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Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently…

Computational Physics · Physics 2019-03-05 Michele Invernizzi , Michele Parrinello

Metadynamics is an established sampling method aimed at reconstructing the free-energy surface relative to a set of appropriately chosen collective variables. In standard metadynamics the free-energy surface is filled by the addition of…

Statistical Mechanics · Physics 2012-07-11 Davide Branduardi , Giovanni Bussi , Michele Parrinello

We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting…

Statistical Mechanics · Physics 2008-03-31 Alessandro Barducci , Giovanni Bussi , Michele Parrinello

In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…

Statistical Mechanics · Physics 2017-12-08 James McCarty , Michele Parrinello

A family of fast sampling methods is introduced here for molecular simulations of systems having rugged free energy landscapes. The methods represent a generalization of a strategy consisting of adjusting a model for the free energy as a…

Computational Physics · Physics 2022-02-07 Pablo F. Zubieta Rico , Juan J. de Pablo

Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to…

Statistical Mechanics · Physics 2018-04-04 Hythem Sidky , Jonathan K. Whitmer

Understanding ion adsorption at electrified metal-electrolyte interfaces is essential for accurate modeling of electrochemical systems. Here, we systematically investigate the free energy profiles of Na$^+$, Cl$^-$, and F$^-$ ions at the…

Chemical Physics · Physics 2026-02-27 Fabrice Roncoroni , Abrar Faiyad , Yichen Li , Tao Ye , Ashlie Martini , David Prendergast

Many biological processes involve numerous coupled degrees of freedom, yet free-energy estimation is often restricted to one-dimensional profiles to mitigate the high computational cost of multidimensional sampling. In this work, we extend…

Statistical Mechanics · Physics 2026-02-12 Daniel Nagel , Tristan Bereau

Quantitative evaluations of the free energy of materials must take into account thermal and zero-point energy fluctuations. While these effects can easily be estimated within a harmonic approximation, corrections arising from the anharmonic…

Materials Science · Physics 2019-06-18 Venkat Kapil , Edgar Engel , Mariana Rossi , Michele Ceriotti

An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force…

Statistical Mechanics · Physics 2008-05-07 David D. L. Minh , Artur B. Adib

The free-energy difference $\Delta F$ between two high-dimensional systems is notoriously difficult to compute, but very important for many applications, such as drug discovery. We demonstrate that an unconventional definition of work…

Soft Condensed Matter · Physics 2024-10-24 Adrianne Zhong , Benjamin Kuznets-Speck , Michael R. DeWeese

In this thesis we examine methodologies for determining free energy differences (FEDs) of phases via Monte Carlo simulation. We identify and address three generic issues that arise in FED calculations; the choice of representation, the…

Statistical Mechanics · Physics 2009-09-29 Arjun R. Acharya

Nonequilibrium, ``fast switching'' estimates of equilibrium free energy differences, Delta F, are often plagued by poor convergence due to dissipation. We propose a method to improve these estimates by generating trajectories with reduced…

Statistical Mechanics · Physics 2009-11-13 Suriyanarayanan Vaikuntanathan , Christopher Jarzynski

We propose a formulation of adaptive computation of free energy differences, in the ABF or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows to present a truly…

Statistical Mechanics · Physics 2015-06-25 Tony Lelievre , Mathias Rousset , Gabriel Stoltz

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In…

Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…

Statistical Mechanics · Physics 2025-11-18 Ping Tuo , Zezhu Zeng , Jiale Chen , Bingqing Cheng

Non-equilibrium path integral methods for computing quantum free energy differences are applied to a quantum particle trapped in a harmonic well of uniformly changing strength with the purpose of establishing the convergence properties of…

Statistical Mechanics · Physics 2009-11-13 Ramses van Zon , Lisandro Hernandez de la Pena , Gilles H. Peslherbe , Jeremy Schofield

Different computational techniques in combination with molecular dynamics computer simulation are used to to determine the wall-liquid and the wall-crystal interfacial free energies of a modified Lennard-Jones (LJ) system in contact with a…

Statistical Mechanics · Physics 2015-06-16 Ronald Benjamin , Jürgen Horbach

Enhanced sampling methods such as metadynamics and umbrella sampling have become essential tools for exploring the configuration space of molecules and materials. At the same time, they have long faced a number of issues such as the…

Chemical Physics · Physics 2021-12-28 Dongdong Wang , Yanze Wang , Junhan Chang , Linfeng Zhang , Han Wang , Weinan E

This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…

Probability · Mathematics 2009-09-15 Pierre Etoré , Gersende Fort , Benjamin Jourdain , Eric Moulines