Variational Methods for Model-based Interacitve Analysis of Flows

本计画旨在对复杂的流动型态，如剪切摩擦、卷曲或漩涡，进行探索性的分析与分类。对于2D和3D中的真实的世界流及其时间演化，完全自动和全局分类是遥不可及的。因此，我们将开发一种流动探索方法，它结合了多尺度变分方法的流型分类与灵活的用户界面的指导。变分函数由保真度项组成，其将所观察到的流局部地与参数化物理或统计学学习模型进行比较，反映图案参数及其形状的概率的先验，以及对用户的指导和偏好进行编码的合适的函数。待开发的分析工具将被应用到由不同类型的图像序列呈现的实验流数据和来自计算流体动力学模拟的流场。用户交互式地选择范围从全球宏观到局部介观流动现象的流动分类的尺度。

This project aims at an explorative analysis and classification of complex flow pattern such as shear friction, curls or vortices. For real world flows in 2D and 3D and their temporal evolution a fully automatic and global classification is far out of reach. Hence, we will develop a flow exploration method which combines a multi-scale variational approach for the classification of flow pattern with a flexible interface for user guidance. The variational functional consists of a fidelity term, which compares the observed flow locally with parametrized physical or statistically learned models, a prior reflecting the probability of the pattern parameters and its shape, and a suitable functional encoding the user’s guidance and preferences. The analysis tool to be developed will be applied to experimental flow data rendered by different types of image sequences and to flow fields from computational fluid dynamics simulation. The user interactively selects the scale for the flow classification ranging from global macroscopic to local mesoscopic flow phenomena.