论文标题
时间前向后的一致性，而不是残余误差，可以测量扩展动态模式分解的预测准确性
Temporal Forward-Backward Consistency, Not Residual Error, Measures the Prediction Accuracy of Extended Dynamic Mode Decomposition
论文作者
论文摘要
扩展动态模式分解（EDMD）是一种流行的数据驱动方法，可近似Koopman操作员对函数字典跨越线性函数空间的作用。 EDMD模型的准确性在很大程度上取决于特定词典的跨度的质量，特别是在Koopman操作员下与不变的距离有多近。出于观察到的观察，即EDMD的残余误差通常用于词典学习，并没有编码功能空间的质量，并且对基础的选择很敏感，我们介绍了一致性索引的新颖概念。我们表明，该措施基于及时使用EDMD，享有许多理想的品质，使其适合于数据驱动的动态系统建模：它可以衡量功能空间的质量，它可以在基础上进行封闭形式计算，并从数据的选择下计算，并为所有功能的相对平均均值误差提供了整个功能的相对均值均值，该功能是所有功能的相对均值。
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on the quality of the particular dictionary's span, specifically on how close it is to being invariant under the Koopman operator. Motivated by the observation that the residual error of EDMD, typically used for dictionary learning, does not encode the quality of the function space and is sensitive to the choice of basis, we introduce the novel concept of consistency index. We show that this measure, based on using EDMD forward and backward in time, enjoys a number of desirable qualities that make it suitable for data-driven modeling of dynamical systems: it measures the quality of the function space, it is invariant under the choice of basis, can be computed in closed form from the data, and provides a tight upper-bound for the relative root mean square error of all function predictions on the entire span of the dictionary.
