Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization


  • Takahiro Kawashima The University of Electro-Communications
  • Hayaru Shouno The University of Electro-Communications
  • Hideitsu Hino The Institute of Statistical Mathematics


Bayesian Learning, Unsupervised & Self-Supervised Learning, Matrix & Tensor Methods, Time-Series/Data Streams


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.




How to Cite

Kawashima, T., Shouno, H., & Hino, H. (2021). Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization. Proceedings of the AAAI Conference on Artificial Intelligence, 35(9), 8083-8091. Retrieved from



AAAI Technical Track on Machine Learning II