论文标题
动态模式分解和最佳预测
The Dynamic-Mode Decomposition and Optimal Prediction
论文作者
论文摘要
动态模式分解（DMD）是一种已建立的数据驱动的方法，用于查找非线性时间序列的时间不断发展的线性模式分解。传统上，这种方法假定所有相关维度都是通过测量来采样的。为了解决数据可能不完整或仅代表对更复杂系统的部分观察的动态系统，我们通过包括Mori-Zwanzig的分解来扩展DMD算法，以得出记忆核，从而捕获未解决变量的平均动力学，因为该动力学将未解决的变量投射到分解尺寸上。然后，我们得出所谓的与内存有关的动态模式分解（MDDMD）。通过数值示例，显示了整体系统的合理近似值的MDDMD方法，只要对解决变量进行单个时间序列测量，整个系统的集合平均动力学。
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled through measurement. To address dynamical systems in which the data may be incomplete or represent only partial observation of a more complex system, we extend the DMD algorithm by including a Mori-Zwanzig Decomposition to derive memory kernels that capture the averaged dynamics of the unresolved variables as projected onto the resolved dimensions. From this, we then derive what we call the Memory-Dependent Dynamic Mode Decomposition (MDDMD). Through numerical examples, the MDDMD method is shown to produce reasonable approximations of the ensemble-averaged dynamics of the full system given a single time series measurement of the resolved variables.
