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

2026-06-25

AI Summary

This work addresses the slow mixing of Langevin dynamics in phase-space regions with high rigidity and complex energy landscapes by proposing the SA-PAL joint sampling scheme. The method integrates SamAdams adaptive timestepping with position-adaptive Langevin (PAL) dynamics, uniquely combining stiffness relaxation monitoring with a rank-one-plus-scalar structured friction tensor and embedding a reversible integrator to enable efficient sampling with only a single force evaluation per step. While rigorously preserving the canonical distribution, SA-PAL substantially enhances sampling efficiency—achieving 1.5–3× faster mixing on the Rosenbrock and Müller-Brown potential energy surfaces and over an order-of-magnitude improvement in other benchmark cases.

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.

Problem

• accelerated sampling
• Langevin dynamics
• adaptive timestepping
• canonical distribution
• mixing rates

Innovation

• adaptive timestepping
• position-adaptive Langevin
• SamAdams
• palindromic integrator
• accelerated sampling