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Title: Turbulence model reduction by deep learning

Abstract

A defining problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce an alternative, data-driven method for parametrizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local gradient of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Univ. of California, San Diego, CA (United States)
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES); National Science Foundation (NSF)
OSTI Identifier:
1632122
Grant/Contract Number:  
FG02-04ER54738; ACI-1548562
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 101; Journal Issue: 6; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING; drift waves; plasma turbulence; turbulent mixing; weak turbulence; artificial neural networks; machine learning

Citation Formats

Heinonen, R. A., and Diamond, Patrick H. Turbulence model reduction by deep learning. United States: N. p., 2020. Web. doi:10.1103/PhysRevE.101.061201.
Heinonen, R. A., & Diamond, Patrick H. Turbulence model reduction by deep learning. United States. https://doi.org/10.1103/PhysRevE.101.061201
Heinonen, R. A., and Diamond, Patrick H. Thu . "Turbulence model reduction by deep learning". United States. https://doi.org/10.1103/PhysRevE.101.061201. https://www.osti.gov/servlets/purl/1632122.
@article{osti_1632122,
title = {Turbulence model reduction by deep learning},
author = {Heinonen, R. A. and Diamond, Patrick H.},
abstractNote = {A defining problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce an alternative, data-driven method for parametrizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local gradient of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.},
doi = {10.1103/PhysRevE.101.061201},
journal = {Physical Review E},
number = 6,
volume = 101,
place = {United States},
year = {2020},
month = {6}
}

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