Speaker: Daniel McBride, UTK

Title: Symplectic numerical integration for constrained Hamiltonian systems
 

Abstract: The accurate and efficient integration of Hamiltonian systems is central to Hamiltonian Monte Carlo, a common method used in high-dimensional Bayesian data analysis. This talk presents symplectic numerical integration methods tailored for Hamiltonian systems arising in moment-constrained data applications. We explore the challenges posed by such constraints, such as maintaining geometric properties, dynamical properties and stability over long integration times. We will also discuss the preservation of the phase space measure structure on a constraint manifold potentially characterized by multiple scales. The talk will cover the development of these integrators, key theoretical results, and numerics as they relate to applications in moment-constrained Bayesian inversion.