A propos du centre ou de la direction fonctionnelle

The Inria University of Lille centre, created in 2008, employs 360 people including 305 scientists in 15 research teams. Recognised for its strong involvement in the socio-economic development of the Hauts-De-France region, the Inria University of Lille centre pursues a close relationship with large companies and SMEs. By promoting synergies between researchers and industrialists, Inria participates in the transfer of skills and expertise in digital technologies and provides access to the best European and international research for the benefit of innovation and companies, particularly in the region.For more than 10 years, the Inria University of Lille centre has been located at the heart of Lille's university and scientific ecosystem, as well as at the heart of Frenchtech, with a technology showroom based on Avenue de Bretagne in Lille, on the EuraTechnologies site of economic excellence dedicated to information and communication technologies (ICT)

Contexte et atouts du poste

This research project is funded by the ANR project MELISSA (MEthodological contributions in statistical Learning InSpired by SurfAce engineering). In MELISSA, members are conducting research in statistical machine learning, following the constraints, the physical background knowledge and the observations of physical phenomena involved in repeated laser impacts on surfaces.

The hired PhD student will be based in the Inria Magnet team (Lille, France) and will be jointly supervised by Marc Tommasi, Batiste Le Bars and Pierre Humbert (CNRS, LaMME, Evry, France). Together, they gather a world-leading expertise in Machine Learning and Conformal Prediction. This project will stimulate existing and emerging collaborations with other research groups on themes at the intersection between machine learning, statistics and physics. For instance, there will be opportunities to collaborate with other members of the MELISSA project in Saint-Étienne (Laboratoire Hubert Curien, Teams MALICE, Data Intelligence and Laser-Matter interaction) and Sorbonne University (Laboratoire ISIR, MLIA Team).

Mission confiée

During this PhD, we aim to develop Conformal Prediction (CP) methods in the context of Physics-informed Machine Learning (PiML). PiML has recently emerged as a promising way to learn efficient surrogate solvers for Partial Differential Equations (PDEs) and to learn prediction models using both real-data and the physical knowledge brought by a PDE.
In this context, several research directions emerge. Regarding CP alone, a lot has been done for a univariate case. However, far less research has been made for structured multivariate and correlated outputs, such as a spatio-temporal ones. Another important research direction is also to develop CP for the problem of model selection and uncertainty minimization when several prediction models are available. These two challenges are particularly relevant in the context of PiML, where the target data are naturally spatio-temporal and where multiple physical knowledge can lead to several potential models. In this case, open questions notably include: can CP be used to measure the uncertainty of PiML models? how can CP be refined to take into account the spatio-temporal nature of the data induced by physical applications? given a family of pretrained PiML, how can we construct a valid prediction set while selecting the model that minimizes the width of the set?

Principales activités

The tentative work-plan for this PhD is as follows:

• Review the existing literature on Conformal Prediction and Physics-informed Machine Learning. Explore the different ways of performing CP for PiML. Apply the standard baselines for the models cited in MELISSA (e.g. Swift-Hohenberg)
• Develop a theoretical Conformal Prediction framework adapted to multivariate or spatio-temporal data. Extend the work of Le Bars, B. and Humbert, P. (2025) to this setting, taking into account the physical knowledge brought by a PDE. Apply this to a neural network being a surrogate solver of a PDE, or to a ML model, learned with a physical prior regularization or not.
• Consider the setting with performing CP with multiple models, and propose new methods for model selection using conformal prediction. Extend this to the PiML problem where we have access to several PDEs being uncertain.
• Show the relevance of the proposed approaches on real-world data coming from the MELISSA applications.

Compétences

The applicant is expected to have studied machine learning and/or statistics, and to have good mathematical skills. Some knowledge in optimization and physics, so as a broad interest for the topic of Physics-informed ML is a plus.

Please follow the guidelines described on https://team.inria.fr/magnet/how-to-apply/ for your application.

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
• Social security coverage

Rémunération

2 200 € monthly gross salary