Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization

被引:0
|
作者
Kawashima, Takahiro [1 ]
Shouno, Hayaru [1 ]
Hino, Hideitsu [2 ]
机构
[1] Univ Electrocommun, Tokyo, Japan
[2] Inst Stat Math, Tokyo, Japan
来源
THIRTY-FIFTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE, THIRTY-THIRD CONFERENCE ON INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE AND THE ELEVENTH SYMPOSIUM ON EDUCATIONAL ADVANCES IN ARTIFICIAL INTELLIGENCE | 2021年 / 35卷
关键词
SYSTEMS;
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
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.
引用
收藏
页码:8083 / 8091
页数:9
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