40 citations · 199 across the 12 of their papers we have counts for
14 papers
Data-driven structure-preserving model reduction for stochastic Hamiltonian systems
Tomasz M. Tyranowski
In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to sto…
Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations
Tomasz M. Tyranowski
In this work we recast the collisional Vlasov-Maxwell and Vlasov-Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic var…
Symplectic model reduction methods for the Vlasov equation
Tomasz M. Tyranowski, Michael Kraus
Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solvin…
Variational integrators for stochastic dissipative Hamiltonian systems
Michael Kraus, Tomasz M. Tyranowski
Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which…
New variational and multisymplectic formulations of the Euler-Poincaré equation on the Virasoro-Bott group using the inverse map
Darryl D. Holm, Tomasz M. Tyranowski
We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler--Poincaré equations defined on the Virasoro-Bott gr…
Stochastic Discrete Hamiltonian Variational Integrators
Darryl D. Holm, Tomasz M. Tyranowski
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics…