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.
9:45 - 10:00 Opening
10:00 - 12:30 Talks
14:00 - 15:30 Talks
15:30 - 16:00 Coffee Break
16:00-17:30 Talks
9:15 - 10:45 Talks
10:45 - 11:15 Coffee Break
11:15 - 12:00 Talks
13:30 - 15:45 Talks
15:45 - 16:00 Closing
Markus Bachmayr (RWTH Aachen)
Variationally correct residual regression for parametric PDEs
Emmanuel de Bézenac (INRIA Paris)
Some insights in operator learning for solving PDEs
Gabriel Clara (Universiteit Twente)
Dropout Regularization Versus L²-Penalization in the Linear Model
Virginie Ehrlacher (ENPC Paris)
Analysis of gradient descent in neural networks for some PDEs
Laurent Navoret (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)
Domain decomposition and adaptive sampling for physics-informed neural networks
Samuel Lanthaler (Caltech)
Generative AI for the statistical computation of fluids
Victor Michel-Dansac (IRMA Strasbourg)
Improving the accuracy of classical methods with physics-informed basis functions
Anthony Nouy (Centrale Nantes)
Nonlinear model reduction using compositional polynomial networks
Niklas Reinhardt (Universität Heidelberg)
Statistical Learning Theory for Neural Operators
Tommaso Taddei (INRIA Bordeaux)
Registration in bounded domains for model reduction of parametric conservation laws
Geneviève Dusson (CNRS, Université de Franche-Comté Besançon)
Carlo Marcati (Università di Pavia)