# 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…

## One Citation

### Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics

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