Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization
Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization
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DOI：
10.1609/aaai.v35i9.16985
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Takahiro Kawashima;Hayaru Shouno;H. Hino
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文献类型：
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作者：
Takahiro Kawashima;Hayaru Shouno;H. Hino
动态模式分解（DMD）及其扩展是数据驱动的方法，这些方法极大地有助于我们对动态系统的理解。但是，由于DMD及其大多数扩展是确定性的，因此很难处理参数和预测的概率表示。在这项工作中，我们提出了一种贝叶斯DMD模型的新型公式。我们的贝叶斯DMD模型与标准DMD的过程一致，该过程首先确定观测值的子空间，然后计算该子空间上的模式。变分矩阵分解使实现DMD的完全基础方案成为可能。此外，我们为不完整数据得出了贝叶斯DMD模型，这证明了概率建模的优势。最后，使用非线性模拟和现实世界数据集来说明所提出的方法的潜力。
Dynamic mode decomposition (DMD) and its extensions are data-driven methods that have substantially contributed to our understanding of dynamical systems. However, because DMD and most of its extensions are deterministic, it is difficult to treat probabilistic representations of parameters and predictions. In this work, we propose a novel formulation of a Bayesian DMD model. Our Bayesian DMD model is consistent with the procedure of standard DMD, which is to first determine the subspace of observations, and then compute the modes on that subspace. Variational matrix factorization makes it possible to realize a fully-Bayesian scheme of DMD. Moreover, we derive a Bayesian DMD model for incomplete data, which demonstrates the advantage of probabilistic modeling. Finally, both of nonlinear simulated and real-world datasets are used to illustrate the potential of the proposed method.