5 papers
A Bregman Proximal Viewpoint on Neural Operators
Abdel-Rahim Mezidi, Jordan Patracone, Saverio Salzo +4
We present several advances on neural operators by viewing the action of operator layers as the minimizers of Bregman regularized optimization problems over Banach function spaces.…
Unrolled-SINDy: A Stable Explicit Method for Non linear PDE Discovery from Sparsely Sampled Data
Fayad Ali Banna, Antoine Caradot, Eduardo Brandao +3
Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown…
Photonic Learning in Ultrafast Laser-Induced Complexity
Fayad Ali Banna, Eduardo Brandao, Anthony Nakhoul +3
How can one design complex systems capable of learning for a given functionality? In the context of ultrafast laser-surface interaction, we unravel the nature of learning schemes t…
Provably Accurate Adaptive Sampling for Collocation Points in Physics-informed Neural Networks
Antoine Caradot, Rémi Emonet, Amaury Habrard +2
Despite considerable scientific advances in numerical simulation, efficiently solving PDEs remains a complex and often expensive problem. Physics-informed Neural Networks (PINN) ha…
Leveraging PAC-Bayes Theory and Gibbs Distributions for Generalization Bounds with Complexity Measures
Paul Viallard, Rémi Emonet, Amaury Habrard +2
In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds,…