Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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)

How to cite: Lu, F. Data-driven Model Reduction for Stochastic Burgers Equations. Preprints 2020, 2020100076 (doi: 10.20944/preprints202010.0076.v1). Lu, F. Data-driven Model Reduction for Stochastic Burgers Equations. Preprints 2020, 2020100076 (doi: 10.20944/preprints202010.0076.v1).

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.

Subject Areas

data-driven modeling; stochastic Burgers equation; closure model; CFL number

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