13 citations · 15 across the 3 of their papers we have counts for
5 papers · 1 filter
Approximation properties of neural ODEs
Arturo De Marinis, Davide Murari, Elena Celledoni +3
We study the approximation properties of neural ordinary differential equations (neural ODEs) in the space of continuous functions. Since a neural ODE requires input and output dim…
Conditional Stability of the Euler Method on Riemannian Manifolds
Marta Ghirardelli, Brynjulf Owren, Elena Celledoni
We derive nonlinear stability results for numerical integrators on Riemannian manifolds, by imposing conditions on the ODE vector field and the step size that makes the numerical s…
Dynamics of the N-fold Pendulum in the framework of Lie Group Integrators
Elena Celledoni, Ergys Çokaj, Andrea Leone +2
Since their introduction, Lie group integrators have become a method of choice in many application areas. Various formulations of these integrators exist, and in this work we focus…
Lie Group integrators for mechanical systems
Elena Celledoni, Ergys Çokaj, Andrea Leone +2
Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data scie…
The Magnus expansion and Post-Lie algebras
Charles Curry, Kurusch Ebrahimi-Fard, Brynjulf Owren
We relate the classical and post-Lie Magnus expansions. Intertwining algebraic and geometric arguments allows to placing the classical Magnus expansion in the context of Lie group…