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math.NA2025
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…
math.NA2024
Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
Joubine Aghili, Emmanuel Franck, Romain Hild +2
It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to…
math.NA2024
Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network
Raphaël Côte, Emmanuel Franck, Laurent Navoret +2
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the…