一致的动态模式分解
Consistent Dynamic Mode Decomposition
AI总结：
本文提出了一种计算动态模式分解(DMD)演化矩阵的新方法，通过数据对齐惩罚项和本构正交约束的变分公式进行分析。该方法不假设数据结构或大小，适用于非线性场景或极小观测集，并对独立于动态的噪声具有鲁棒性。核心思想是引入正则化项以正向和反向动态，使用交替乘子法(ADMM)高效求解，每迭代步需两次 Sylvester 方程求解。数值方案经验证收敛，与现有方法在多个基准动态系统上进行了比较。
摘要：
我们提出了一种新的方法用于计算动态模式分解(DMD)演化矩阵，用于分析动态系统。与现有大多数方法不同，我们的方法基于由数据对齐惩罚项和本构正交约束组成的变分公式。我们的方法不假设数据的结构或大小，因此适用于广泛的问题，包括非线性场景或极小的观测集。此外，我们的技术对独立于动态的噪声具有鲁棒性，并且不需要输入数据为序列。我们的核心思想是引入正则化项用于正向和反向动态。所获得的最小化问题通过交替乘子法(ADMM)高效求解，每迭代步需要两次Sylvester方程求解。我们的数值方案经经验验证收敛，与证明收敛的ADMM方案相似。我们在多个基准动态系统上将我们的方法与各种最先进的方法进行了比较。
英文摘要：
We propose a new method for computing Dynamic Mode Decomposition (DMD) 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 non-linear 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
