论文标题
投影辅助动态模式的大规模数据分解
Projection assisted Dynamic Mode Decomposition of large scale data
论文作者
论文摘要
我们有大量的时间序列格式的数据，以实现众多现象。快照，分辨率和许多其他因素的数量在我们寻求确定给定问题中的动态时发挥了作用。处理数据时的预处理和后处理步骤可能与资源有关，用于收集我们在数据上执行的数据和计算以创建问题的模型的硬件。动态模式分解（DMD）是一种基于数据的建模工具，该工具可以识别矩阵以在某个时候瞬间映射数量到将来的数量相同数量。可以通过将高维时空数据投影到概率框架中的较低维子空间来生成模型。过去已经使用了采样和高斯投影，以提高计算的效率。在这里，我们设计了DMD的优化版本，该版本利用时间延迟坐标和投影矩阵。在我们的提案中，我们讨论了两个投影矩阵 - 一个是受Krylov子空间的启发，另一个是受到Krylov子空间的启发，促进和利用稀疏性，以在产生模型中带来计算益处。在与双重回旋有关的数据（存在于海洋混合）和2D可压缩信号的数据上测试时，获得了令人满意的结果。这种DMD方案背后的动机来自以下事实：来自许多现象的数据是“大”和“高度振荡”的。
We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing steps while working with the data may be related to the resources in terms of the hardware used to collect data and computations that we perform on the data to create a model for the problem. Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. It is possible to generate a model by projecting the high dimensional spatiotemporal data to a lower dimensional subspace in a probabilistic framework. Sampling and gaussian projection have been used in the past to increase efficiency in the computation. Here, we design an optimized version of DMD that utilizes time delay coordinates and a projection matrix. In our proposal, we discussed about two projection matrices -- one is inspired by the Krylov subspace and the other promotes and leverages sparsity to bring computational benefits in producing a model. Satisfactory results are obtained as they are tested on data related to Double gyre (present in ocean mixing) and on a 2D compressible signal. The motivation behind this scheme of DMD comes from the fact that data from many phenomena are 'big' and 'highly oscillatory.'
