一种鲁棒的平移本征正交分解：用于分解多重传输流的近端方法
A robust shifted proper orthogonal decomposition: Proximal methods for decomposing flows with multiple transports
AI总结：
提出一种扩展sPOD的新方法，通过直接优化共动场、惩罚核范数并加入鲁棒性项，利用近端算法分解多重传输流，在合成和实际流动数据上展现出优异分离能力且保持可解释性。
摘要：
我们提出了一种分解多重传输流的新方法，进一步扩展了平移本征正交分解（sPOD）。sPOD试图通过共动数据场的总和来逼近传输主导流。所提方法源于sPOD，但直接优化共动场并惩罚其核范数，以促进分解中各个数据的低秩性。此外，我们在分解中加入鲁棒性项，可处理插值误差和数据噪声。利用凸优化工具，我们推导出三种近端算法来求解该分解问题。我们报告了与现有方法在合成数据基准上的数值比较，并展示了我们的方法在1D和2D不可压缩及反应流上的分离能力。所产生的方法论是一种新分析范式的基础，对于各个共动场，其结果具有与POD相同的可解释性。
英文摘要：
We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields. The proposed methods stem from sPOD but optimize the co-moving fields directly and penalize their nuclear norm to promote low rank of the individual data in the decomposition. Furthermore, we add a robustness term to the decomposition that can deal with interpolation error and data noises. Leveraging tools from convex optimization, we derive three proximal algorithms to solve the decomposition problem. We report a numerical comparison with existing methods against synthetic data benchmarks and then show the separation ability of our methods on 1D and 2D incompressible and reactive flows. The resulting methodology is the basis of a new analysis paradigm that results in the same interpretability as the POD for the individual co-moving fields.
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