PhD contract: Active Control of Görtler Vortices through Stability Analysis and Machine Learning (M/F)

Job Description

Thesis Subject

At the CNRS, on the Futuroscope site, the Pprime Institute is recruiting a PhD student as part of the BENEFIT project, funded by the French National Research Agency (ANR), to work on active flow control and machine learning.


1- CONTEXT
--------------------
Active flow control aims to modify velocity fields to reduce drag, improve heat transfer, and optimise momentum mixing. Two approaches currently dominate: physics-based methods (hydrodynamic stability), offering high interpretability but limited to linearised regimes; and machine learning, capturing complex nonlinear behaviour at the cost of model opacity. BENEFIT synthesises these paradigms by integrating stability analysis directly into machine learning processes. The targeted configuration concerns Görtler vortices --- pairs of longitudinal counter-rotating vortices in boundary layers over concave walls --- structures relevant for aerospace and energy applications given their propensity to promote momentum mixing and thermal homogenisation.

2- OBJECTIVES
--------------------
-Objective 1: Physical characterisation through stability analysis (sensitivity, optimal perturbations, resolvent methods) of Görtler vortices, identifying dominant modes and regions amenable to control.
-Objective 2: Reduced-order modelling via autoencoders and discovery of explicit control laws (SINDy or genetic programming) guided directly by the instability mechanisms identified.
-Objective 3: Development of reduced-order models integrating control effects directly, enabling adaptation without requiring additional simulations.


3- RESEARCH PROGRAMME, METHODOLOGIES AND MEANS
-----------------------

-Phase 1 (Months 1-12): Stability analysis using LightKrylov and LightROM. Identification of parameters governing amplification, quantification of perturbation efficacy, synthesis into physical portraits defining the dictionary of perturbations and critical observables.
-Phase 2 (Months 6-24): Construction of autoencoders for compression of high-dimensional fields. Sparse identification (SINDy) or genetic programming (GEP) for derivation of explicit, interpretable control laws, validated against high-fidelity simulations.
-Phase 3 (Months 18-36): Development of reduced-order models integrating control effects, validated against simulations and IUSTI experimental data.
-Means: LightKrylov/LightROM libraries, Incompact3d solver, Pprime CPU/GPU infrastructure, IUSTI experimental database.


4- PRINCIPAL TASKS AND RESPONSIBILITIES
-----------------------

a.Stability analyses: Perform sensitivity, optimal perturbations and resolvent methods; synthesise results into physical portraits.
b.Reduced-order models: Train autoencoders and validate against high-fidelity data.
c.Control laws: Apply SINDy and genetic programming to derive explicit, interpretable expressions.
d.Control integration: Reformulate reduced-order models incorporating control inputs directly.
e.Documentation: Produce quarterly reports, scientific articles and complete thesis writing.
f.Collaboration: Participate in BENEFIT project meetings and regular supervisor interfaces.
g.Dissemination: Present results at seminars and international conferences.
h.Training: Develop mastery of stability theory, machine learning, reduced-order modelling and high-performance computing.

The candidate must hold a Master's degree in Fluid Mechanics, Applied Mathematics or Machine Learning. He or she must demonstrate an aptitude for interdisciplinary work and machine learning, and drive to transcend disciplinary boundaries

Desired background in stability analysis and control, machine learning, dimensionality reduction and high-performance computing.

Your Work Environment

The PhD student will be registered at the MIMME Doctoral School (https://mimme.ed.univ-poitiers.fr/).

Institut Pprime is a dedicated research unit (UPR) of the CNRS.
Its scientific activities span a broad spectrum ranging from materials physics to mechanical engineering, including fluid mechanics, thermal sciences and combustion.

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

CNRS

The research professions