A lipschitzian global optimization algorithm and machine learning for fluid dynamics

The research conducted and resumed in this thesis covers two different topics. In chapter 1, I focused my research on the development of a new Global Optimization algorithm informed with an estimate of the Lipschitz constant of the objective function. Estimation of the Lipschitz constant is obtained using the tools from the Extreme Value Theory. To extract the information of the local behavior of the objective function, I proposed a clustering strategy to enlighten the algorithm of the local Lipschitz constants. In chapters 2, 3, and 4, I show my research by developing and applying Machine Learning methodologies to three Fluid Dynamics phenomena of different nature. Specifically, in chapter 2, I propose a new framework for design space dimensionality reduction for shape optimization based on Probabilistic Linear Latent Variable models. The new framework performs the classical reduction of the number of the design variables, which is crucial to speed up the convergence of the optimization process. Furthermore, It provides the uncertainty of the new geometrical parametrization by introducing a constraint in the optimization problem based on the Mahalanobis distance. In chapter 3, my research is concentrated on the extraction and the interpretation of highly nonlinear turbulent phenomena measured with the Particle Image Velocimetry technique. Data-driven analysis is carried out for two high Reynolds number vortices flows namely for uniform and buoyant jets and 4- and 7-bladed propeller wakes. In chapter 4, I focused on the prediction of the ship motion at a high sea state level. For this application, Deep Learning methods for sequential data such as Recurrent-type Neural Networks have very desirable properties due to the high nonlinearities present inside the system. Besides the model's predictive performance, the uncertainty information is retrieved from a Bayesian perspective through Variational Inference.