The most robust representations of flow trajectories are Lagrangian coherent structures
The most robust representations of flow trajectories are Lagrangian coherent structures
复制标题
流动轨迹最稳健的表示是拉格朗日相干结构
DOI：
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发表时间：
2021
影响因子：
3.7
通讯作者：
D. Richter
中科院分区：
文献类型：
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作者：
Theodore MacMillan;D. Richter
摘要什么是最稳健的方式来传达流轨迹？为了回答这个问题，我们使用两个神经网络分别解构（编码器）和重建（解码器）轨迹，其中信息通过称为自动编码器的设置中的低维潜在空间在两个网络之间传递。为了确保它们的通信是鲁棒的，我们在通过这个潜在空间的编码信息中添加噪声。在低噪声限制下，潜在空间结构本质上是非空间的，类似于主成分分析（PCA）的模式。然而，随着信噪比的降低，我们发现拉格朗日相干结构（LCS）作为最紧凑的表示，仍然允许解码器准确地重建轨迹。这种关系为PCA和LCS分析提供了更高的可解释性，并有助于弥合两种流量分析方法之间的差距。
Abstract What is the most robust way to communicate flow trajectories? To answer this question, we employ two neural networks to respectively deconstruct (the encoder) and reconstruct (the decoder) trajectories, where information is passed between the two networks through a low-dimensional latent space in a set-up known as an autoencoder. To ensure that their communications are robust, we add noise to the coded information passed through this latent space. In the low-noise limit the latent space structures are non-spatial in nature, resembling modes of a principle component analysis (PCA). However, as the signal-to-noise ratio is decreased, we uncover Lagrangian coherent structures (LCS) as the most compact representations which still allow the decoder to accurately reconstruct trajectories. This relationship offers increased interpretability to both PCA and LCS analysis, and helps to bridge the gap between two methods of flow analysis.