### Data-Driven Fluid Mechanics: Combining First Principles and Machine Learning

Machine Learning for Fluid Mechanics: Analysis, Modeling, Control and Closures

### About the lecture Series

This is the first lecture series from the von Karman Institute for Fluid Dynamics dedicated to machine learning for fluid mechanics. Machine learning is driving comprehensive economic and social transformations and is rapidly shaping fluid mechanics’ research. This revolution is driven by the unprecedented amount of high-quality data provided by our ever-increasing experimental and numerical capabilities. Machine learning extracts knowledge from data without the need of first principles and introduces a new paradigm to applied scientists: use data to discover, rather than validate, new hypotheses and models. This new paradigm enlarges the available methodological portfolio of fluid dynamicists but challenges undergraduate students and practitioners alike in gathering the required know-how from all the disciplines that are intersected by its methods. These include computer science, statistics, optimization, signal processing, pattern recognition, nonlinear dynamics, and control.

The Lecture Series took place at the Université libre de Bruxelles from 24 to 28 february 2020.

### Content of the lecture series

#### Part I: Coherent Structures

Lecture 1 - Prof. B.R. Noack Analysis, Modeling and Control of the Cylinder Wake

Lecture 2 - Prof. J. Jiménez Coherent Structures in Turbulent Flows

Lecture 3 - Prof. S.T.M. Dawson The Proper Orthogonal Decomposition

Lecture 4 - Prof. P.J. Schmid The Dynamic Mode Decomposition: From Koopman Theory to Applications

#### Part II: Mathematical Analysis

Lecture 5 - Prof. Mendez Mathematical Tools, Part I: Continuous and Discrete LTI Systems

Lecture 6 - Prof. Discetti Mathematical Tools, Part II: Time-Frequency Analysis

Lecture 7 - Prof. Mendez Generalized Modal Analysis and Multiscale POD

Lecture 8 - Prof. Ianiro Applications and Good Practice

#### Part III: Dynamical Systems

Lecture 9 - Prof. P.J. Schmid Modern Tools for the Stability Analysis of Fluid Flows

Lecture 10 - Prof. S.T.M. Dawson Linear Dynamical Systems and Control

Lecture 11 - Prof. S.L. Brunton Nonlinear Dynamical Systems

Lecture 12 - Prof. S.L. Brunton Methods for System Identification

#### Part IV: Reduced-Order Modeling

Lecture 13 - Prof. S.L. Brunton Introduction to Machine Learning Methods

Lecture 14 - Prof. S.L. Brunton Machine Learning in Fluids: Pairing Methods with Problems

Lecture 15 - Prof. B.R. Noack Machine Learning for Reduced-Order Modeling

Lecture 16 - Prof. A. Parente Advancing Reacting Flow Simulations with Data-Driven Models: Chemistry Accelerations and Reduced-Order Modeling

#### Part V: Control, Closure and Perspectives

Lecture 17 - Prof. S. Görtz Reduced-Order Modeling for Aerodynamic Applications and MDO

Lecture 18 - Prof. B.R. Noack Machine Learning for Turbulence Control

Lecture 19 - Prof. J. Jiménez The Computer as Turbulence Researcher