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arXiv · 2208.04506

Second Order Ensemble Langevin Method for Sampling and Inverse Problems

Ziming Liu·Andrew M. Stuart·Yixuan Wang
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Abstract

We propose a sampling method based on an ensemble approximation of second order Langevin dynamics. The log target density is appended with a quadratic term in an auxiliary momentum variable and damped-driven Hamiltonian dynamics introduced; the resulting stochastic differential equation is invariant to the Gibbs measure, with marginal on the position coordinates given by the target. A preconditioner based on covariance under the law of the dynamics does not change this invariance property, and is introduced to accelerate convergence to the Gibbs measure. The resulting mean-field dynamics may be approximated by an ensemble method; this results in a gradient-free and affine-invariant stochastic dynamical system. Numerical results demonstrate its potential as the basis for a numerical sampler in Bayesian inverse problems.

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BibTeXRIS

Ziming Liu, Andrew M. Stuart, Yixuan Wang. 2022-08-09. Second Order Ensemble Langevin Method for Sampling and Inverse Problems. https://arxiv.org/abs/2208.04506

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