Paper Info
Title
Hamiltonian Monte Carlo On Lie Groups And Constrained Mechanics On Homogeneous Manifolds
Abstract
In this paper we show that the Hamiltonian Monte Carlo method for compact Lie groups constructed in [20] using a symplectic structure can be recovered from canonical geometric mechanics with a bi-invariant metric. Hence we obtain the correspondence between the various formulations of Hamiltonian mechanics on Lie groups, and their induced HMC algorithms. Working on Gxg we recover the Euler-Arnold formulation of geodesic motion, and construct explicit HMC schemes that extend [20,21] to non-compact Lie groups by choosing metrics with appropriate invariances. Finally we explain how mechanics on homogeneous spaces can be formulated as a constrained system over their associated Lie groups. In some important cases the constraints can be naturally handled by the symmetries of the Hamiltonian.
Year
DOI
Venue
2019
10.1007/978-3-030-26980-7_69
GEOMETRIC SCIENCE OF INFORMATION
Keywords
Field
DocType
Hamiltonian Monte Carlo, Lie groups, Homogeneous manifolds, MCMC, Symmetric spaces, Sampling, Symmetries, Symplectic integrators
Lie group,Geometric mechanics,Hamiltonian (quantum mechanics),Hybrid Monte Carlo,Symplectic geometry,Mechanics,Hamiltonian mechanics,Mathematics,Homogeneous space,Geodesic
Conference
Volume
ISSN
Citations 
11712
0302-9743
0
PageRank 
References 
Authors
0.34
5
1
Name
Order
Citations
PageRank
Alessandro Barp122.44