可行，要么是因为仅有粗观测可用；在这两种情况下，都需要仅演化这些变量的数据驱动降阶模型。即使控制方程已知，它们在粗变量上的投影也不是封闭的，核心困难在于表示未解析尺度的反馈，使得降阶模型能够再现投影的高分辨率系统的统计和动力学特性。我们通过一个基于分数的框架来解决这个问题，构建了一个准地转湍流的降阶模型，其平稳分布通过构造与从数据中学习到的分布一致，其动力学被校准以再现各个波数壳中能量的有限时间相关性。所得模型以高精度再现了解析流动的平稳统计，且其校准在计算上廉价，因为它不需要对模型进行前向积分。
英文摘要
In many turbulent flows, the quantities of interest are coarse-grained variables, either because resolving the fine scales is computationally prohibitive or because only coarse observations are available; in both cases, data-driven reduced-order models that evolve only these variables are required. Even when the governing equations are known, their projection onto the coarse variables is not closed, and the central difficulty lies in representing the feedback of the unresolved scales so that the reduced model reproduces the statistical and dynamical properties of the projected high-resolution system. We address this problem with a score-based framework, constructing a reduced-order model of quasi-geostrophic turbulence whose stationary distribution coincides by construction with the distribution learned from data and whose dynamics are calibrated to reproduce the finite-time correlations of the energies in individual wavenumber shells. The resulting model reproduces the stationary statistics of the resolved flow with high accuracy, and its calibration is computationally inexpensive because it requires no forward integration of the model.
Comments28 pages, 5 figures
