Low-dimensional representation of intermittent geophysical turbulence with high-order statistics-informed neural networks (H-SiNN)

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.