Low-dimensional representation of intermittent geophysical turbulence with High-Order Statistics-informed Neural Networks (H-SiNN)

2023/10/06 by Raffaello Foldes, Enrico Camporeale, Foldes, Raffaello +3
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2310.04186

openalex publication_date 2023/10/06 · openalex created_date 2024/01/16 · openalex updated_date 2026/08/01

Abstract

We present a novel machine learning approach to reduce the dimensionality of state variables in stratified turbulent flows governed by the Navier-Stokes equations in the Boussinesq approximation. The aim of the new method is to perform an accurate reconstruction of the temperature and the three-dimensional velocity of geophysical turbulent flows developing non-homogeneities, starting from a low-dimensional representation in latent space, yet conserving important information about non-Gaussian structures captured by high-order moments of distributions. To achieve this goal we modify the standard Convolutional Autoencoder (CAE) by implementing a customized loss function that enforces the accuracy of the reconstructed high order statistical moments. We present results for compression coefficients up to 16 demonstrating how the proposed method is more efficient than a standard CAE in performing dimensionality reduction of simulations of stratified geophysical flows characterized by intermittent phenomena, as observed in the atmosphere and the oceans.

Citations

• The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
• Deep Multi-fidelity Gaussian Processes
• Generation of Turbulent States using Physics-Informed Neural Networks
• Convolutional autoencoder for the spatiotemporal latent representation of turbulence

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