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Publication in SIAM Journal on Numerical Analysis

Boltzmann measures on level-sets of reaction coordinates can be sampled by projection-based sampling schemes.

News from Dec 06, 2021

Calculating averages with respect to probability measures on submanifolds is often necessary in various application areas such as molecular dynamics, computational statistical mechan- ics and Bayesian statistics. In recent years, various numerical schemes have been proposed in the literature to study this problem based on appropriate reversible constrained stochastic dynamics. In this paper we present and analyze a nonreversible generalization of the projection-based scheme developed by Zhang [ESAIM M2AN, 54 (2020), pp. 391-430]. This scheme consists of two steps: starting from a state on the submanifold, we first update the state using a nonreversible stochastic differential equation which takes the state away from the submanifold, and in the second step we project the state back onto the manifold using the long-time limit of an ordinary differential equa- tion. We prove the consistency of this numerical scheme and provide quantitative error estimates for estimators based on finite-time running averages. Furthermore, we present theoretical analysis which shows that this scheme outperforms its reversible counterpart in terms of asymptotic variance. We demonstrate our findings on an illustrative test example.

U. Sharma and W. Zhang,
Non-reversible sampling schemes on sub-manifolds.
SIAM J. Numer. Anal. 59(6), 2989-3031 (2021).

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