Data-Driven Optimization Approach for Inverse Problems : Application to Turbulent Mixed-Convection Flows

Abstract: Optimal control of turbulent mixed-convection flows has attracted considerable attention from researchers. Numerical algorithms such as Genetic Algorithms (GAs) are powerful tools that allow to perform global optimization. These algorithms are particularly of great interest in complex optimization problems where cost functionals may lack smoothness and regularity. In turbulent flow optimization, the hybridization of GA with high fidelity Computational Fluid Dynamics (CFD) is extremely demanding in terms of computational time and memory storage. Thus, alternative approaches aiming to alleviate these requirements are of great interest. Nowadays, data driven approaches gained attention due to their potential in predicting flow solutions based only on preexisting data. In the present paper, we propose a near-real time data-driven genetic algorithm (DDGA) for inverse parameter identification problems involving turbulent flows. In this optimization framework, the parametrized flow data are used in their reduced form obtained by the POD (Proper Orthogonal Decomposition) and solutions prediction is made by interpolating the temporal and the spatial POD subspaces through a recently developed Riemannian barycentric interpolation. The validation of the proposed optimization approach is carried out in the parameter identification problem of the turbulent mixed-convection flow in a cavity. The objective is to determine the inflow temperature and inflow velocity corresponding to a given temperature distribution in a restricted area of the spatial domain. The results show that the proposed genetic programming optimization framework is able to deliver good approximations of the optimal solutions within less than two minutes.