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Efficient Langevin sampling with position-dependent diffusion

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arxiv 2501.02943 v2 pith:MFDLNR6W submitted 2025-01-06 math.NA cs.NA

Eugen Bronasco , Benedict Leimkuhler , Dominic Phillips , Gilles Vilmart This is my paper · ORCID
classification math.NAcs.NA
keywords samplingdiffusionmethodnumericalorderaccuratealgebraicanalysis
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We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the sampling bias is performed using the algebraic framework of exotic aromatic Butcher-series. Numerical experiments confirm the theoretical order of convergence and illustrate the efficiency of the new method.

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  1. Backward error analysis for matrix discretizations of 2-D Euler equations

    math.NA 2026-07 accept novelty 8.0 of 10

    ISOSYRK methods on Zeitlin’s Euler–Zeitlin system admit n-independent exponentially small modified-Hamiltonian errors for times exp(c/ε) when h = ε ℏ_n.

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