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Center for Nonlinear Studies |
Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong, multiscale, and statistically nontrivial fluctuations of the velocity field. This has opened longstanding fundamental challenges with vast technological relevance. For instance, turbulent fluctuations hinder convergence of statistical estimators, making even the bare quantification of the turbulence intensity or of the Reynolds number highly demanding in terms of data volumes. Also, high-statistical fidelity closure models, parametrizing the influence of small unresolved scales on the dynamics of large, resolved ones, remain outstanding.In this two-part talk, I will discuss the capability of recent deep neural models at learning features of turbulent velocity signals. First, I will show how deep neural networks can accurately estimate the Reynolds number within 15% accuracy, from a statistical sample as small as two large-scale eddy turnover times. In contrast, physics-based statistical estimators are limited by the convergence rate of the central limit theorem and provide, for the same statistical sample, at least a hundredfold larger error. Second, I will present a closure, based on a deep recurrent network, that quantitatively reproduces, within statistical errors, Eulerian and Lagrangian structure functions and the intermittent statistics of the energy cascade, including those of subgrid fluxes. To achieve high-order statistical accuracy, and thus a stringent statistical test, I consider shell models of turbulence. These results encourage the development of similar approaches for three-dimensional Navier-Stokes turbulence.In collaboration with R. Benzi, V. Menkovski, G. Ortali, G. Rozza, F. Toschi.Refs.- G. Ortali, A. Corbetta, G. Rozza, F Toschi. Numerical proof of shell model turbulence closure. Phys. Rev. Fluids. 7, L082401, 2022- A. Corbetta, V. Menkovski, R. Benzi, F. Toschi. Deep learning velocity signals allows to quantify turbulence intensity. Sci. Adv. 7: eaba7281, 2021
Host: Vitaliy Gyrya (T-5) and Daniel Livescu (CCS-2)