Capabilities and limitations of time-lagged autoencoders for slow mode discovery in dynamical systems
Capabilities and limitations of time-lagged autoencoders for slow mode discovery in dynamical systems
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DOI：
10.1063/1.5112048
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发表时间：
2019-08-14
影响因子：
4.4
通讯作者：
Ferguson, Andrew L.
中科院分区：
文献类型：
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作者：
Chen, Wei;Sidky, Hythem;Ferguson, Andrew L.
时滞自编码器（TAEs）已被提出作为一种基于深度学习回归的方法来发现动态系统中的慢模式。然而，对非线性TAEs的严格分析仍然缺乏。在这项工作中，我们通过理论和数值分析讨论了TAEs的能力和局限性。从理论上讲，我们推导了非线性TAE在慢模式发现中的性能界限，并表明通常情况下TAE学习慢模式和最大方差模式的混合。在数值上，我们举例说明了TAEs可以或不能正确识别两个示例系统中的领先最慢模式的情况：二维“华盛顿环城公路”电位和显性水中的丙氨酸二肽分子。我们还将TAE结果与使用无状态可逆变分方法（srv）获得的结果进行了比较，srv是一种基于变分的神经网络方法，用于慢模式发现，并表明srv可以正确地发现TAEs失败的慢模式。由AIP出版社授权出版。
Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical analyses. Theoretically, we derive bounds for nonlinear TAE performance in slow mode discovery and show that in general TAEs learn a mixture of slow and maximum variance modes. Numerically, we illustrate cases where TAEs can and cannot correctly identify the leading slowest mode in two example systems: a 2D "Washington beltway" potential and the alanine dipeptide molecule in explicit water. We also compare the TAE results with those obtained using state-free reversible variational approach for Markov processes nets (SRVs) as a variational-based neural network approach for slow mode discovery and show that SRVs can correctly discover slow modes where TAEs fail. Published under license by AIP Publishing.