13 citations · 15 across the 8 of their papers we have counts for
5 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…
Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integrators
Håkon Noren, Sølve Eidnes, Elena Celledoni
We introduce the mean inverse integrator (MII), a novel approach to increase the accuracy when training neural networks to approximate vector fields of dynamical systems from noisy…
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…