8 papers
Structural schemes for hamiltonian systems
Stéphane Clain, Emmanuel Franck, Victor Michel-Dansac
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled diff…
Non-linear control variate in δf particle-in-cell methods using symplectic neural networks
Victor Fournet, Martin Campos Pinto, Emmanuel Franck +1
We present a novel δf particle-in-cell (PIC) method for the kinetic simulation of electrostatic plasmas in which the bulk density, acting as a control variate, is evolved using sy…
Implementation of a shooting technique for quantum optimal control on spin qudits
Paul-Louis Etienney, Denis JankoviÄ, Killian Lutz +3
High-fidelity quantum control is a cornerstone of scalable quantum technologies. We introduce a shooting-based optimization framework that generates smooth, experimentally realisti…
Enriching continuous Lagrange finite element approximation spaces using neural networks
Hélène Barucq, Michel Duprez, Florian Faucher +5
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural netw…
Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
Emmanuel Franck, Victor Michel-Dansac, Laurent Navoret +1
This work is devoted to the numerical approximation of high-dimensional advection-diffusion equations. It is well-known that classical methods, such as the finite volume method, su…
Generalizing the SINDy approach with nested neural networks
Camilla Fiorini, Clément Flint, Louis Fostier +4
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinea…