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arXiv · 2606.26881

Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics

Benedict Leimkuhler·Peter A. Whalley
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Abstract

We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: \emph{SamAdams} adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and \emph{position-adaptive Langevin} (PAL) dynamics, which concentrates friction along the local force direction while preserving the canonical distribution as the exact invariant measure. The resulting combined scheme (SA-PAL) is implemented in a palindromic integrator which requires only one force evaluation per iteration through suitable organisation of the integration steps and by exploiting the rank-one-plus-scalar structure of the PAL friction tensor. We test the method on various model problems: the Rosenbrock function, a thin entropic channel, the Mueller-Brown potential, and a Bayesian parameterisation problem with a sparsity-inducing shrinkage prior. On the Rosenbrock and Mueller-Brown potentials mixing rates are improved by 1.5-3 times compared to fixed stepsize integration. Efficiency gains of more than an order of magnitude are documented in the other examples.

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Benedict Leimkuhler, Peter A. Whalley. 2026-06-25. Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics. https://arxiv.org/abs/2606.26881

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