Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups

Meng Wu; François Gay-Balmaz

doi:10.1007/978-3-031-38299-4_23

Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups

Meng Wu
, François Gay-Balmaz

PSL research University & IPSL

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	English
Title of host publication	Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings
Editors	Frank Nielsen, Frédéric Barbaresco
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	212-220
Number of pages	9
ISBN (Print)	9783031382987
DOIs	https://doi.org/10.1007/978-3-031-38299-4_23
Publication status	Published - 1 Jan 2023
Event	The 6th International Conference on Geometric Science of Information, GSI 2023 - St. Malo, France Duration: 30 Aug 2023 → 1 Sept 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14072 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	The 6th International Conference on Geometric Science of Information, GSI 2023
Country/Territory	France
City	St. Malo
Period	30/08/23 → 1/09/23

Keywords

Hamiltonian systems on Lie groups
Stochastic Hamiltonian systems
Variational integrators

Access to Document

10.1007/978-3-031-38299-4_23

Cite this

Wu, M., & Gay-Balmaz, F. (2023). Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups. In F. Nielsen, & F. Barbaresco (Eds.), Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings (pp. 212-220). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14072 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-38299-4_23

Wu, Meng ; Gay-Balmaz, François. / Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups. Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings. editor / Frank Nielsen ; Frédéric Barbaresco. Springer Science and Business Media Deutschland GmbH, 2023. pp. 212-220 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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.",

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Wu, M & Gay-Balmaz, F 2023, Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups. in F Nielsen & F Barbaresco (eds), Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14072 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 212-220, The 6th International Conference on Geometric Science of Information, GSI 2023, St. Malo, France, 30/08/23. https://doi.org/10.1007/978-3-031-38299-4_23

Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups. / Wu, Meng; Gay-Balmaz, François.
Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings. ed. / Frank Nielsen; Frédéric Barbaresco. Springer Science and Business Media Deutschland GmbH, 2023. p. 212-220 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14072 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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Wu M, Gay-Balmaz F. Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups. In Nielsen F, Barbaresco F, editors, Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 212-220. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-38299-4_23