BU-MBAR: A hybrid solution strategy for the MBAR equations

Fabio Müller; Francesco Alesiani; Henrik Christiansen

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arXiv · 2609.03541

BU-MBAR: A hybrid solution strategy for the MBAR equations

Fabio Müller·Francesco Alesiani·Henrik Christiansen

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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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Fabio Müller, Francesco Alesiani, Henrik Christiansen. 2026-09-03. BU-MBAR: A hybrid solution strategy for the MBAR equations. https://arxiv.org/abs/2609.03541

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