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

A book based on the von Karman Institute Lecture Series
Machine Learning for Fluid Mechanics: Analysis, Modeling, Control and Closures

About the book

Data-Driven Fluid Mechanics: Combining First Principles and Machine Learning
Edited by Miguel A. Mendez, Bernd R. NoackSteven L. Brunton

The book is available on Cambridge University Press and on

This book originated from a one-week course from the von Karman Institute (VKI) for fluid dynamics ( and is intended for scientists and engineers interested in data-driven and machine learning methods for fluid mechanics. Big data and machine learning are driving profound technological progress across nearly every industry, and they are rapidly shaping fluid mechanics' research.

This revolution is driven by the ever-increasing amount of high-quality data, provided by rapidly improving experimental and numerical capabilities. Machine learning extracts knowledge from data without the need for first principles and introduces a new paradigm: use data to discover, rather than validate, new hypotheses and models. This revolution brings challenges and opportunities.

Data driven methods are an essential part of the methodological portfolio of fluid dynamicists, motivating students and practitioners to gathering practical knowledge from a diverse range of disciplines. These fields include computer science, statistics, optimization, signal processing, pattern recognition, nonlinear dynamics, and control. Fluid mechanics is historically a big data field and offers a fertile ground to develop and apply data-driven methods, while also providing valuable shortcuts, constraints, and interpretations based on its powerful connections to first principles physics. Thus, hybrid approaches that leverage both data-driven methods and first principles approaches, are the focus of active and exciting research.

This book presents an overview and a pedagogical treatment of some of the data-driven and machine learning tools that are leading research advancements in model-order reduction, system identification, flow control, and data-driven turbulence closures.

The book’s table of content can be downloaded here.

Why is a book needed?

Fluid Mechanics is historically a field of Big Data and hence offers a fertile ground to the data-driven paradigm, which has already provided insights in grand challenges such as turbulence control or turbulence modeling. As Machine Learning continuously augments or replaces more traditional methods, the demand for dedicated courses on the topic and qualified people has exponential grown in industry and academia alike. In aerospace and mechanical engineering programs, more and more prestigious universities are creating new chairs and opening new positions on machine learning for fluid dynamics.

Online Material

The book is supported by supplementary material, including codes, experimental and numerical data, exercises. The video of the lectures that were given in the VKI lecture series are available here. Please note that the structure of the course was slightly different from the one of the book.
For each of the book’s chapter, a folder containing material provided by the authors is available at:

Readers interested in gaining a working knowledge on the subject are encouraged and expected to download this material, study it along with the book, and test it on their own data. The large repertoire of computing tools implemented, together with the relevant datasets provided, offer a unique opportunity to learn by practicing with real experimental and numerical data.