Second Order Ensemble Langevin Method for Sampling and Inverse Problems

@article{Liu2022SecondOE,
  title={Second Order Ensemble Langevin Method for Sampling and Inverse Problems},
  author={Ziming Liu and Andrew M. Stuart and Yixuan Wang},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.04506}
}
. 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… 

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