BayesianDMDExamples

Illustrative Examples in the BDMD-VMF paper:
Takahiro Kawashima, Hayaru Shouno, Hideitsu Hino, "Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization," in AAAI-21.

Working Directory

Please set your working directory examples/.

Examples

File	Description	Recommended environment(s)
examples/examples_nlse.jl	Example of the nonlinear Schörodinger equation	julia (≥ 1.5.0)
examples/examples_burgers.jl	Example of the Burgers' equation	julia (≥ 1.5.0)
examples/hugadb.jl	Example of gyroscope data (BDMD-VMF)	julia (≥ 1.5.0)
examples/hugadb_var2.r, examples/hugadb_var2.stan	Example of gyroscope data (VAR(2))	R (≥ 4.0.0)

Nonlinear Schörodinger Equation

Run examples/examples_nlse.jl to execute. The data is simulated by the pseudo-spectral method. Required libraries for Julia are below:

Library	Recommended ver.
Plots	≥ 1.5.8
CSV	≥ 0.7.7
DataFrames	≥ 0.21.6
JLD2	≥ 0.1.14
StatsBase	≥ 0.33.0
PDMats	≥ 0.10.1
ProgressMeter	≥ 1.3.2
Distributions	≥ 0.23.8
DifferentialEquations	≥ 6.15.0
FFTW	≥ 1.2.2
Random
LinearAlgebra

Burgers' Equation

Run examples/examples_burgers.jl to execute. The data is simulated by the Crank-Nicolson method. Required libraries for Julia are below:

Library	Recommended ver.
Plots	≥ 1.5.8
CSV	≥ 0.7.7
DataFrames	≥ 0.21.6
JLD2	≥ 0.1.14
StatsBase	≥ 0.33.0
PDMats	≥ 0.10.1
ProgressMeter	≥ 1.3.2
Distributions	≥ 0.23.8
Random
LinearAlgebra

Gyroscope Data

Run examples/hugadb.jl to execute. To obtain a result by the Bayesian VAR(2) model, execute examples/hugadb_var2.r before running examples/hugadb.jl. Required libraries for Julia are below:

Library	Recommended ver.
Plots	≥ 1.5.8
CSV	≥ 0.7.7
DataFrames	≥ 0.21.6
JLD2	≥ 0.1.14
StatsBase	≥ 0.33.0
PDMats	≥ 0.10.1
ProgressMeter	≥ 1.3.2
Distributions	≥ 0.23.8
KernelDensity	≥ 0.6.0
Random
LinearAlgebra

In addition, required library for R are below:

Library	Recommended ver.
rstan	≥ 2.21.2
dplyr	≥ 1.0.0