Algebraic structures and numerical methods for invariant measure sampling of Langevin dynamics

Diplôme Thèse Algebraic structures and numerical methods for invariant measure sampling of Langevin dynamics eng 2025-03-27 2025-03-26 author Bronasco Eugen 925179 director Vilmart Gilles 0000-0003-4593-1012 637852 Section de mathématiques (MATH) director Manchon Dominique 119 10.13097/archive-ouverte/unige:185162 urn:nbn:ch:unige-1851623 Sc. 5897 <p>We develop the framework of exotic forests to study the algebraic structures underlying numerical integrators for sampling the invariant measure of Langevin dynamics. Leveraging these algebraic structures, we introduce a formal algorithm for generating order conditions for invariant measure sampling and prove that a large subset of these conditions is satisfied automatically. Building on these insights, we derive an efficient second-order integrator for sampling the invariant measure of Langevin dynamics with position-dependent diffusion.</p> <p>We then consider a broader set of exotic forests that includes graph structures known as aromas and stolons, which play a crucial role in geometric numerical integration. We analyze their associated composition and substitution laws, enabling the study of integrator composition, post-processing, backward error analysis, and modified equation techniques within the Butcher series framework. Given the rapidly increasing complexity of the forest structures we consider, we develop a Haskell package to automate computations involving algebras over forests.</p> Dewey 510 25 Section de mathématiques 11 false 847 Analyse numérique a0fd6271-fe06-472d-b025-9a9faaca4244 Thesis Public Bronasco_thesis_corrected.pdf 20642912 application/pdf 017a00ff369e060ab18469040ca81a11af416633670c9367c8964dfbb5061096 e2cdab5a-e260-4ea2-9cee-aaf972da27f9 Imprimatur Public Imprimatur.pdf 46932 application/pdf 26720581a5be1ab2bb8299f792b308723d0d4e0272620617656f7d8494c4c902 openAccess Faculté des sciences / Section de mathématiques

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Algebraic structures and numerical methods for invariant measure sampling of Langevin dynamics				2025	209	128

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