CLOSED CALL!

As part of the workshop, participants are invited to submit a detailed abstract for possible oral or poster presentation. During the selection process, the committee is keen to give the best possible visibility to doctoral students, researchers and teacher-researchers. When submitting your application by e-mail (maths-ia@inria.fr), please include the following details: surname/first name, institution, status, title/abstract.

Application deadline: February 20, 2025

Financial support for the mission may be granted by the committee upon justified request.

The “Mathematical Foundations of AI” day, jointly organized by the DATAIA Institute and SCAI, in association with the scientific societies: the Fondation Mathématique Jacques Hadamard (FMJH), the Fondation Sciences Mathématiques de Paris-FSMP, the MALIA group of the Société Française de Statistique, the Société Savante Francophone d'Apprentissage Machine (SSFAM) and the Research network on Uncertainty Quantification (RT-UQ) aims to offer an overview of some promising research directions at the interface between statistical learning and AI.

This new edition will be devoted to the quantification of uncertainties in AI. The day is devoted to three plenary talks given by renowned researchers and specialists in the field: Radu Stoica (Inria Nancy, Institut Elie Cartan de Lorraine), Pietro Congedo (Inria Saclay, CMAP) and Yingzhen Li (Imperial College London, UK). It is also an opportunity for young researchers to present their work via short talks (see call for papers).

Organizing Committee

• Marianne Clausel (Univ. Lorraine)
• Emilie Chouzenoux (INRIA Saclay, DATAIA Institute)

Scientific Committee

• Ricardo Borsoi (CNRS, CRAN)
• Stéphane Chrétien (Univ. Lyon 2)
• Sylvain Le Corff (Sorbonne University)

• Myriam Tami (CentraleSupélec)

   

• 9am - 10am | Keynote 1 : Radu Stoica (Inria Nancy, Elie Cartan de Lorraine Institute)

Random structures and patterns in spatial data
through marked point processes with interactions

Abstract : the useful information contained in space-time data is often represented by geometric structures and patterns. geometric structures and patterns. One example is the filaments or clusters of galaxies in our universe. The filaments or clusters of galaxies in our universe are a case in point. Two situations need to be taken into account. Firstly, the pattern of interest is hidden in the data set, so it must be detected. Secondly, the structure of interest is observed, so it needs to be appropriately characterized. Probabilistic modeling and Bayesian statistical inference are approaches that can provide answers to these questions. This talk presents the use of marked point processes to detect and characterize such structures. Tagged point processes with interactions are used to model the pattern of interest. The proposed models are well-defined and locally stable. Depending on the model, Monte Carlo and exact algorithms are discussed to simulate the proposed models. Based on these ingredients, a global optimization and a posteriori sampling algorithm are presented to detect and characterize the model of interest, respectively.  Application examples in astronomy and environmental sciences are also presented.

Biography: Radu S. Stoica is Full Professor of Mathematics at the University of Lorraine (France). His research combines stochastic geometry, spatial statistics and Bayesian inference for probabilistic modeling and statistical description of random structures and patterns. The results of his work consist of data-adaptive methods, based on Gibbs-Markov models, Monte Carlo algorithms and inference procedures, capable of characterizing and detecting structures and patterns that are either hidden or directly observed in the data. Areas of application include astronomy, geosciences, image analysis and network sciences. Prior to his current position, Radu Stoica was Associate Professor at the University of Lille (France). He has also worked as a researcher at INRAe Avignon (France), Jaume I University (Spain) and CWI Amsterdam (Netherlands).

• 10am - 10:30am | Coffee Break

• 10:30am - 11:30am | Keynote 2 : Pietro Congedo (Inria Saclay, CMAP)

Uncertainty Quantification in scientific computing:
A machine learning perspective

Abstract: Uncertainty quantification (UQ) in scientific computing aims to rigorously analyze and mitigate the impact of uncertainties in mathematical models and simulations. Its objectives include identifying, propagating and reducing uncertainties from various sources such as model inputs, parameters, and observations to assess their influence on computational outputs. The integration of Machine Learning (ML) in this context has unlocked new possibilities, leading to substantial advancements. However, it also presents significant challenges, particularly regarding proper usage, interpretation, and reliability. In this talk, we first survey the most promising directions for development by revisiting the primary tasks of UQ, ranging from forward propagation to calibration problems. Next, we demonstrate how to design a hybrid numerical scheme that couples a traditional fluid dynamics solver with a neural network to approximate chemical reactions. This approach leverages the strengths of neural networks, including their accuracy, dimensionality reduction capabilities in big data contexts, and computational efficiency due to their matrix-vector structure, resulting in significant acceleration factors. We apply this cost-effective hybrid scheme to hypersonic reentry simulations. Finally, we illustrate how model uncertainty can be reduced through calibration and active learning strategies, presenting concrete examples in aerospace applications. 

Biography: Pietro Marco Congedo is an Inria Research Director at the Center for Applied Mathematics at École Polytechnique, team leader of the Inria team-project PLATON (in collaboration with École Polytechnique and CNRS), and Scientific Director of the Joint CWI-Inria International Lab. He graduated with honors in Materials Engineering from the University of Lecce (Italy). Following a Master’s degree in Fluid Mechanics from Arts et Métiers (Paris, France), he obtained his Ph.D. in Energy Systems from the University of Lecce in 2007. He has extensive experience in uncertainty quantification and robust optimization methods for scientific computing, with applications in aeronautics, hypersonics, and real-gas flows. He has participated in several Horizon Europe and CleanSky projects, as well as major industrial collaborations.

• 11:30am - 12:15pm | Short contributive talks (20mn)

• 12:15pm - 1:45pm | Lunch Break

• 1:45pm - 2:45pm | Keynote 3 : Yingzhen Li (Imperial College London, UK)

• 2:45pm - 3:30pm | Sweet Break

• 3:30pm - 5pm | Short contributive talks (20mn)