Miguel Alfonso Mendez

Associate Professor at the von Karman Institute for Fluid Dynamics

Teaching

Since 2019, I have taught primarily at the von Karman Institute for Fluid Dynamics (VKI) in the Research Master (RM) program. This one-year, English-language Master-after-Master (60 ECTS) combines advanced courses with an individual research project. The cohort is highly selective, with about 30–35 students from around 16 countries each year. All students already hold a Master’s degree—usually in aerospace or mechanical engineering, physics, or applied mathematics—and some are already PhD candidates. Their strong preparation creates a stimulating environment at the interface between graduate education and active research.

In addition, I regularly teach in the VKI Lecture Series: week-long intensive courses in fluid dynamics, aerodynamics, thermodynamics, and computational methods, taught in English to graduate students, researchers, and industry professionals by leading experts in their fields.

Courses Taught. My teaching trajectory began in 2018 with contributions to the course Differential Equations for Fluid Dynamics (DEFM). In 2019, I took full responsibility for this course, which I reformed and broadened into Fundamentals of Fluid Dynamics (FFD).

Today, I serve as the main instructor and coordinator for six full courses and contribute to three others. I am also the primary academic lead for a new specialization within the Research Master program: Data-Driven Fluid Mechanics. Furthermore, I direct the annual Hands-on Machine Learning for Fluid Dynamics lecture series, which is approaching its sixth edition and has been attended by over 700 participants worldwide. I also co-organize lecture series on Particle Image Velocimetry (two editions) and on Flow Control (inaugural edition in 2026) in collaboration with Prof. Discetti (UCM3), as well as the lecture series Machine Learning for Fluid Dynamics (two editions) in collaboration with Prof. Parente (ULB).

The following gives a brief overview of the material I cover in the courses at the Research Master programme (full information available on the VKI syllabus: RM_SYLLABUS_2526.pdf ).

  • Fundamentals of Fluid Dynamics, FFD (22 h, 2.5 ECTS). Started in 2017 as DEFM, adapted in 2019. — A graduate-level review of the core principles and advanced concepts of fluid mechanics. The course begins with the derivation of conservation laws in integral and differential form, flow kinematics, and constitutive relations, then progresses through incompressible, inviscid, and Stokes-flow models, dimensional analysis, and similarity theory. Advanced topics include vorticity dynamics, dispersive and non-dispersive wave propagation, and the fundamentals of both modal and non-modal stability analysis, with an emphasis on eigenfunction-based formulations and transient growth mechanisms. The course provides students with a rigorous foundation and the analytical tools required to formulate and analyze problems of research relevance.
  • Signal Processing (second part), SPII (12 h, 1.5 ECTS). Started in 2019. — A graduate-level course that revisits and deepens key concepts in spectral and time–frequency analysis for analog and digital signals. The course covers the sampling and discretisation of continuous-time systems, including the link between differential equations and recursive relations, the use of Laplace and Z-transforms, and the mapping of poles and stability properties between continuous and discrete domains. It then addresses the transition from continuous to discrete Fourier transforms, generalized linear transforms and associated inner-product structures, wavelet transforms, and multiresolution analysis. The module further introduces the design and implementation of digital filters (FIR and IIR), with particular attention to real-time versus offline processing. Finally, the use of filter banks for data decomposition, multiresolution representations, and signal reconstruction is presented through applications drawn from engineering and applied physics.
  • Introduction to Measurement Techniques, IMT (4 lectures, 25% of the course). Started in 2019. — This module covers both the fundamentals and selected advanced techniques in experimental fluid mechanics. My contribution includes four lectures organized in three modules:
    1. Principles of Measurement Systems, introducing statistical treatment and Linear Time-Invariant (LTI) theory for measurement, static and dynamic characteristics, uncertainty propagation, and system calibration through impulse and step responses;
    2. Image Processing for Optical Metrology, presenting core concepts in image enhancement, linear and nonlinear filtering, and anisotropic diffusion methods; and
    3. Introduction to Particle Image Velocimetry (PIV), outlining the principles of optical velocimetry, from hardware configuration and particle dynamics to image interrogation and post-processing. This last module covers two lectures.
  • Tools for Scientific Computing, TSC (12 h, 1 ECTS). Started in 2022. — An optional course introducing open-source computational tools for addressing practical problems. The course begins with the fundamentals of Python programming and core scientific libraries (NumPy, SciPy, Matplotlib), then covers tools for numerical methods and data processing, as well as more advanced topics such as object-oriented programming, graphical user interfaces, machine-learning libraries (mainly scikit-learn), and good practices for debugging, packaging, and version control using GitHub.
  • Data-Driven Modal Analysis, DDMA (12 h, 1 ECTS). Started in 2022. — Introduces the mathematical and physical foundations of coherent-structure identification in fluid dynamics. It begins with a review of linear algebra and numerical factorizations—QR, eigenvalue decompositions, and singular value decomposition (SVD)—which underpin the construction and interpretation of modal bases, and the link between the discrete and continuous settings, including a brief review of Hilbert spaces. It then presents the classical approaches of Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), including their use for Galerkin-projection-based reduced-order models. The course concludes with advanced extensions such as Multiscale POD, Spectral POD, and a brief introduction to operator-theoretic methods rooted in resolvent analysis.
  • Machine Learning for Fluid Dynamics I, MLFD (12 h, 1 ECTS). Started as Data Driven Fluid Mechanics (DDFM) in 2021, adapted in 2025. — Introduces the mathematical foundations of machine learning and their application to flow problems. The course begins with a review of essential topics in numerical linear algebra, probability theory and calculus, followed by the general formulation of learning as a functional-approximation problem, emphasizing training, generalizability, and statistical consistency. It then covers linear and nonlinear parametric regression methods—from Radial Basis Functions to Artificial Neural Networks—together with the fundamentals of numerical optimization used for their training.
  • Machine Learning for Fluid Dynamics II, MLFD II (24 h, 2 ECTS). Started as Data Driven Fluid Mechanics (DDFM) in 2021, adapted in 2025. — Complements the previous with advanced topics framed within the Bayesian and kernel-based formalisms. The course covers Gaussian Processes and their multifidelity extensions, Bayesian optimization, and the kernelization of inner products for nonlinear regression. It also introduces linear and nonlinear dimensionality reduction methods (bridging to data-driven decompositions) and provides an overview of generative AI concepts. Throughout, the emphasis is on integration with engineering applications in fluid dynamics, including turbulence modeling, inference, and super-resolution through penalized learning and architectural constraints.
  • Digital Twinning, Data Assimilation and Control, DTAC (18 h, 2 ECTS). Started in 2024. — Focused on the real-time modeling and control of fluid systems within the framework of digital twinning. The course begins with the fundamentals of microcontrollers and electronics (Arduino, Raspberry Pi, ESP32) for real-time monitoring and basic control using simple sensors and actuators, complemented by laboratory sessions. The second part covers nonlinear system identification through recursive least squares and adjoint methods, and data assimilation via Kalman filters and their extensions. The final module discusses model-based and model-free control strategies, including an introduction to reinforcement learning and the modern actor–critic framework as well as a brief overview of reinforcement twinning.
  • Hands-on Machine Learning for Fluid Dynamics (32 h, 3 ECTS). Started in 2021. — An intensive one-week course designed for both VKI Research Master students and external participants (typically around 100). It integrates selected material from MLFD I, MLFD II and DTAC into a cohesive, tutorial-based program centered on practical implementation. Since 2024, RM students enrolled in the Data-Driven Fluid Mechanics specialization and external participants have attended the same core program, although additional lectures are provided to RM students before and after the workshop to complement the hands-on component.