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Data-driven Model Reduction for Stochastic Burgers Equations
Version 1
: Received: 1 October 2020 / Approved: 5 October 2020 / Online: 5 October 2020 (11:46:15 CEST)
A peer-reviewed article of this Preprint also exists.
Lu, F. Data-Driven Model Reduction for Stochastic Burgers Equationations. Entropy 2020, 22, 1360. Lu, F. Data-Driven Model Reduction for Stochastic Burgers Equationations. Entropy 2020, 22, 1360.
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 variables’ 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 and optimal 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 CFL number agrees with the full model’s.
Keywords
data-driven modeling; stochastic Burgers equation; closure model; CFL number
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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