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A Unified Discrete Gradient-SAV Framework for Structure-Preserving Integration
Elena Celledoni, David MartÃn de Diego, Brynjulf Owren +1
The paper introduces a unified framework that combines discrete gradient methods with the Scalar Auxiliary Variable (SAV) approach to create structure‑preserving integrators for bo…
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…