用扩散模型修复湍流中漂浮物的缺失轨迹数据，效果优于传统方法。
Stochastic Reconstruction of Gappy Lagrangian Turbulent Signals by Conditional Diffusion Models
- 基于条件扩散模型，从不完整轨迹中随机重建速度与位置。
- 重建结果保留非高斯、间歇性强的多尺度统计特征，准确率更高。
- 适用于大气气球、海洋漂流器等复杂场景，可扩展至粒子扩散等问题。
我们提出一种随机方法，用于重建小物体在广泛时空尺度的湍流中被动输运时缺失的空间和速度数据，例如大气中的小型气球或海洋中的漂流器。该方法采用最近提出的条件生成式扩散模型这一数据驱动机器学习技术。针对两类典型问题进行求解：三维各向同性均匀湍流中的追踪质点，以及由美国国家海洋和大气管理局（NOAA）资助的全球漂流器计划提供的二维轨迹。结果显示，两种情况下，该方法均能重建出具有显著尺度相关特性的速度信号，这些特性高度非高斯且具有间歇性。方法的一大优势在于对数据缺失的位置与形状具有灵活性，并能自然利用不同分量间的相关性，从而在逐点重建与统计表达能力上均优于高斯过程回归。该方法在多种其他拉格朗日问题中也展现出应用前景，包括湍流中的多粒子分散、天体物理与等离子体物理中的带电粒子动力学，以及行人运动建模。
原文摘要 · Abstract (English)
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the atmosphere or drifters in the ocean. Our approach makes use of conditional generative diffusion models, a recently proposed data-driven machine learning technique. We solve the problem for two paradigmatic open problems, the case of 3D tracers in homogeneous and isotropic turbulence, and 2D trajectories from the NOAA-funded Global Drifter Program. We show that for both cases, our method is able to reconstruct velocity signals retaining non-trivial scale-by-scale properties that are highly non-Gaussian and intermittent. A key feature of our method is its flexibility in dealing with the location and shape of data gaps, as well as its ability to naturally exploit correlations between different components, leading to superior accuracy, with respect to Gaussian process regressions, for both pointwise reconstruction and statistical expressivity. Our method shows promising applications also to a wide range of other Lagrangian problems, including multi-particle dispersion in turbulence, dynamics of charged particles in astrophysics and plasma physics, and pedestrian dynamics.
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