不变动力学结构与不确定性量化之间的桥梁
A bridge between invariant dynamical structures and uncertainty quantification
摘要：
我们开发了一个新的量化器，向前的时间不确定性的轨迹，从数据集生成的模型的解决方案。我们的不确定性量词定义在相空间中的轨迹发展，我们表明，它有一个丰富的结构，直接关系到相空间结构的动力系统理论，如双曲轨迹和稳定和非稳定流形。我们将我们的方法应用于海洋数据集，以及确定性动力系统理论的标准基准模型。我们的研究结果的一个重要应用是，它们允许从不同的海洋数据集描述的运输性能的定量比较。这是特别有趣的今天，当各种各样的来源，因为我们的方法提供了评估这些数据集在各种情况下的有效使用的途径。
英文摘要：
We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it has a rich structure that is directly related to phase space structures from dynamical systems theory, such as hyperbolic trajectories and their stable and unstable manifolds. We apply our approach to an ocean data set, as well as standard benchmark models from deterministic dynamical systems theory. A significant application of our results, is that they allow a quantitative comparison of the transport performance described from different ocean data sets. This is particularly interesting nowadays when a wide variety of sources are available, since our methodology provides avenues for assessing the effective use of these data sets in a variety of situations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
