Coarse-graining Hamiltonian systems using WSINDy.

ABSTRACT: Weak form equation learning and surrogate modeling has proven to be computationally efficient and robust to measurement noise in a wide range of applications including ODE, PDE, and SDE discovery, as well as in coarse-graining applications, such as homogenization and mean-field descriptions of interacting particle systems. In this work we extend this coarse-graining capability to the setting of Hamiltonian dynamics which possess approximate symmetries associated with timescale separation. A smooth ε -dependent Hamiltonian vector field Xε possesses an approximate symmetry if the limiting vector field X0=limε→0Xε possesses an exact symmetry. Such approximate symmetries often lead to the existence of a Hamiltonian system of reduced dimension that may be used to efficiently capture the dynamic

SUBMITTER: Messenger DA 

PROVIDER: S-EPMC11196701 | biostudies-literature | 2024 Jun

REPOSITORIES: biostudies-literature