Use of machine learning tools in fluid mechanics for the data-driven reduction, reconstruction and prediction of a fluid flow fluctuating velocity field ; Utilisation de l’apprentissage automatique en mécanique des fluides pour la réduction, la reconstruction et la prédiction orientée données du champ de vitesse fluctuante d’un écoulement

Fluid mechanics is an important part in industrial questions. The modelisation, reduction and control of fluid flows require to solve a nonlinear and multiscale optimisation problem. In the age of artificial intelligence, there is a craze to solve these optimisation problems using the wealth of experimental and numerical data. In this context, the objective of the manuscript is to present how machine learning tools can be used for the data-driven estimation of fluid flow velocity fields. In particular, we aim at reducing, reconstructing and predicting four increasing complexity flows: the laminar wake of a cylinder, a spatial mixing layer, the turbulent wake of a square cylinder and the flow around an isolated tower. To do so, we start by reformulating the reduction, the reconstruction and the prediction problems. For the reduction, we use autoencoders to find a latent space and rewrite the flow with with a low rank approximation. Different methods are used: proper orthogonal decomposition, linear autoencoder, linear variational autoencoder and variational autoencoder. For the reconstruction, we use supervised learning tools to estimate the latent state from limited measurements of the fluctuating velocity field. The methods include the linear regression (in its multitask and single task formulation), the support vector regression (linear regression in higher dimensional space), the shallow neural network and gradient boosted trees. For the prediction, we search for a finite approximation of the Koopman operator to linearly advance in time observations of the latent state. Different refinements of the core dynamical mode decomposition algorithm are used: direct models, higher order DMD (use of delayed coordinates), extended DMD and DMD with dictionnary learning. The results show that machine learning is a promising direction to establish fluid flow estimation models. However, the deployment of models for highly turbulent flows remains questionable mainly because of robustness issues. ; La mécanique des fluides ...