Scientific Machine Learning: error control and analysis
Besançon, January 15-16 2025
The purpose of this workshop is to stimulate the discussion on a priori and a posteriori error analysis in Scientific Machine Learning (SciML) and Model Reduction, and to foster the development of mathematical techniques for error control in SciML.
The topics of the workshop include neural networks and neural operators for PDEs, nonlinear reduced order modeling, low-rank approximation, operator learning, interactions between model order reduction and SciML, etc.
Schedule at a glance
Wednesday, January 15
9:55 - 10:00 Opening
10:00 - 12:15 Talks
13:45 - 15:15 Talks
15:15 - 15:45 Coffee Break
15:45 - 18:00 Talks
Thursday, January 16
9:00 - 10:30 Talks
10:30 - 11:00 Coffee Break
11:00 - 12:30 Talks
14:00 - 14:45 Talks
14:45 - 15:00 Coffee Break
15:00 - 16:30 Talks
Speakers & talk titles
Markus Bachmayr (RWTH Aachen)
Variationally correct residual regression for parametric PDEsEmmanuel de Bézenac (INRIA Paris)
Some insights in operator learning for solving PDEsGabriel Clara (Universiteit Twente)
Dropout Regularization Versus L²-Penalization in the Linear ModelVirginie Ehrlacher (ENPC Paris)
Analysis of gradient descent in neural networks for some PDEsEmmanuel Franck (IRMA Strasbourg)
Structure preserving learning for ODE and PDE
Nicola Rares Franco (Politecnico di Milano)
Opening the black-box: approximation and generalization properties of convolutional neural networks in surrogate modeling
Diane Guignard (University of Ottawa)
Library-based nonlinear reduced modeling
Alexander Heinlein (TU Delft)
Samuel Lanthaler (Caltech)
Generative AI for the statistical computation of fluidsVictor Michel-Dansac (IRMA Strasbourg)
Improving the accuracy of classical methods with physics-informed basis functionsAnthony Nouy (Centrale Nantes)
Nonlinear model reduction using compositional polynomial networksNiklas Reinhardt (Universität Heidelberg)
Statistical Learning Theory for Neural OperatorsTommaso Taddei (INRIA Bordeaux)
Registration in bounded domains for model reduction of parametric conservation laws
Organizers
Geneviève Dusson (CNRS, Université de Franche-Comté Besançon)
Carlo Marcati (Università di Pavia)