Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics

Carlos Granero-Belinchon (1, 2, 3)

1 ODYSSEY - Océan Dynamique Observations Analyse
2 IMT Atlantique - MEE - Département Mathematical and Electrical Engineering
3 Lab-STICC_OSE - Equipe Observations Signal & Environnement

We define and study a fully-convolutional neural network stochastic model, NN-Turb, which generates a 1-dimensional field with some turbulent velocity statistics. In particular, the generated process satisfies the Kolmogorov 2/3 law for second order structure function. It also presents negative skewness across scales (i.e. Kolmogorov 4/5 law) and exhibits intermittency as characterized by skewness and flatness. Furthermore, our model is never in contact with turbulent data and only needs the desired statistical behavior of the structure functions across scales for training.

Mots clés: Turbulence; Generative Models; Neural Networks

Domaines: Dynamique des Fluides [physics.flu-dyn]; Traitement du signal et de l'image [eess.SP]; Analyse de données, Statistiques et Probabilités [physics.data-an]; Machine Learning [stat.ML]

Carlos Granero-Belinchon. Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics. Physica D: Nonlinear Phenomena, 2023, 458, pp.133997. ⟨10.1016/j.physd.2023.133997⟩. ⟨hal-03861273v3⟩