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

TL;DR

This paper introduces a neural network-based method that effectively reduces the dimensionality of complex geophysical turbulence data while preserving non-Gaussian statistical features, improving upon standard autoencoders.

Contribution

The authors develop a High-Order Statistics-informed Neural Network (H-SiNN) that incorporates high-order moments into the loss function for better statistical preservation during dimensionality reduction.

Findings

H-SiNN outperforms standard CAEs in compressing turbulent flow data

The method maintains non-Gaussian statistical structures in low-dimensional representations

Achieves effective compression with coefficients up to 16

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.