Lieu : IHP, amphi Yvonne Choquet-Bruhat (second étage du bâtiment Perrin)
14.00 : Olympio Hacquard (Kyoto University)
Titre : Persistence diagrams, use and limitations
Résumé : Persistence diagram is a central tool in topological data analysis, aiming at characterizing all topological information present in a data set. We will show how to use it to perform a regression task, by providing a topological characterization of functional noise. Given its high level of detail, persistence diagrams suffer from some computational drawbacks making their practical use limited. We will present some alternative topological descriptors based on Euler characteristic computation that provide a high classification performance at a much reduced computational cost. This presentation is based on joint works with Krishnakumar Balasubramanian, Gilles Blanchard, Vadim Lebovici, Clément Levrard and Wolfgang Polonik.
15.00 : Nathan Doumèche (Sorbonne Université)
Titre : Efficient learning with physical priors
Résumé : Physics-informed machine learning is a new framework which intends to integrate constraints of different kinds into machine learning models in order to make them more interpretable and more efficient. In this context, we have developed a common framework to integrate various kinds of linear constraints such as additive models, adaptive modelling, transfer learning, hierarchical forecasting, and PDE constraints. This common framework makes it possible to provide exact formulas for the minimizer of the empirical risk under such constraints. Moreover, these formulas only involve linear algebra, and can be run on polynomial time on GPU. In this talk, we will illustrate this principle with several examples from PDE solving, electricity load forecasting, and tourism demand forecasting. (Joint work with Francis Bach, Gérard Biau, Claire Boyer and Yannig Goude.)
16.00 : Mathilde Mougeot (ENS Paris-Saclay)
Titre : Physics Informed Machine Learning models & Industrial applications
Résumé : In recent years, significant progress has been made in setting up decision support systems based on machine learning exploiting very large databases. In many research or production environments, the available databases are not very large, and the question arises as to whether it makes sense to rely on machine learning models in this context. Especially in the industrial sector, designing accurate machine learning models with an economy of data is nowadays a major challenge. This talk presents Physical Informed Machine Learning models that leverage Physics to implement machine learning models with an economy of data.
References:
Fixed-Budget Online Adaptive Learning for Physics-Informed Neural Networks. Towards Parameterized Problem Inference TNK Nguyen, et al. International Conference on Computational Science, 2023.
Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering process, TNK Nguyen, et aL Engineering Applications of Artificial Intelligence, 2023.