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We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct…

Statistical Mechanics · Physics 2011-12-30 Jian-Sheng Wang , Robert H. Swendsen

Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…

Computation · Statistics 2025-12-23 Ravi Prasad

We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical Quantum Monte Carlo methods properly extended to quantum and thermal crystals, simulated by Coupled Electron Ion Monte…

Materials Science · Physics 2020-03-25 Vitaly Gorelov , Markus Holzmann , David M. Ceperley , Carlo Pierleoni

We explore different ways to simplify the evaluation of the smooth overlap of atomic positions (SOAP) many-body atomic descriptor [Bart\'{o}k et al., Phys. Rev. B 87, 184115 (2013)]. Our aim is to improve the computational efficiency of…

Computational Physics · Physics 2019-09-16 Miguel A. Caro

Physics-based, atom-centered machine learning (ML) representations have been instrumental to the effective integration of ML within the atomistic simulation community. Many of these representations build off the idea of atoms as having…

Computational Physics · Physics 2024-03-29 Arthur Y. Lin , Kevin K. Huguenin-Dumittan , Yong-Cheol Cho , Jigyasa Nigam , Rose K. Cersonsky

Machine Learning Inter-atomic Potentials (MLIPs) have become a common tool in use by computational chemists due to their combination of accuracy and speed. Yet, it is still not clear how well these tools behave at or near transitions states…

Chemical Physics · Physics 2022-11-15 Aaron Philip , Guoqing Zhou , Benjamin Nebgen

Treating realistically the ambient water is one of the main difficulties in applying Monte Carlo methods to protein folding. The solvent-accessible area method, a popular method for treating water implicitly, is investigated by means of…

Soft Condensed Matter · Physics 2007-05-23 Hsiao-Ping Hsu , Bernd A. Berg , Peter Grassberger

Langevin algorithms are popular Markov chain Monte Carlo (MCMC) methods for large-scale sampling problems that often arise in data science. We propose Monte Carlo algorithms based on the discretizations of $P$-th order Langevin dynamics for…

Machine Learning · Statistics 2025-08-26 Thanh Dang , Mert Gurbuzbalaban , Mohammad Rafiqul Islam , Nian Yao , Lingjiong Zhu

Machine learning (ML) enables the development of powerful methods for predicting thermophysical properties with unprecedented scope and accuracy. However, technical barriers like cumbersome implementation in established workflows hinder…

Computational Engineering, Finance, and Science · Computer Science 2025-09-04 Marco Hoffmann , Thomas Specht , Nicolas Hayer , Hans Hasse , Fabian Jirasek

Machine learning (ML) has become critical for post-acquisition data analysis in (scanning) transmission electron microscopy, (S)TEM, imaging and spectroscopy. An emerging trend is the transition to real-time analysis and closed-loop…

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…

Methodology · Statistics 2016-12-08 Blazej Miasojedow , Wojciech Niemiro , Jan Palczewski , Wojciech Rejchel

In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the…

Statistics Theory · Mathematics 2017-07-31 Arnak S. Dalalyan

We develop a machine-learning framework to predict the electron localization function (ELF) of pure, dense hydrogen directly from atomic geometry, bypassing explicit electronic-structure calculations. Trained on first-principles data…

The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…

Computation · Statistics 2019-12-18 Mark Girolami , Ben Calderhead , Siu A. Chin

Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…

High Energy Physics - Phenomenology · Physics 2020-10-21 Matthew D. Klimek , Maxim Perelstein

Point defects critically influence the properties of materials and devices, yet density functional theory (DFT) remains computationally demanding for defect supercell calculations. Machine learning interatomic potentials (MLIPs) offer high…

Materials Science · Physics 2026-04-09 Zhenxing Dai , Zhong Yang , Mingjue Ni , Menglin Huang , Hongjun Xiang , Xin-Gao Gong , Shiyou Chen

Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures…

Machine Learning · Statistics 2026-04-24 Ayoub Belhadji , Daniel Sharp , Youssef Marzouk

In the last few years we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer (BO) approximation, the Coupled Electron-Ion Monte Carlo Method (CEIMC). Electronic…

Computational Physics · Physics 2007-05-23 Carlo Pierleoni , David M. Ceperley

Metal hydrides are promising candidates for hydrogen storage applications. From a materials discovery perspective, an accurate, efficient computational workflow is urgently required that can rapidly analyze/predict thermodynamic properties…

Materials Science · Physics 2023-08-08 Swati Rana , Dayadeep S. Monder , Abhijit Chatterjee

Machine learning potentials (MLPs) represent atomic interactions with quantum mechanical accuracy offering an efficient tool for atomistic simulations in many fields of science. However, most MLPs rely on local atomic energies without…

Chemical Physics · Physics 2024-10-07 Emir Kocer , Redouan El Haouari , Christoph Dellago , Jörg Behler
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