基于最优域位移的流集合FTLE计算
FTLE for Flow Ensembles by Optimal Domain Displacement
AI总结：
针对流集合FTLE场中脊线模糊难以区分不确定性来源的问题，提出通过计算最优域位移对齐集合成员脊线的新方法，无需显式几何提取即可在视觉上区分脊线位置、锐度与分离强度的不确定性。
摘要：
FTLE（Finite Time Lyapunov Exponent，有限时间李雅普诺夫指数）计算是拉格朗日流分析的标准方法之一。FTLE场中主要关注的是代表双曲拉格朗日相干结构的脊线。随着积分时间的增加，FTLE脊线趋于变得锐利清晰，脊线的锐度是分离强度的指标。在流中额外考虑不确定性会导致FTLE场中的脊线更加模糊。这种模糊脊线有多种原因：要么脊线的位置不确定，要么脊线的强度不确定，要么不确定性低但分离较弱。现有的不确定FTLE计算方法无法区分脊线中这些不同的不确定性来源。我们引入了一种新方法来定义和可视化流集合的FTLE场。在计算和比较集合成员的FTLE场之前，我们计算域的最优位移，以尽可能使集合成员的脊线相互对齐。我们的方法无需对脊线进行显式的几何提取和对齐。额外考虑这些位移可以在视觉上区分脊线位置、脊线锐度和分离强度的不确定性。我们将该方法应用于几个合成和真实的集合数据集。
英文摘要：
FTLE (Finite Time Lyapunov Exponent) computation is one of the standard approaches to Lagrangian flow analysis. The main features of interest in FTLE fields are ridges that represent hyperbolic Lagrangian Coherent Structures. FTLE ridges tend to become sharp and crisp with increasing integration time, where the sharpness of the ridges is an indicator of the strength of separation. The additional consideration of uncertainty in flows leads to more blurred ridges in the FTLE fields. There are multiple causes for such blurred ridges: either the locations of the ridges are uncertain, or the strength of the ridges is uncertain, or there is low uncertainty but weak separation. Existing approaches for uncertain FTLE computation are unable to distinguish these different sources of uncertainty in the ridges. We introduce a new approach to define and visualize FTLE fields for flow ensembles. Before computing and comparing FTLE fields for the ensemble members, we compute optimal displacements of the domains to mutually align the ridges of the ensemble members as much as possible. We do so in a way that an explicit geometry extraction and alignment of the ridges is not necessary. The additional consideration of these displacements allows for a visual distinction between uncertainty in ridge location, ridge sharpness, and separation strength. We apply the approach to several synthetic and real ensemble data sets.
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