From the 2 of 9 linked papers with an AI index.
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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…
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…
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…
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…
Neural networks for the approximation of Euler's elastica
Elena Celledoni, Ergys Ãokaj, 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…