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Updated: Feb 23, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Stratified UWHAM and Its Stochastic Approximation for Multicanonical Simulations Which Are Far from Equilibrium
Bin W Zhang1, Nanjie Deng2, Zhiqiang Tan3
1Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States.
Abstract:
We describe a new analysis tool called Stratified unbinned Weighted Histogram Analysis Method (Stratified-UWHAM), which can be used to compute free energies and expectations from a multicanonical ensemble when a subset of the parallel simulations is far from being equilibrated because of barriers between free energy basins which are only rarely (or never) crossed at some states. The Stratified-UWHAM equations can be obtained in the form of UWHAM equations but with an expanded set of states. We also provide a stochastic solver, Stratified RE-SWHAM, for Stratified-UWHAM to remove its computational bottleneck. Stratified-UWHAM and Stratified RE-SWHAM are applied to study three test topics: the free energy landscape of alanine dipeptide, the binding affinity of a host-guest binding complex, and path sampling for a two-dimensional double well potential. The examples show that when some of the parallel simulations are only locally equilibrated, the estimates of free energies and equilibrium distributions provided by the conventional UWHAM (or MBAR) solutions exhibit considerable biases, but the estimates provided by Stratified-UWHAM and Stratified RE-SWHAM agree with the benchmark very well. Lastly, we discuss features of the Stratified-UWHAM approach which is based on coarse-graining in relation to two other maximum likelihood-based methods which were proposed recently, that also coarse-grain the multicanonical data.
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