Big data and machine learning are driving extensive economic and social changes and are permeating every area of applied science. Face or voice recognition, real-time language translators, self-driving cars, advanced social media, and customer analytics are just some of the products that the data revolution has provided in the last decade. The success of these products relies on the ability of the underlying algorithms to recognize (and classify) the relevant information out of an unwieldy large amount of data and learn from it, by building simple models that enable fast and accurate predictions. Every area of applied science is increasingly benefitting from such powerful tools.

Big Data in Fluid Mechanics is historically a field of big data as experimental and numerical methods provide datasets of ever-growing size and resolution. The ongoing big data revolution, which has its roots in computer science, statistics, pattern recognition, and artificial intelligence fields, is now entering the fluid mechanic community and is extensively improving the way we analyze data and extract knowledge from it.

This new course aims at providing a unified treatment of the machine learning tools that are now paving the way towards advanced methods for model order reduction, system identification, and flow control. The course will gather ideas and notions from various fields, starting from the data decompositions that were pioneered in fluid mechanics and moving towards machine learning methods that were initially developed in machine vision, pattern recognition, and artificial intelligence. This material will be supported with a comprehensive review of the mathematical background and the theory of dynamical systems, including a review on stability analysis for fluid flows and system identification. Furthermore, the lectures will be complemented with a practical exercise and coding sessions that will provide hands-on experience and a reference/starting point to develop a computational proficiency on the subject.

The covered spectra of topics will range from introductory to state of the art research methods, to make the participants capable of exploiting the enormous opportunity offered by the current big data revolution, and able to keep track of the rapid evolution of the field. At the end of the course, the attendees will be capable of designing advanced tools to analyze numerical and experimental data, perform model order reduction, data-driven system identification, and flow control. Whilst the course is intended primarily for the use by fluid dynamics practitioners, it is believed that most of its content will flow through the technological pipeline into a broad spectrum of applications that could include automotive, aeronautical, wind energy, ship designers, and process engineers.

The lecture series will host a poster session, which will allow the participants to further exchange and interact with the lecturers. All the participants are encouraged to submit a 1-page abstract before November 1st, 2019. Please note that the number of participants is limited and admission will be granted on a first come, first served basis.

The Lecture Series codirectors are Miguel A. Mendez from the von Karman Institute (Belgium), Andrea Ianiro from Universidad Carlos III de Madrid (Spain), Bernd R. Noack from LIMSI, CNRS, Université de Paris-Saclay (FRANCE) and Steven L. Brunton from University of Washington (USA).

Monday 24 February 2020: Coherent Structures

08:30 Registration

09:00 Welcome address

09:30 Analysis, Modeling and Control of the Cylinder Wake
Prof. B.R. Noack, LIMSI, CNRS, Université de Paris-Saclay, France

10:45 Coffee Break

11:15 Coherent Structures in Turbulent Flows
Prof. J. Jiménez, Universidad Politecnica de Madrid, Spain

12:30 Lunch

14:00 The Proper Orthogonal Decomposition
Prof. S.T.M. Dawson, Illinois Institute of Technology, USA

15:15 Coffee Break

15:45 The Dynamic Mode Decomposition: From Koopman Theory to Applications
Prof. P.J. Schmid, Imperial College London, UK

17:00 Reception

Tuesday 25 February 2020: mathematical Analysis

09:00 Mathematical Tools, Part I: Continuous and Discrete LTI Systems
Prof. M.A. Mendez, von Karman Institute for Fluid Dynamics, Belgium

10:15 Coffee Break

10:45 Mathematical Tools, Part II: Time-Frequency Analysis
Prof. S. Discetti, Universidad Carlos III de Madrid, Spain

12:00 Poster Session – posters will be on display during the entire Lecture Series

12:45 Lunch

14:00 Generalized and Multiscale Data-Driven Modal Analysis
Prof. M.A. Mendez, von Karman Institute for Fluid Dynamics, Belgium

15:15 Coffee Break

15:45 Applications and Good Practice
Prof. A. Ianiro, Universidad Carlos III de Madrid, Spain

17:00 End of day

Wednesday 26 February 2020: Dynamical Systems

09:00 Modern Tools for the Stability Analysis of Fluid Flows
Prof. P.J. Schmid, Imperial College London, UK

10:30 Coffee Break

11:00 Linear Dynamical Systems and Control
Prof. S.T.M. Dawson, Illinois Institute of Technology, USA

12:15 Lunch

14:00 Nonlinear Dynamical Systems
Prof. S.L. Brunton, University of Washington, USA

15:15 Coffee Break

15:45 Methods for System Identification
Prof. S.L. Brunton, University of Washington, USA

17:00 End of day

Thursday 27 February 2020: Reduced Order Modeling

09:00 Introduction to Machine Learning Methods
Prof. S.L. Brunton, University of Washington, USA

10:30 Coffee Break

11:00 Machine Learning in Fluids: Pairing Methods with Problems
Prof. S.L. Brunton, University of Washington, USA

12:30 Lunch

14:00 Machine Learning for Reduced-Order Modeling
Prof. B.R. Noack, LIMSI-CNRS, France

15:15 Coffee Break

15:45 Visit of the VKI Laboratories

17:00 Posters and General Discussion

18:00 End of day

Friday 28 February 2020: Control, Closures and Perspectives

09:00  Reduced-Order Modeling for Aerodynamic Applications and MDO
Dr. S. Görtz, German Aerospace Center (DLR), Germany

10:15 Coffee Break

10:45 Machine Learning for Turbulence Control
Prof. B.R. Noack, LIMSI-CNRS, France

12:00 Lunch

13:45 The Computer as Turbulence Researcher
Prof. J. Jiménez, Universidad Politecnica de Madrid, Spain

15:00 Coffee Break

15:30 Round Table

17:00 End of day