Bayesian Dynamic Mode Decomposition

Bayesian Dynamic Mode Decomposition

Naoya Takeishi, Yoshinobu Kawahara, Yasuo Tabei, Takehisa Yairi

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
Main track. Pages 2814-2821. https://doi.org/10.24963/ijcai.2017/392

Dynamic mode decomposition (DMD) is a data-driven method for calculating a modal representation of a nonlinear dynamical system, and it has been utilized in various fields of science and engineering. In this paper, we propose Bayesian DMD, which provides a principled way to transfer the advantages of the Bayesian formulation into DMD. To this end, we first develop a probabilistic model corresponding to DMD, and then, provide the Gibbs sampler for the posterior inference in Bayesian DMD. Moreover, as a specific example, we discuss the case of using a sparsity-promoting prior for an automatic determination of the number of dynamic modes. We investigate the empirical performance of Bayesian DMD using synthetic and real-world datasets.
Keywords:
Machine Learning: Time-series/Data Streams
Machine Learning: Unsupervised Learning
Uncertainty in AI: Uncertainty in AI