M/F researcher "Quantum-inspired approaches for the simulation of turbulent flows"

Job Description

Missions

The candidate's mission will be to explore the simulation of turbulent flows using a tensor network representation of the Navier–Stokes equations. Unlike recent approaches based on tensor networks, which simulate fluid flows in physical space using finite difference operators, our focus will be on a Fourier-space description of spatially periodic velocity fields, taking direct inspiration from Fourier pseudo-spectral methods used in standard DNS codes. The implementation of a Fourier-based tensor network solver is already in the works within our team (based on existent tensor network libraries in Julia) and is expected to be functional by the start of the post-doctoral project.

The first objective will be to evaluate to which extent this approach is capable of reproducing the physics of turbulent flows. The goal is to determine whether this framework can be practically applied either as a full replacement of standard DNS or as a reduced-order model reproducing the main features of turbulent flows (energy spectra, scale-by-scale energy transfers, intermittency, …). Some effort may be dedicated to finding a tensor network topology (tensor train, tree tensor network, …) allowing to optimally represent vector fields arising from turbulence simulations. Then, this framework will be applied to investigate aspects such as Reynolds number effects in highly turbulent flows. Ultimately, this approach may also be used to seek for extreme events precursors. This typically requires very long simulation times which may only be achieved using frugal numerical approaches or reduced-order models.

Activity

Below are listed some possible activities of the successful candidate. Some of these activities can be adapted according to the candidate's profile and the advancement of the project.
• Get familiar with recent literature on tensor network approaches and their applications in fluid dynamics.
• Get familiar with existing libraries for working with tensor networks in the Julia programming language (ITensors.jl, Tensor4all.jl, …).
• Implement different tensor network topologies (e.g. tree tensor networks).
• Compare different strategies (topology, tensor order…) to seek for an optimally compressed representation of turbulent velocity fields and of relevant operators in tensor network form.
• Perform numerical simulations of turbulent flows and compare results with standard DNS solvers.
• Attempt to simulate high Reynolds numbers flows out of reach for standard DNS methods, and investigate Reynolds numbers effects beyond what is currently possible.
• Perform mathematical and numerical analysis of tensor network methods.
• Work on GPU implementation of tensor network solvers.
• Disseminate research results through peer-reviewed publications and presentations at international conferences.

Your Profil

Skills

Desired experience :
• Experience in numerical simulation and scientific computing.
• Experience in development and implementation of numerical methods.
• Experience in scientific programming.
• Familiarity with Fourier-based numerical methods is an asset.
• Ability to work in a collaborative international research environment.
Required degree :
• PhD in Fluid Mechanics, Physics, Applied Mathematics, Scientific Computing, or a related field.
Application package :
• A detailed curriculum vitae and a letter of motivation.

Your Work Environment

Joint Research Unit (UMR 5519) of the Centre National de la Recherche Scientifique (CNRS), the Institut National Polytechnique de Grenoble (Grenoble INP) and the University Grenoble-Alpes (UGA). LEGI carries out a wide range of research activities with a common ground: fluid mechanics and related transport phenomena.
Scientific Background
The efficient and accurate simulation of highly turbulent flows is one of the main challenges in numerical fluid dynamics. Turbulence is a complex nonlinear phenomenon characterised by a very wide range of interacting scales, which limits the investigation of highly turbulent regimes using scale-resolving direct numerical simulations (DNS) – the main numerical approach enabling progress in our fundamental understanding of turbulence. As computing hardware reaches the physical limits of miniaturisation, future advances in high Reynolds number DNS using existing methods can only be expected to be incremental. This calls for a completely different paradigm for accurately simulating turbulent flows at extreme Reynolds numbers – either using classical hardware or upcoming quantum computing platforms – all while reducing computational resource requirements.
Recent years have seen the emergence of a promising solution inspired by standard numerical techniques used in quantum mechanics to deal with many-body problems. In that context, the number of degrees of freedom required to fully describe a quantum system grows exponentially with the number of particles, which quickly renders the problem intractable. However, in many systems the interactions are not random (they have some structure) and are often short-ranged, which allows to dramatically reduce the effective number of degrees of freedom. In practice, this is achieved by approximating an (extremely large) high-dimensional tensor fully describing the system as the product of (much smaller) low-dimensional tensors which mainly encode short-range interactions. This representation is generally known as a tensor network.
Much more recently, tensor network approaches have been adapted to numerical solve partial differential equations arising in a variety of physical systems, including in particular the Navier–Stokes equations governing fluid turbulence. Here, the main idea is to reduce a full-grid solution spanning a wide range of physical scales onto a compressed tensor network representation – effectively reducing the number of degrees of freedom. This compression may be expected to be particularly efficient in systems characterised by scale separation and scale-local interactions, which is precisely a major feature of turbulent flows. Besides, many useful operators (Fourier transforms, convolutions, finite differences, …) accept low-rank tensor network representations, which in principle enables the efficient simulation of physical systems in tensor network form. Besides the potential of enabling relatively frugal computations of high Reynolds numbers flows in classical computing platforms, such an approach may also pave the way towards the simulation of turbulent flows in quantum computers.
The project will be carried out within the MOST team (Turbulence Modelling and Simulation) at LEGI (Laboratory for Industrial and Geophysical Flows) in Grenoble. The MOST team gathers specialists in the high-performance numerical simulation of turbulent flows, who develop and apply a variety of state-of-the-art numerical approaches to the study of turbulence in diverse fundamental and applied settings. LEGI is a leading French fluid dynamics laboratory focussing on aspects such as turbulent flows, particle transport, renewable energy production and environmental and geophysical flows using various experimental and numerical approaches. The successful candidate will benefit from a stimulating scientific environment and access to high-performance computing resources.
This post-doctoral position is part of the ALEAS project (“Thwarting extreme events in turbulent flows”) funded by CNRS' High-risk high-return research programme. In this ambitious project, state-of-the-art experimental and numerical approaches are developed and employed with the aim of identifying precursors to extreme events in turbulent flows. Within the ALEAS project, the present post-doctoral position seeks to explore and develop novel a novel quantum-inspired numerical approach which may eventually allow to study highly turbulent flows over long simulation times, as needed to investigate rare and extreme events.
Scientific supervisor : Juan Ignacio Polanco - MOST team

Constraints and risks

No risk identified.

Compensation and benefits

Compensation

between 3041,58€ and 4216,70€ gross monthly depending on experience

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