Lie-Butcher

Post-processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds

Announce Type: new Abstract: In this work, we propose a novel intrinsic approach to the approximation of ergodic SDEs on Riemannian manifolds, which include Riemannian Langevin dynamics. In opposition to the standard extrinsic approaches such as penalization methods and projection methods, our methodology does not use embeddings or coordinates and only relies on natural geometric operations: geodesics, parallel transport,... We give a criterion for high order of accuracy for the invariant...