BU-MBAR: A hybrid solution strategy for the MBAR equations
Abstract
The multi-state Bennett acceptance ratio (MBAR) equations combine the data collected under different thermodynamic conditions in a statistically optimal way. Due to their practical importance, several solution strategies have been devised to optimize the convergence of the resulting set of coupled equations. However, even with graphics processing unit (GPU) acceleration, the convergence of these methods can still be either unstable or slow. We propose a new approach where the equations are interpreted as the limit of infinitesimal bin width of the respective weighted histogram analysis method (WHAM). In the proposed binned-to-unbinned MBAR (BU-MBAR) method, the bin width is adapted dynamically to ensure a stable and efficient convergence to the asymptotic solution.
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BibTeX
@misc{muller2026bumbar,
title = {{BU-MBAR: A hybrid solution strategy for the MBAR equations}},
author = {Fabio Müller and Francesco Alesiani and Henrik Christiansen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03541},
eprint = {2609.03541},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03541},
}
RIS
TY - UNPB
TI - BU-MBAR: A hybrid solution strategy for the MBAR equations
AU - Fabio Müller
AU - Francesco Alesiani
AU - Henrik Christiansen
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03541
UR - https://arxiv.org/abs/2609.03541
AB - The multi-state Bennett acceptance ratio (MBAR) equations combine the data collected under different thermodynamic conditions in a statistically optimal way. Due to their practical importance, several solution strategies have been devised to optimize the convergence of the resulting set of coupled equations. However, even with graphics processing unit (GPU) acceleration, the convergence of these methods can still be either unstable or slow. We propose a new approach where the equations are interpreted as the limit of infinitesimal bin width of the respective weighted histogram analysis method (WHAM). In the proposed binned-to-unbinned MBAR (BU-MBAR) method, the bin width is adapted dynamically to ensure a stable and efficient convergence to the asymptotic solution.
ER -