6 papers
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…
1-Lipschitz Neural Networks on Hadamard Manifolds
Davide Murari, Marta Ghirardelli, Ben Adcock +4
Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability. Most existing constraining strategies are designed for Euclidean space…
Learning Forced Multibody Dynamics on Lie Groups
Martine Dyring Hansen, Marta Ghirardelli, Elena Celledoni +2
The paper presents a learning architecture that models mechanical system dynamics using discrete forced Euler-Lagrange equations on Lie groups, requiring only position measurements…
Mixed Precision Training of Neural ODEs
Elena Celledoni, Brynjulf Owren, Lars Ruthotto +1
Exploiting low-precision computations has become a standard strategy in deep learning to address the growing computational costs imposed by ever larger models and datasets. However…
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…