论文标题

部分可观测时空混沌系统的无模型预测

It's a Wrap! Visualisations that Wrap Around Cylindrical, Toroidal, or Spherical Topologies

论文作者

Chen, Kun-Ting

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key information is hidden, such as geographic paths on the spherical surface being wrapped across the boundaries of the flat map. Similarly, cyclical time-series data has no beginning or end. When such cyclical data is presented on a traditional linear chart, the viewer needs to perceive continuity of the visualisation across the chart's boundaries. Mentally reconnecting the chart across such a boundary may induce additional cognitive load. More complex data such as a network diagram with hundreds or thousands of links between data points leads to a densely connected structure that is even less "flat" and needs to wrap around in multiple dimensions. To improve the usability of these visualisations, this thesis explores a novel class of interactive wrapped data visualisations, i.e., visualisations that wrap around continuously when interactively panned on a two-dimensional projection of surfaces of 3D shapes, specifically, cylinder, torus, or sphere. We start with a systematic exploration of the design space of interactive wrapped visualisations, characterising the visualisations that help people understand the relationship within the data. Subsequently, we investigate a series of wrappable visualisations for cyclical time series, network, and geographic data. We show that these interactive visualisations better preserve the spatial relations in the case of geospatial data, and better reveal the data's underlying structure in the case of abstract data such as networks and cyclical time series. Furthermore, to assist future research and development, we contribute layout algorithms and toolkits to help create pannable wrapped visualisations.

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