Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The standard formulation of DMD is subject to strict assumptions concerning the time-spacing of the snapshots and is biased by measurement noise. Variations on the method have been developed to address these shortcomings, but the problem is still open. Motivated by the effectiveness of Galerkin methods in the field of model discovery, a weak formulation of DMD is presented, weak-DMD. Weak-DMD precludes timestep considerations and also filters noise. Results for two nuclear engineering applications and the flow of fluid past a cylinder are given and compared with a state of the art DMD algorithm.

翻译：动态模态分解（DMD）是一种用于逼近系统时空模态的数据驱动方法。该方法通过状态变量的一系列时间快照近似系统的特征向量和特征值。DMD的标准公式对快照的时间间隔有严格假设，并且会受到测量噪声的偏差影响。虽然已有多种改进方法被提出以解决这些不足，但该问题仍未完全解决。受伽辽金方法在模型发现领域有效性的启发，本文提出了一种弱形式DMD——弱DMD。弱DMD无需考虑时间步长问题，同时能够过滤噪声。文中给出了两个核工程应用实例以及流体流经圆柱体的结果，并与当前最先进的DMD算法进行了对比。