This project lies at the crossroad between statistical physics, fluid dynamics turbulence, scientific computing and machine learning. Turbulence is among the chaotic systems with highest impact on our daily lives. It comes with complex statistical properties and multi-scale correlations in space and time, which are far from being thoroughly understood. This comes with strong practical implications including heavy computational costs of fluid flow simulations due to the absence of general and accurate turbulence models and scarce capacity of efficient flow control.

Recent evidence shows that neural networks can quantify properties of chaotic systems better than the current state of the art. This suggests that neural networks can capture certain hidden structures or symmetries better than humans and other traditional approaches. In this project we aim, first, at understanding these hidden features in the case of turbulence and complex fluid flows and, second, at using them to construct efficient and effective flow control systems.

In recent work [1], the capability of machine learning models to perform highly accurate estimates of the Reynolds number of turbulent velocity signals was shown, by employing very short time-series (the typical time-scale of the phenomena). State-of-the-art methods based on statistical analyses would require, on the other hand, orders of magnitude more data to deliver such accuracy. This is an example of the capability of machine learning to perform more with less data and a source for a new generation of fundamental turbulence studies. Additionally, reinforcement learning has been shown to be a promising tool for the control of turbulent flows [2]. These preliminary studies will be further extended in the context of this project trying also a combination of these topics with model order reduction.

[1] Deep learning velocity signals allows to quantify turbulence intensity
Alessandro Corbetta, Vlado Menkovski, Roberto Benzi, Federico Toschi
https://arxiv.org/abs/2003.14358

[2] Controlling Rayleigh-Bénard convection via Reinforcement Learning
Gerben Beintema, Alessandro Corbetta, Luca Biferale, Federico Toschi
https://arxiv.org/abs/2003.14358

Project description 

In this project we will combine and further develop the scientific and technological know-how of TU/e and SISSA research groups towards the use of Machine Learning techniques. The aim of the project is to develop tools that will allow a deeper understanding, modeling and control capabilities for turbulent flows.

The PhD candidate will develop innovative tools for the analysis, modeling, reduction and control of chaotic flows, aimed at answering the following questions: 

• Can we advance our understanding of turbulence phenomenology combining state-of-the-art statistical tools and reverse engineering of self-discovered machine learning tools?
• Can we improve, through supervised and unsupervised approaches, current models for turbulence increasing fidelity and reducing computational costs?
• Can we, using reinforcement learning, better understand the fundamental physics of the energy cascade in turbulent flows?
• Can we  have better computational performances by exploring Model Reduction techniques?
• Can we  increase complexity thanks to efficient model order reduction?

Location 

This project will be carried out within the Fluids and Flows (F&F) group at the Department of Applied Physics (https://www.tue.nl/en/research/research-groups/fluids-and-flows/) of Eindhoven University of Technology and  within the PhD program in Mathematical Analysis, Modelling and Applications at SISSA (Trieste, Italy).

We are looking for an enthusiastic and motivated PhD-student with a solid knowledge of mathematics, physics, numerical methods and computational techniques. You have an MSc in physics, mathematics or engineering. You have experience with numerical simulations and have affinity with (high-performance) computing, knowledge of machine learning and model reduction is a plus. As an ideal candidate you should be able to work in a team and be able to communicate with people in other disciplines. You also have good written and oral communication skills in English.

We offer:

• An exciting job in stimulating research environments: Fluids and Flows group at TU/e and Area Matematica at SISSA, with strong national and international collaborations.
• A full-time appointment for four years (start date on or before November 1st 2020) at Eindhoven University of Technology http://www.tue.nl/en/
• Gross monthly salary from € 2325 (first year) to € 2972 (fourth year) in line with the Collective Agreement for Dutch Universities
• An attractive package of fringe benefits, including end-of-year allowance, a personal development program for PhD students (PROOF program), and excellent sport facilities
• We aim for a dual-doctorate program where the student will obtain a PhD diploma from both TU/e and SISSA.