Data-Driven Approximation of Koopman-Invariant Subspaces with Tunable Accuracy
Data-Driven Approximation of Koopman-Invariant Subspaces with Tunable Accuracy
复制标题
精度可调的库普曼不变子空间的数据驱动逼近
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
J. Cortés
中科院分区：
文献类型：
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作者：
Masih Haseli;J. Cortés
本文研究了确定有限维函数空间的问题，这些空间在Koopman算子的应用下接近（在预定义的精度水平内）不变。给定一个字典的功能跨越一个有限维的功能空间和一组数据快照收集从一个潜在的非线性动力系统，我们定义了一个衡量如何接近的功能空间的字典的跨度是不变的库普曼运营商。该测量提供了确定函数空间的预测精度的方法。给定一个期望的精度水平，我们提出了一个数值算法，称为可调对称子空间分解（T-SSD），找到一个字典的功能与原始字典的跨度，满足it. Starting从原始字典的元素，T-SSD算法进行迭代删除的功能，违反了准确度界。我们证明了T-SSD收敛到一个字典满足精度标准后，有限数量的迭代。
This paper studies the problem of identifying finite-dimensional functional spaces that are close (within a predefined level of accuracy) to being invariant under the application of the Koopman operator. Given a dictionary of functions spanning a finite-dimensional functional space and a set of data snapshots gathered from a potentially nonlinear dynamical system, we define a measure of how close a functional space in the span of the dictionary is to being invariant under the Koopman operator. This measure provides a way of determining the prediction accuracy of the functional space. Given a desired level of accuracy, we propose a numerical algorithm, termed Tunable Symmetric Subspace Decomposition (T-SSD), to find a dictionary of functions with elements in the span of the original dictionary that satisfies it. Starting from the original dictionary, the T-SSD algorithm proceeds by iteratively removing the functions that violate the accuracy bound. We prove that T-SSD converges to a dictionary satisfying the accuracy criteria after a finite number of iterations.