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Reduced representations of Rayleigh–Bénard flows via autoencoders

Published online by Cambridge University Press:  05 March 2025

Melisa Y. Vinograd Open the ORCID record for Melisa Y. Vinograd [Opens in a new window]  and
Patricio Clark Di Leoni Open the ORCID record for Patricio Clark Di Leoni [Opens in a new window]
Melisa Y. Vinograd
Affiliation:
Departamento de Ingeniería, Universidad de San Andrés, Buenos Aires, Victoria 1644, Argentina Departamento de Física, Universidad de Buenos Aires, CABA 1868, Argentina
Patricio Clark Di Leoni*
Affiliation:
Departamento de Ingeniería, Universidad de San Andrés, Buenos Aires, Victoria 1644, Argentina CONICET, CABA 1414, Argentina
*
Corresponding author: Patricio Clark Di Leoni, pclarkdileoni@udesa.edu.ar
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Abstract

We analysed the performance of convolutional autoencoders in generating reduced-order representations of the temperature field of two-dimensional Rayleigh–Bénard flows at $\textit{Pr} =1$ and Rayleigh numbers extending from $10^6$ to $10^8$, capturing the range where the flow transitions to turbulence. We present a way of estimating the minimum number of dimensions needed by the autoencoders to capture all the relevant physical scales of the data that is more apt for highly multiscale flows than previous criteria applied to lower-dimensional systems. We compare our architecture with two regularized variants as well as with linear methods, and find that manually fixing the dimension of the latent space produces the best results. We show how the estimated minimum dimension presents a sharp increase around $Ra\sim 10^7$, when the flow starts to transition to turbulence. Furthermore, we show how this dimension does not follow the same scaling as the physically relevant scales, such as the dissipation length scale and the thermal boundary layer.

JFM classification

Mathematical Foundations: Machine learning Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1006 , 10 March 2025 , A10
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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