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 $\mathcal{K}$. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural network.

中文翻译：

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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$\mathcal{ķ}$。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。