npj Computational Materials

Large scale hybrid Monte Carlo simulations for structure and property prediction (大规模杂化蒙特卡洛模拟预测材料的结构和性质)
Sergei Prokhorenko, Kruz Kalke, Yousra Nahas & Laurent Bellaiche
npj Computational Materials 4:80 (2018)
doi:s41524-018-0137-0
Published online:21 December 2018
Abstract| Full Text | PDF OPEN

摘要:蒙特卡洛方法是现代计算物理学中最早、应用最广泛的算法之一。在凝聚态物理中，这种技术最受欢迎的是Metropolis蒙卡方法。虽然Metropolis抽样方法具有很强的鲁棒性和可操作性，但它并不适用于能量和力的计算。为了寻找一种更有效的计算方法，本研究探索了杂化蒙特卡洛采样方法（一种广泛用于量子电动力学的算法）在长程相互作用系统的结构预测方案方面的能力。我们的研究结果表明，杂化蒙特卡洛算法是一种优秀的计算方案，其不仅显著优于Metropolis抽样方法，而且可以弥补材料科学应用中的分子动力学，同时允许对包含数百万个粒子的系统进行超大规模模拟计算。　　

Abstract:The Monte Carlo method is one of the first and most widely used algorithms in modern computational physics. In condensed matter physics, the particularly popular flavor of this technique is the Metropolis Monte Carlo scheme. While being incredibly robust and easy to implement, the Metropolis sampling is not well-suited for situations where energy and force evaluations are computationally demanding. In search for a more efficient technique, we here explore the performance of Hybrid Monte Carlo sampling, an algorithm widely used in quantum electrodynamics, as a structure prediction scheme for systems with long-range interactions. Our results show that the Hybrid Monte Carlo algorithm stands out as an excellent computational scheme that can not only significantly outperform the Metropolis sampling but also complement molecular dynamics in materials science applications, while allowing ultra-large-scale simulations of systems containing millions of particles.

Editorial Summary

Monte Carlo simulations: scaling-up property prediction (蒙特卡洛模拟：材料性能的大规模预测)

该研究采用杂化蒙特卡洛抽样算法对数百万粒子的大规模体系进行结构搜索和性能预测。来自美国阿肯色大学的Laurent Bellaiche团队，在有限温度下，对具有长程相互作用的固态系统（如铁电、弛豫铁电体和多铁材料）的有效哈密顿模型进行了杂化蒙特卡洛（HMC）采样。他们将结果与Metropolis蒙卡算法（MMC）和热分子动力学（MD）的结果进行了比较。他们发现，在选定的模型案例中，HMC方案明显优于MMC和MD。通过对面向GPU的并行化架构实现的HMC算法，可以对粒子数达到106的体系进行大规模的HMC仿真。该算法也可用于大规模密度泛函理论计算，从而开辟更广阔的应用前景。

A hybrid Monte Carlo sampling algorithm is adopted to predict structures and properties in large-scale simulations with millions of particles. A team led by Laurent Bellaiche from the University of Arkansas perform hybrid Monte Carlo (HMC) sampling on effective Hamiltonian models of solid-state systems with long-range interactions, such as ferroelectric, relaxor and multiferroic materials at finite temperatures. They compare the results with those obtained by the Metropolis Monte Carlo (MMC) algorithm and thermalized molecular dynamics (MD). They find that the HMC scheme significantly outperforms MMC and MD for selected model cases. By implementing the HMC algorithm for GPU-oriented parallelization architectures, they can perform HMC simulations for a large scale material simulations with the particle number reaching 106. This algorithm may also be implemented for large-scale density functional theory calculations so that a more broad space of applications might open.