Modal decomposition and machine learning to develop robust models
One of the greatest challenges our society encounters is addressing climate change. To alleviate its impacts, it is essential to investigate various alternatives and create new technologies capable of reducing atmospheric pollution. Fluid mechanics, a science with numerous applications, can be harnessed for this purpose, such as enhancing the efficiency of combustion systems, examining methods to diminish air pollution in urban environments, and optimizing the design of aircraft to improve their efficiency. To examine these issues, reduced-order models (ROMs) grounded in physical principles are proposed, employing (i) modal decompositions (singular value decomposition – SVD, higher-order dynamic mode decomposition – HODMD), and (ii) machine learning techniques (neural networks) integrated with these decompositions. This research applies these methods to tackle the aforementioned challenges while also presenting new approaches to develop efficient and accurate ROMs for different applications, such as accelerating computational fluid dynamic (CFD) numerical simulations, data assimilation, flow control and studying the flow physics in big databases.