Research Master 2021-2022 (session in Preparation)

Data Driven Fluid Mechanics and Machine Learning (DDFM), 2 ECTS

This course was designed in 2018 and first delivered in the AA 2018/2019. Since 2022, a compressed version has been opened to externals in the form of an 'Hands on Course' (see the course page). This is an optional course for students that wants to specialize in data driven methods in the second semester of the research master. It consists of 30 hours of lectures which include 6 seminars given by PhD students or invited lectures. The table of content for the AA 2021/2022 is the following:

  • Introduction to Machine Learning (M. A. Mendez)

  • A Review of Optimization Tools (T. Verstraete Mendez)

  • Genetic Algorithms (GA) and Genetic Programming (GP)  (M.A. Mendez and J. Dominique)

  • Seminar 1: Genetic Programming for Noise Prediction (J. Dominique)

  • Regularized and Sparse Regression Methods (M. A. Mendez)

  • Bayesian Tools, Gaussian Processes and Bayesian Optimization (M. A. Mendez)

  • Uncertainty quantification and Bayesian inference (M. Arnst, from Univ. Liege)

  • Seminar 2: How Games of Chance Help us improve Physical Models (A. del Val)

  • Seminar 3: Sampling Methods for Bayesian Inverse Problems (J. Coheur, Univ. Liege)

  • Introduction to ANNs and Deep Learning (J. van Den Berghe and M.A. Mendez)

  • Seminar 4: Turbulence Modeling (M. Fiore)

  • Seminar 5: PDE Discovery from Data (G. Tod, CRI)

  • Linear Dimensionality Reduction and Autoencoders (M.A. Mendez)

  • Nonlinear Dimensionality Reduction and Manifold Learning (M.A. Mendez)

  • Introduction to Optimal Control and Reinforcement Learning (M. A. Mendez and F. Pino)

  • Seminar 6: Reinforcement Learning for Flow Control (F. Pino)


Advanced Signal Processing (SP, II), 5 Lectures (10 h), 1 ECTS

This is the second part of the course 'Signal Processing', which I give together with Prof. Schram. The first part covers the full range of tools for statistical treatment and frequency analysis. These are required to support the students during the laboratory activities carried out in the first part of the semester. The second reviews the mathematical underpinnings of these topics in more detail, focusing on the linear algebra involved. This introduces the students to data-driven modal analysis and dimensionality reduction and builds solid foundations for the DDFM course in the second semester.

  • Linear Algebra, Projections and Linear Transforms (M. A. Mendez)

  • Time- Frequency Analysis and Wavelets (M. A. Mendez)

  • LTI Systems, Digital Filters and Multi Resolution Analysis (M.A. Mendez)

  • Introduction to Modal Analysis (M.A. Mendez)

  • Proper Orthogonal Decomposition and Dynamic Mode Decomposition (M. A. Mendez)

Tools for Scientific Computing (TSC), 5 Lectures (10h) , 1 ECTS

This course was designed together with J. Christophe and F. J. Torres Herrador. It consists of 5 lectures and a final project:

  • Python Fundamentals (F. Torres Herrador and J. Christophe)

  • PIV using Python: a tutorial exercise (M. A. Mendez)

  • Object Oriented Programming and Parallel Computing (J. Christophe)

  • Debugging, Good Practices, Packaging and Repositories (F. Torres Herrador )

  • Tools for Machine Learning (M. A. Mendez)

Fundamentals of Fluid Dynamics (FFD), 15 Lectures (30 h), 2.5 ECTS.

This course is an extension and a re-adaptation of the previous 'Differential Equation of Fluid Dynamics' (DDFM), given by Prof. J. M. Buchlin until 2018 and by me in the AA. 2018-2019. The revised and extended version counts on the contribution of various colleagues form the VKI Faculty. Here's the table of contents

  • Conservation Laws (M.A. Mendez)

  • Constitutive Laws and Kinematics (M.A. Mendez)

  • Boundary Layers (G. Degreez)

  • Compressible Flows (T. Magin)

  • Kinetic Theory of Gasses (T. Magin)

  • Similarity and Scaling Laws (M.A. Mendez)

  • Special Forms of the Energy Equation (M.A. Mendez)

  • Vorticity and Potential Flows (M.A. Mendez)

  • Waves in Fluids (M.A. Mendez)

  • Dynamical Systems and Stability (M.A. Mendez)

  • Turbulence (J. van Beeck)

  • Acoustics (C.Schram)

  • Multiphase Flows (D. Laboureur)

  • Turbomachinery (T. Verstraete)

  • Transport Phenomena and Heat Transfer (D. Laboureur)

  • Exam Rehearsal (M. Mendez)

Introduction to Measurement Techniques (IMT).

This course is available to externals as a VKI Lecture Series (see course page for all the lectures). The lectures I cover are:

  • Principles of Measurement Systems: Static and Dynamic characteristics (2h)

  • Image Processing for Optical Metrology (2h)

  • Particle Image Velocimetry, Part 1 (1h30)