This article introduces a new Neural Network stochastic model to generate a 1-dimensional stochastic field with turbulent velocity statistics. Both the model architecture and training procedure ground on the Kolmogorov and Obukhov statistical theories of fully developed turbulence, so guaranteeing descriptions of 1) energy distribution, 2) energy cascade and 3) intermittency across scales in agreement with experimental observations. The model is a Generative Adversarial Network with multiple multiscale optimization criteria. First, we use three physics-based criteria: the variance, skewness and flatness of the increments of the generated field that retrieve respectively the turbulent energy distribution, energy cascade and intermittency across scales. Second, the Generative Adversarial Network criterion, based on reproducing statistical distributions, is used on segments of different length of the generated field. Furthermore, to mimic multiscale decompositions frequently used in turbulence's studies, the model architecture is fully convolutional with kernel sizes varying along the multiple layers of the model. To train our model we use turbulent velocity signals from grid turbulence at Modane wind tunnel.
We define and study a fully-convolutional neural network stochastic model, NN-Turb, which generates 1-dimensional fields with turbulent velocity statistics. Thus, 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. 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.
We address Lagrangian drift simulation in geophysical dynamics and explore deep learning approaches to overcome known limitations of state-of-the-art model-based and Markovian approaches in terms of computational complexity and error propagation. We introduce a novel architecture, referred to as DriftNet, inspired from the Eulerian Fokker-Planck representation of Lagrangian dynamics. Numerical experiments for Lagrangian drift simulation at the sea surface demonstrates the relevance of DriftNet w.r.t. state-of-the-art schemes. Benefiting from the fully-convolutional nature of Drift-Net, we explore through a neural inversion how to diagnose modelderived velocities w.r.t. real drifter trajectories.
Nowadays, thermal infrared satellite remote sensors enable to extract very interesting information at large scale, in particular Land Surface Temperature (LST). However such data are limited in spatial and/or temporal resolutions which prevents from an analysis at fine scales. For example, MODIS satellite provides daily acquisitions with 1Km spatial resolutions which is not sufficient to deal with highly heterogeneous environments as agricultural parcels. Therefore, image super-resolution is a crucial task to better exploit MODIS LSTs. This issue is tackled in this paper. We introduce a deep learning-based algorithm, named Multi-residual U-Net, for super-resolution of MODIS LST single-images. Our proposed network is a modified version of U-Net architecture, which aims at super-resolving the input LST image from 1Km to 250m per pixel. The results show that our Multi-residual U-Net outperforms other state-of-the-art methods.
We study the shape of convective rolls in the Marine Atmospheric Boundary Layer from Synthetic Aperture Radar images of the ocean. We propose a multiscale analysis with structure functions which allow an easy generalization to analyse high-order statistics and so to finely describe the shape of the rolls. The two main results are : 1) second order structure function characterizes the size and direction of rolls just like correlation or power spectrum do, 2) high order statistics can be studied with skewness and Flatness which characterize the asymmetry and intermittency of rolls respectively. From the best of our knowledge, this is the first time that the asymmetry and intermittency of rolls is shown from radar images of the ocean surface.