TY - GEN
T1 - Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups
AU - Wu, Meng
AU - Gay-Balmaz, François
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - Motivated by recent advances in stochastic geometric modelling in fluid dynamics, we derive a variational integrator for stochastic Hamiltonian systems on Lie groups by using a discrete version of the stochastic phase space principle. The structure preserving properties of the resulting scheme, such as its symplecticity and preservation of coadjoint orbits are given, as well as a discrete Noether theorem associated to subgroup symmetries. Preliminary numerical illustrations are provided.
AB - Motivated by recent advances in stochastic geometric modelling in fluid dynamics, we derive a variational integrator for stochastic Hamiltonian systems on Lie groups by using a discrete version of the stochastic phase space principle. The structure preserving properties of the resulting scheme, such as its symplecticity and preservation of coadjoint orbits are given, as well as a discrete Noether theorem associated to subgroup symmetries. Preliminary numerical illustrations are provided.
KW - Hamiltonian systems on Lie groups
KW - Stochastic Hamiltonian systems
KW - Variational integrators
UR - https://www.scopus.com/pages/publications/85173542988
U2 - 10.1007/978-3-031-38299-4_23
DO - 10.1007/978-3-031-38299-4_23
M3 - Conference contribution
AN - SCOPUS:85173542988
SN - 9783031382987
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 212
EP - 220
BT - Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer Science and Business Media Deutschland GmbH
T2 - The 6th International Conference on Geometric Science of Information, GSI 2023
Y2 - 30 August 2023 through 1 September 2023
ER -