303 citations · 796 across the 37 of their papers we have counts for
4 papers · 1 filter
Neural networks for the approximation of Euler's elastica
Elena Celledoni, Ergys Çokaj, Andrea Leone +5
Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational princi…
B-stability of numerical integrators on Riemannian manifolds
Martin Arnold, Elena Celledoni, Ergys Çokaj +2
We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration fr…
Designing Stable Neural Networks using Convex Analysis and ODEs
Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt +3
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lip…
Predictions Based on Pixel Data: Insights from PDEs and Finite Differences
Elena Celledoni, James Jackaman, Davide Murari +1
As supported by abundant experimental evidence, neural networks are state-of-the-art for many approximation tasks in high-dimensional spaces. Still, there is a lack of a rigorous t…