Concept
Hamiltonian system
Publications associées (65)
Structure-preserving approaches and data-driven closure modeling for model order reduction
In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...
EPFL2022Locally active globally stable dynamical systems: Theory, learning, and experiments
Aude Billard, Nadia Barbara Figueroa Fernandez
State-dependent dynamical systems (DSs) offer adaptivity, reactivity, and robustness to perturbations in motion planning and physical human-robot interaction tasks. Learning DS-based motion plans from non-linear reference trajectories is an active research ...
SAGE PUBLICATIONS LTD2022Structure-Preserving Reduced Basis Methods For Poisson Systems
Jan Sickmann Hesthaven, Cecilia Pagliantini
We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...
AMER MATHEMATICAL SOC2021Scattering Map for the Vlasov–Poisson System
We construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as t→−∞ to asymptotic dynamics as t→+∞. The main novelty is the construction of modified wave operators, but we also obtain a ...
2021Symplectic dynamical low rank approximation of wave equations with random parameters
Fabio Nobile, Eleonora Musharbash, Eva Vidlicková
In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...
2020Reduction of the sign problem near T=0 in quantum Monte Carlo simulations
Frédéric Mila, Jonathan D'Emidio
Building on a recent investigation of the Shastry-Sutherland model [S. Wessel et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to eliminate the Monte Carlo sign problem near the zero-temperature limit in frustrated quantum spin models ...
AMER PHYSICAL SOC2020Dynamical Reduced Basis Methods for Hamiltonian Systems
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...
2019