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Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of…

Statistical Mechanics · Physics 2026-04-02 Maximilian Schebek , Nikolas M. Froböse , Bettina G. Keller , Jutta Rogal

The accurate prediction of phase diagrams is of central importance for both the fundamental understanding of materials as well as for technological applications in material sciences. However, the computational prediction of the relative…

Statistical Mechanics · Physics 2024-11-26 Maximilian Schebek , Michele Invernizzi , Frank Noé , Jutta Rogal

We present a machine-learning approach, based on normalizing flows, for modelling atomic solids. Our model transforms an analytically tractable base distribution into the target solid without requiring ground-truth samples for training. We…

In this work the free energy of solid phases is computed for the Lennard-Jones potential and for a model of NaCl. The free energy is evaluated through the Einstein crystal/molecule methodologies using the Molecular Dynamics programs:…

Soft Condensed Matter · Physics 2012-10-16 J. L. Aragones , C. Valeriani , C. Vega

Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems…

Computational Physics · Physics 2026-03-31 Emil Hoffmann , Maximilian Schebek , Leon Klein , Frank Noé , Jutta Rogal

This paper introduces a method for computing the Helmholtz free energy using the flow matching technique. Unlike previous work that utilized flow-based models for variational free energy calculations, this method provides bounds for free…

Computational Physics · Physics 2025-01-03 Lu Zhao , Lei Wang

We describe a self-contained procedure to evaluate the free energy of liquid and solid phases of an alloy system. The free energy of a single-element solid phase is calculated with thermodynamic integration using the Einstein crystal as the…

Statistical Mechanics · Physics 2021-02-05 Lin Yang , Yang Sun , Zhuo Ye , Feng Zhang , Mikhail I. Mendelev , Cai-Zhuang Wang , Kai-Ming Ho

The recently proposed Einstein molecule approach is extended to compute the free energy of molecular solids. This method is a variant of the Einstein crystal method of Frenkel and Ladd[J. Chem. Phys. 81,3188 (1984)]. In order to show its…

Statistical Mechanics · Physics 2009-01-14 E. G. Noya , M. M. Conde , C. Vega

Boltzmann generators (BGs) are now recognized as forefront generative models for sampling equilibrium states of many-body systems in the canonical ensemble, as well as for calculating the corresponding Helmholtz free energy. Furthermore,…

Statistical Mechanics · Physics 2023-05-16 Steyn van Leeuwen , Alberto Pérez de Alba Ortíz , Marjolein Dijkstra

The Gibbs free energy is the fundamental thermodynamic potential underlying the relative stability of different states of matter under constant-pressure conditions. However, computing this quantity from atomic-scale simulations is far from…

Materials Science · Physics 2018-02-14 Bingqing Cheng , Michele Ceriotti

We propose a new method to compute the free energy or enthalpy of fluids or disordered solids by computer simulation . The main idea is to construct a reference system by freezing one representative configuration, and then carry out a…

Computational Physics · Physics 2011-03-16 Friederike Schmid , Tanja Schilling

We devise automated workflows for the calculation of Helmholtz and Gibbs free energies and their temperature and pressure dependence and provide the corresponding computational tools. We employ non-equilibrium thermodynamics for evaluating…

Materials Science · Physics 2021-10-13 Sarath Menon , Yury Lysogorskiy , Jutta Rogal , Ralf Drautz

We present a machine-learning model based on normalizing flows that is trained to sample from the isobaric-isothermal ensemble. In our approach, we approximate the joint distribution of a fully-flexible triclinic simulation box and particle…

Computational Physics · Physics 2023-09-07 Peter Wirnsberger , Borja Ibarz , George Papamakarios

In this work, we consider the problem of training a generator from evaluations of energy functions or unnormalized densities. This is a fundamental problem in probabilistic inference, which is crucial for scientific applications such as…

Machine Learning · Computer Science 2024-08-30 Dongyeop Woo , Sungsoo Ahn

We perform deep variational free energy calculations to investigate the dense hydrogen system at 1200 K and high pressures. In this computational framework, neural networks are used to model the free energy through the proton Boltzmann…

Computational Physics · Physics 2025-07-01 Xinyang Dong , Hao Xie , Yixiao Chen , Wenshuo Liang , Linfeng Zhang , Lei Wang , Han Wang

The accurate estimation of free energy differences between two states is a long-standing challenge in molecular simulations. Traditional approaches generally rely on sampling multiple intermediate states to ensure sufficient overlap in…

Statistical Mechanics · Physics 2026-03-17 Maximilian Schebek , Jiajun He , Emil Hoffmann , Yuanqi Du , Frank Noé , Jutta Rogal

Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in "one shot", vast computational…

Machine Learning · Statistics 2019-07-15 Frank Noé , Simon Olsson , Jonas Köhler , Hao Wu

Sets of free energy differences are useful for finding the equilibria of chemical reactions, while absolute free energies have little physical meaning. However finding the relative free energy between two macrostates by subtraction of their…

Statistical Mechanics · Physics 2012-11-26 Joshua T. Berryman , Tanja Schilling

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…

Soft Condensed Matter · Physics 2024-09-16 Gerhard Jung , Giulio Biroli , Ludovic Berthier

We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model…

Strongly Correlated Electrons · Physics 2023-09-26 Hao Xie , Zi-Hang Li , Han Wang , Linfeng Zhang , Lei Wang
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