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Published December 22, 2022 | Submitted
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Second Order Ensemble Langevin Method for Sampling and Inverse Problems


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.

Additional Information

Attribution 4.0 International (CC BY 4.0) The work of ZL is supported by IAIFI through NSF grant PHY2019786. The work of AMS is supported by NSF award AGS1835860, the Office of Naval Research award N00014-17-1-2079 and by a Department of Defense Vannevar Bush Faculty Fellowship.

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August 20, 2023
October 24, 2023