Higher order dynamic mode decomposition beyond aerospace engineering

Abstract

It is a well known fact that fluid dynamics play a crucial rule in countless fields in scientific and industrial applications, including nature and medicine (ocean currents, fluid motion around jellyfish, blood circulation...), in energy production (wind turbines, tidal energy, combustion...) and of course in transportation and aerospace (trains, automobiles, aerospace shape optimization, cross-flow instability...). Understanding all these complex fluid dynamics problems is not an easy task and it requires a routinely description and quantification. Data-science and its diverse technique have arisen as a powerful tool to tackle these fluid dynamics problems, techniques such as machine learning and artificial intelligence, data processing and decision making, modeling and simulations are but a few of the promising tools described so far. In this work, we focus on data-driven techniques. In particular, we are introducing the fully data-driven technique, the higher order dynamic mode decomposition (HODMD). This technique was originally developed for the fluid mechanics field, but rapidly grew and covered several other fields and applications. A short review comparing two different applications will be shown in this contribution. We will first present our proposed technique, explain its solid mathematical foundations and highlight its capabilities (robustness, denoising properties, efficiency regardless of the amounts of data...). Next, we show the applicability of the HODMD technique to two, very different and quite complex problems: (i) a compressible, turbulent jet and (ii) pattern identification in medical dataset, consisting of echocardiography images.

Keywords

• Fluid dynamics
• Higher order dynamic mode decomposition
• Data-driven methods
• Aerospace