Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization
Authors: Takahiro Kawashima, Hayaru Shouno, Hideitsu Hino8083-8091
AAAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, both of nonlinear simulated and real-world datasets are used to illustrate the potential of the proposed method. In this section, we report the application of the proposed BDMD-VMF method to both simulated and real data. By using simulated data generated from nonlinear partial differential equations (PDEs), we confirm that BDMD-VMF yields almost the same results as DMD. |
| Researcher Affiliation | Academia | 1 The University of Electro-Communications, Tokyo, Japan 2 The Institute of Statistical Mathematics, Tokyo, Japan |
| Pseudocode | Yes | The DMD algorithm is as follows: 1. Compute the K-th truncated SVD of Y 0 Y 0 U KLKV K, where U K CD K and V K CT 1 K are composed of left and right singular vectors, respectively. The matrix LK CK K is a diagonal matrix consisting of the K largest singular values. Now, A can be approximated by A Y 1V KL 1 K U K. 2. Map A CD D to A CK K using the K left singular vectors U K of Y 0: A = U K AU K = U KY 1V KL 1 K CK K. 3. Compute the eigendecomposition of A A wk = λk wk, k = 1, . . . , K. This yields the K largest eigenvalues of A as {λk} and the corresponding eigenvectors, which are called DMD modes, as {U K wk}. |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described, such as a specific repository link, an explicit code release statement, or code in supplementary materials. |
| Open Datasets | Yes | As synthetic datasets, we used sequential datasets from two nonlinear PDEs: the nonlinear Schr odinger equation (NLSE) and Burgers equation. The Hu Ga DB dataset (Chereshnev and Kert esz-Farkas 2018) contains signals collected from six sensors placed on the right and left thighs, shins, and feet of 18 participants. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) needed to reproduce the data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers like Python 3.8, CPLEX 12.4) needed to replicate the experiment. |
| Experiment Setup | Yes | Throughout the simulations reported below, we generated 7,500 MCMC samples and discarded the first 5,000 considering a burn-in periods. Unless otherwise specified, we employed appropriate weakly informative priors for any parameters. We determined the number of modes K for which DMD can capture input dynamics, through preliminary experiments. |