4 papers
Neural non-canonical Hamiltonian dynamics for long-time simulations
Clémentine Courtès, Emmanuel Franck, Michael Kraus +2
This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numer…
Hermite Semi-Lagrangian schemes on triangular meshes for advection equations
Ali Elarif, Michel Mehrenberger, Laurent Navoret
High-order Hermite semi-Lagrangian schemes on unstructured triangular grids are proposed for advection equations, based on Bell and Argyris finite elements. Nodal semi-Lagrangian s…
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…
Reduced Particle in Cell method for the Vlasov-Poisson system using auto-encoder and Hamiltonian neural
Emmanuel Franck, Laurent Navoret, Vincent Vigon +2
Hamiltonian particle-based simulations of plasma dynamics are inherently computationally intensive, primarily due to the large number of particles required to obtain accurate solut…