Consistent Dynamic Mode Decomposition
Consistent Dynamic Mode Decomposition
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DOI：
10.1137/18m1233960
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发表时间：
2019-01-01
影响因子：
2.1
通讯作者：
Bertozzi, Andrea
中科院分区：
文献类型：
--
作者：
Azencot, Omri;Yin, Wotao;Bertozzi, Andrea
我们提出了一种新的方法来计算动态模式分解演化矩阵，我们用来分析动力系统。与大多数现有的方法不同，我们的方法是基于变分公式组成的数据对齐惩罚条款和本构正交约束。我们的方法不对数据的结构或大小做任何假设，因此它适用于广泛的问题，包括非线性场景或极小的观测集。此外，我们的技术是强大的噪声是独立的动态，它不需要输入数据是连续的。我们的主要思想是引入一个正则化项的前向和后向动力学。所得到的最小化问题有效地解决了使用交替方法的乘数（ADMM），需要两个西尔维斯特方程求解每次迭代。我们的数值方案收敛的经验，是类似于一个可证明收敛的ADMM计划。我们比较我们的方法，各种国家的最先进的方法在几个基准动力系统。
We propose a new method for computing dynamic mode decomposition evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of data alignment penalty terms and constitutive orthogonality constraints. Our method does not make any assumptions on the structure of the data or their size, and thus it is applicable to a wide range of problems including nonlinear scenarios or extremely small observation sets. In addition, our technique is robust to noise that is independent of the dynamics and it does not require input data to be sequential. Our key idea is to introduce a regularization term for the forward and backward dynamics. The obtained minimization problem is solved efficiently using the alternating method of multipliers (ADMM) which requires two Sylvester equation solves per iteration. Our numerical scheme converges empirically and is similar to a provably convergent ADMM scheme. We compare our approach to various state-of-the-art methods on several benchmark dynamical systems.