Phd Position F - M Multi-Fidelity Bayesian Optimization In Aerodynamics For Large-Scale Computing Infrastructures H/F

INRIA

PhD Position F/M Multi-fidelity Bayesian Optimization in aerodynamics for large-scale computing infrastructures
Le descriptif de l'offre ci-dessous est en Anglais
Type de contrat : CDD

Niveau de diplôme exigé : Bac +5 ou équivalent

Fonction : Doctorant

A propos du centre ou de la direction fonctionnelle

Inria is the French National Institute for Research in Digital Science, of which the Inria Côte d'Azur University Center is a part. With strong expertise in computer science and applied mathematics, the research projects of the Inria Côte d'Azur University Center cover all aspects of digital science and technology and generate innovation. Based mainly in Sophia Antipolis, but also in Nice and Montpellier, it brings together 47 research teams and nine support services. It is active in the fields of artificial intelligence, data science, IT system security, robotics, network engineering, natural risk prevention, ecological transition, digital biology, computational neuroscience, health data, and more. The Inria Center at Université Côte d'Azur is a major player in terms of scientific excellence, thanks to the results it has achieved and its collaborations at both European and international level.

Contexte et atouts du poste

The Acumes project-team is a joint team between Inria and the Jean-Alexandre Dieudonné Mathematics Laboratory (LJAD) of the Côte d'Azur University. The research carried out focuses on the analysis and optimization of systems governed by partial differential equations, with multi-disciplinary applications ranging from the mechanics of fluids and structures to the modeling of biological phenomena, road and pedestrian traffic. The team is also focusing on deep learning methods to effectively combine data and physical models.

Mission confiée

The optimization of complex systems, based on numerical simulations, is currently growing strongly in the industrial field, for example in aeronautics or telecommunications. The approach consists in coupling an optimization algorithm, which will seek for the optimal value of a set of parameters, to a simulator estimating the value of the cost function for each set of parameters proposed. A major difficulty lies in the computational time required for each simulation, which can amount to several hours when fine numerical models are used. Optimization must therefore take into account a highly constrained computational budget, which, in practice, is often limited to a few dozen simulations.

In this difficult context, Bayesian optimization methods have recently demonstrated their ability to provide interesting results. The approach consists in building, on the basis of some observations of the cost function, a statistical model of Gaussian Process type, which is then enriched iteratively by determining the parameters maximizing an acquisition function and by simulating the corresponding configurations.

In the perspective of relying on extremely expensive simulations, we are interested in this thesis in extending this method to multi-fidelity optimization in the context of large-scale computational infrastructures. The idea is to mix several estimation levels of the cost function during the optimization, to progress more quickly. Indeed, assuming that there are different methods for the estimation of the cost function, hierarchical in terms of accuracy and computational cost, the algorithm can certainly sometimes rely on less accurate, but also less expensive, estimates, if these are sufficiently correlated with the fine estimates. The objective is then to converge towards the optimum, for the finest estimate, by using as much as possible coarser estimates. An important point of the algorithm is the selection of the level of fidelity to use for each new simulation, via a multi-fidelity acquisition function. For this, we seek to determine which level is the most relevant, in terms of information provided and computational cost. In the context of large-scale computing facilities, additional criteria should also be considered, such as simulator scalability, available resources or energy consumption.
An expected result of this thesis is the definition of different formulations for this key step, and their comparison for a set of computational scenarios. Some advanced cases, e.g. multi-criteria optimization problems and asynchronous algorithms will also be investigated.

The algorithms developed will be validated on benchmark problems, and then applied to aerodynamic design exercises. In the context of aerodynamic simulations, the different fidelity levels can be defined by adjusting the space/time discretization, the flow model or by using surrogate models from pre-computed databases. In such case the hierarchy between fidelities is unknown and the multi-information source framework would be considered. Finally, additional test-cases (geophysics, micro-swimmers) will be considered in the framework of Sage-HPC PEPR project, in collaboration with research partners.

Principales activités

The doctoral student will be part of Acumes Project-Team at Inria Research Center. At first, he/she will have to become familiar with Bayesian optimization methods and multi-fidelity algorithms. He/she will develop new approaches and will test them on benchmark problems and complex applications.

The methodological contributions of the thesis will lead to the publication of articles in international journals and participation to international conferences. Software contributions may give rise to the distribution of packages implementing the algorithms developed.

Compétences

The candidate must hold a Master's degree (or equivalent) in applied mathematics or machine learning. An experience in optimization or numerical simulation would be a plus.

Avantages

- Subsidized meals
- Partial reimbursement of public transport costs
- Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
- Possibility of teleworking and flexible organization of working hours
- Professional equipment available (videoconferencing, loan of computer equipment, etc.)
- Social, cultural and sports events and activities
- Access to vocational training
- Contribution to mutual insurance (subject to conditions)

Rémunération

Gross Salary per month: 2300 €