50 citations · 330 across the 31 of their papers we have counts for
6 papers · 1 filter
Differential geometry and stochastic dynamics with deep learning numerics
Line Kühnel, Alexis Arnaudon, Stefan Sommer
In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently u…
Stochastic metamorphosis with template uncertainties
Alexis Arnaudon, Darryl Holm, Stefan Sommer
In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincaré theory. In the metamor…
Bridge Simulation and Metric Estimation on Landmark Manifolds
Stefan Sommer, Alexis Arnaudon, Line Kuhnel +1
We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition d…
A Geometric Framework for Stochastic Shape Analysis
Alexis Arnaudon, Darryl D. Holm, Stefan Sommer
We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is i…
The Stochastic Energy-Casimir Method
Alexis Arnaudon, Nader Ganaba, Darryl Holm
In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of…
-Strands on symmetric spaces
Alexis Arnaudon, Darryl D. Holm, Rossen I. Ivanov
We study the -strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces…