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ISOKANN: Invariant subspaces of Koopman operators learned by a neural network.
The Journal of Chemical Physics ( IF 3.1 ) Pub Date : 2020-09-16 , DOI: 10.1063/5.0015132
Robert Julian Rabben 1 , Sourav Ray 1 , Marcus Weber 1
Affiliation  

The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural network.

中文翻译:

ISOKANN:由神经网络学习的Koopman算子的不变子空间。

确定动力学系统中稀有事件发生率的问题是众所周知的,但仍然很难解决。解决该问题的最新尝试利用了这样一个事实,即动态系统可以由线性算子(例如Koopman算子)表示。从数学上讲,罕见事件问题归结为寻找这些Koopman算子的不变子空间的困难ķ。在本文中,我们描述了一种使用人工神经网络学习不变子空间基本函数的方法。
更新日期:2020-09-21
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