慢时标动力学的稀疏辨识
Sparse Identification of Slow Timescale Dynamics
摘要：
在多个不同的时间尺度上演化的多尺度现象在整个科学中普遍存在。经常出现的情况是，持续的和近似周期的快尺度的控制方程是规定的，而紧急慢尺度演化是未知的。然而，在实践中，粗粒度的、慢尺度的动力学往往是最有兴趣的。在这项工作中，我们提出了一个准确和有效的方法提取慢时标动态信号表现出多个时间尺度，服从平均。该方法依赖于跟踪信号在均匀间隔的时间间隔与长度给定的快速时标，这是发现使用聚类技术结合动态模式分解的周期。然后使用稀疏回归技术来发现描述从一个数据点到下一个数据点的迭代的映射。我们发现，对于足够不同的时间尺度，这个发现的映射可以用来发现连续时间缓慢的动态，从而提供了一种新的工具，用于提取多个时间尺度上的动态。
英文摘要：
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the emergent slow scale evolution is unknown. Yet the course-grained, slow scale dynamics is often of greatest interest in practice. In this work we present an accurate and efficient method for extracting the slow timescale dynamics from signals exhibiting multiple timescales that are amenable to averaging. The method relies on tracking the signal at evenly-spaced intervals with length given by the period of the fast timescale, which is discovered using clustering techniques in conjunction with the dynamic mode decomposition. Sparse regression techniques are then used to discover a mapping which describes iterations from one data point to the next. We show that for sufficiently disparate timescales this discovered mapping can be used to discover the continuous-time slow dynamics, thus providing a novel tool for extracting dynamics on multiple timescales.
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