Paper Info
Title
Data-Driven Model Reduction For Stochastic Burgers Equations
Abstract
We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable's trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model's stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system's mean Courant-Friedrichs-Lewy (CFL) number agrees with that of the full model.
Year
DOI
Venue
2020
10.3390/e22121360
ENTROPY
Keywords
DocType
Volume
data-driven modeling, stochastic Burgers equation, closure model, CFL number
Journal
22
Issue
ISSN
Citations 
12
1099-4300
1
PageRank 
References 
Authors
0.36
0
1
Name
Order
Citations
PageRank
Fei Lu 0007132.04