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Stable reproducibility of turbulence dynamics by machine learning

Satoshi Matsumoto ^1,*, Masanobu Inubushi ^1,2,3, and Susumu Goto ¹

¹Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
²Department of Applied Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
³Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, Cambridge, United Kingdom

^*Contact author: s_matsumoto@fm.me.es.osaka-u.ac.jp

Phys. Rev. Fluids 9, 104601 – Published 11 October, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.104601

Abstract

We investigate the stability and accuracy of a machine-learning-based turbulence closure model. To this end, we construct a turbulence closure model for a shell model, which is a toy model of turbulence, based on the inference of sub-grid scale (SGS) variables using a recurrent neural network, and conduct an extensive parameter survey of the constructed model. The model stably and accurately reproduces the statistics of grid-scale variables when the cutoff wave number $κ_{c}$ is higher than $0.2 η^{- 1}$ , where $η$ denotes the Kolmogorov length. This is because in this case, SGS variables are subordinate to grid-scale ones. On the other hand, when $κ_{c}$ is lower than $0.2 η^{- 1}$ , the model becomes stochastically unstable. However, an appropriate regularization in the inference step of SGS variables realizes a sufficiently long lifetime of the model.

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Stable reproducibility of turbulence dynamics by machine learning

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