303 citations · 717 across the 42 of their papers we have counts for
4 papers · 1 filter
Dynamical systems' based neural networks
Elena Celledoni, Davide Murari, Brynjulf Owren +2
Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is…
Using aromas to search for preserved measures and integrals in Kahan's method
Geir Bogfjellmo, Elena Celledoni, Robert McLachlan +2
The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit pr…
Deep neural networks on diffeomorphism groups for optimal shape reparameterization
Elena Celledoni, Helge Glöckner, Jørgen Riseth +1
One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization rea…
Learning Hamiltonians of constrained mechanical systems
Elena Celledoni, Andrea Leone, Davide Murari +1
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in c…