Computational and Applied Mathematics seminar

Abstract: This talk explores the problem of sampling the invariant measure of Langevin dynamics through the lens of exotic aromatic forests — a specialized class of graphs forming an algebra that represents the algebra of differential operators. Such algebraic structures play a fundamental role in particular for the numerical analysis of numerical integrators. We establish the connection between exotic aromatic forests and numerical methods, introducing the relevant algebraic structures and their applications. A key focus is the construction of a novel method of order two for invariant measure sampling, derived using the framework of exotic aromatic forests. Additionally, we demonstrate how these tools generate order conditions with favorable algebraic properties, facilitate the representation of composition and substitution in numerical integrators, and support backward error analysis and the computation of modified equations. We conclude with an overview of a new Haskell package designed to automate computations involving graph algebras.

Papers and preprints available at: www.unige.ch/~bronasco