https://doi.org/10.1140/epje/s10189-023-00321-7
Regular Article - Flowing Matter
Neural network complexity of chaos and turbulence
1
Département des sciences de la Terre et de l’atmosphère, Université du Québec à Montréal, H3C 3P8, Montréal, QC, Canada
2
Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland
3
Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, 69978, Tel-Aviv, Israel
4
Simons Center for Geometry and Physics, SUNY, 11794, Stony Brook, NY, USA
a
whittaker.tim@courrier.uqam.ca
Received:
31
March
2023
Accepted:
10
July
2023
Published online:
20
July
2023
Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work, we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real-world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
