Zuse Institute Berlin (ZIB), Takustr. 7, 14195 Berlin, Germany.
J Chem Phys. 2020 Sep 21;153(11):114109. doi: 10.1063/5.0015132.
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.
动态系统中稀有事件的速率确定问题是一个众所周知但仍难以解决的问题。最近，人们试图通过利用动态系统可以用线性算子表示的事实来克服这个问题，例如 Koopman 算子。从数学上讲，稀有事件问题归结为找到这些 Koopman 算子 K 的不变子空间的困难。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函数的方法。
