From the 1 of 5.5k papers with an AI index.
- Centre National de la Recherche ScientifiqueFR1.7k papers
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- École Normale Supérieure - PSLFR292 papers
- Sorbonne UniversitéFR291 papers
- École Normale Supérieure de LyonFR233 papers
- Centre Inria de l'Université Grenoble AlpesFR216 papers
- Université Paris-SaclayFR208 papers
- Université Grenoble AlpesFR204 papers
- Lyon 1 UniversitéFR191 papers
- Centre Inria d'Université Côte d'AzurFR183 papers
306 papers · 1 filter
Neural Network Preconditioning: A Case Study for the Solution of the Parametric Helmholtz Equation
Luc Giraud, Carola Kruse, Paul Mycek +2
This work presents a hybrid numerical approach for solving linear systems arising from the discretization of the two-dimensional parametric Helmholtz equation. A convolutional neur…
A Fully Discrete Nonnegativity-Preserving FEM for a Stochastic Heat Equation
Owen Hearder, Claude Le Bris, Ana Djurdjevac
We consider a stochastic heat equation with nonlinear finite-rank space-coloured multiplicative noise that admits a unique nonnegative solution when given nonnegative initial data.…
Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs
Kateřina Škardová, Alexandre Daby-Seesaram, Martin Genet
We present the Finite Element Neural Network Interpolation (FENNI) framework, a sparse neural network architecture extending previous work on Embedded Finite Element Neural Network…
A generalized spectral concentration problem and the varying masks algorithm
Erwan Faou, Yoann Le Henaff
In this paper we generalize the spectral concentration problem as formulated by Slepian, Pollak and Landau in the 1960s. We show that a generalized version with arbitrary space and…
Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form
Hendrik Ranocha, Mario Ricchiuto
We develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requi…
Low-rank plus diagonal approximations for Riccati-like matrix differential equations
Silvère Bonnabel, Marc Lambert, Francis Bach
We consider the problem of computing tractable approximations of time-dependent d x d large positive semi-definite (PSD) matrices defined as solutions of a matrix differential equa…