A Multilevel Method for Many-Electron Schrödinger Equations Based on the Atomic Cluster Expansion

IF 3 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Scientific Computing Pub Date : 2024-01-16 DOI:10.1137/23m1565887

Dexuan Zhou, Huajie Chen, Cheuk Hin Ho, Christoph Ortner

引用次数: 0

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 1, Page A105-A129, February 2024.
Abstract. The atomic cluster expansion (ACE) [R. Drautz, Phys. Rev. B, 99 (2019), 014104] yields a highly efficient and interpretable parameterization of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we extend the practical applicability of the ACE framework to the computation of many-electron wave functions. To that end, we develop a customized variational Monte Carlo algorithm that exploits the sparsity and hierarchical properties of ACE wave functions. We demonstrate the feasibility on a range of proof-of-concept applications to one-dimensional systems.

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基于原子团簇扩展的多电子薛定谔方程多级方法

SIAM 科学计算期刊》，第 46 卷第 1 期，第 A105-A129 页，2024 年 2 月。摘要。原子团簇展开（ACE）[R. Drautz, Phys. Rev. B, 99 (2019), 014104]产生了一种高效且可解释的对称多项式参数化，在多粒子系统性质建模方面取得了巨大成功。在本研究中，我们将 ACE 框架的实际应用扩展到多电子波函数的计算。为此，我们开发了一种定制的变分蒙特卡洛算法，利用了 ACE 波函数的稀疏性和层次性。我们在一系列一维系统的概念验证应用中证明了这一算法的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.