In the era of Big Data, methods for the automatic discovery of regularities in large datasets are essential tools in all applied sciences. Fluid Mechanics is no exception. With the constantly growing capabilities of Computational Fluid Dynamics (CFD) and the developments of spatiotemporally resolved measurement techniques such as Particle Image Velocimetry (PIV), researchers are often challenged by the quest of identifying relevant dynamics (or coherent structures and patterns) out of seemingly chaotic turbulent flows. One of the main tools for this distillation process is modal analysis, which includes methods for linear dimensionality reduction that have been pioneered in fluid dynamics. In addition to these, the ongoing machine learning revolution is enlarging the methodological portfolio of the fluid dynamicist with a wealth of nonlinear methods.
This seminar gives an overview of linear and nonlinear methods of dimensionality reduction for fluid dynamics. Starting from the notion of autoencoder, the seminar introduces a generalized framework for classic linear tools such as the Proper Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD), as well as hybrid methods such as the Multi-Scale proper Orthogonal Decomposition (mPOD). Finally, after introducing the notion of nonlinear kernels and artificial neural networks (ANN), the seminar presents nonlinear tools such as kernel PCA and ANN autoencoders. Perspectives on the future developments of the field and the growing role of Machine Learning for fluid mechanics will be given.
Speaker Bio
A. Mendez has received his Ph.D. in engineering science from “Université Libre de Bruxelles” in 2018, and he is currently Assistant Professor at the von Karman Institute for Fluid Dynamics, where he teaches differential equations for fluid mechanics, signal processing, and experimental fluid mechanics at the Research Master program (Master after Master). During his work, he has extensively used data-driven methods for post-processing numerical and experimental data, image processing and coherent structure identification. Besides experimental fluid mechanics and data processing, his main research activities include engineering modelling of fluid flows, machine learning, and flow control. He is the organizer of a new VKI Lecture Series titled ‘Machine Learning for Fluid Mechanics: Analysis, Modeling Control, and Closures, together with Prof. B. Noack (HIT, LIMSI-CNRS), Prof. A. Ianiro (Univ Carlos III) and Prof. S. Brunton (Univ of Washinton).
