论文标题
对Koopman本征函数和不变子空间的平行学习，以进行准确的长期预测
Parallel Learning of Koopman Eigenfunctions and Invariant Subspaces For Accurate Long-Term Prediction
论文作者
论文摘要
我们提出了一种并行数据驱动的策略，以识别与未知动态系统相关的Koopman操作员下不变的有限函数功能空间。我们基于对称子空间分解（SSD）算法，这是一种集中式方法，在数据采样的轻度条件下，可证明在任意有限的二维功能空间中发现了最大的Koopman-Invariant子空间和所有Koopman eigenFunctions。一个处理器网络，每个人都知道一个通用函数字典，并配备了一组本地数据快照，并在有向的通信图上反复进行交互。每个处理器都会收到其邻居对不变字典的估计，并通过应用SSD及其本地数据的SSD来完善其估计，该数据由其自己的词典和邻居的字典跨越了子空间的相交。我们确定网络拓扑的条件，以确保算法在原始字典的跨度中识别最大的Koopman-invariant子空间，从而表征其时间，计算和通信复杂性，并确定其针对通信失败的鲁棒性。
We present a parallel data-driven strategy to identify finite-dimensional functional spaces invariant under the Koopman operator associated to an unknown dynamical system. We build on the Symmetric Subspace Decomposition (SSD) algorithm, a centralized method that under mild conditions on data sampling provably finds the maximal Koopman-invariant subspace and all Koopman eigenfunctions in an arbitrary finite-dimensional functional space. A network of processors, each aware of a common dictionary of functions and equipped with a local set of data snapshots, repeatedly interact over a directed communication graph. Each processor receives its neighbors' estimates of the invariant dictionary and refines its estimate by applying SSD with its local data on the intersection of the subspaces spanned by its own dictionary and the neighbors' dictionaries. We identify conditions on the network topology to ensure the algorithm identifies the maximal Koopman-invariant subspace in the span of the original dictionary, characterize its time, computational, and communication complexity, and establish its robustness against communication failures.
