Implementation and Comparative Analysis of Machine Learning Methods for the closed-loop control of fluid flows

The steep ascent of machine learning techniques has also had an impact on fluid mechanics in the past few years. In the light of its great achievements in solving complex problems, machine learning-based techniques seem to be a very promising solution to address flow control problems. Due to its inherent nonlinearities, non-convexity, and high-dimensionality, it offers a challenge for machine learning methods that learn by trial and error, such as the cutting-edge technique known as Deep Reinforcement Learning (DRL). This work aims at studying the performances of such an approach in three test cases: the 1D linear advection equation, the 1D Burgers equation, and the control of a von Kàrmàn Vortex Street behind a 2D cylinder at Re=100 (J. Rabaud et al. 2019). The performance of two machine learning techniques, DRL and Bayesian Optimisation (BO), was assessed. Moreover, a thorough hyperparameters optimisation campaign is carried out, to find the best tuning for the RL algorithm at stake. Finally, a benchmark will be carried out, to gain an overview of how machine learning approaches relate to other optimisation approaches for optimal closed-loop control.