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CAREER: Research and training in advanced computational methods for quantum and statistical mechanics

职业：量子和统计力学高级计算方法的研究和培训

基本信息

批准号：
1454939
负责人：
Jianfeng Lu
金额：
$ 42万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-09-01 至 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1454939&HistoricalAwards=false
关键词：
CAREER Research training advanced computational

项目摘要

Ab initio simulations have become widely used scientific workhorses with applications in physics, chemistry, materials science, and many related fields, but the reach of simulations is limited by computational complexity. To go beyond current capabilities in realistic and predictive ab initio simulations, it is necessary to address the current bottlenecks. This project aims to greatly enlarge the scope of ab initio simulations and open up major new areas for electronic-structure-theory-based predictive methodologies that are not possible today. This research lies at the intersection of multiple disciplines. The project connects advanced state-of-the-art techniques in computational mathematics to challenging problems arising from chemistry and materials science. The integrated research program will bring together ideas and techniques, which will not only help advance the application areas, but also has the potential to open up new research areas in mathematics.The research goal of this project is to innovate and analyze efficient algorithms based on advanced computational mathematics for electronic structure theory and computational statistical mechanics, which will greatly advance the scope of ab initio simulations with applications in chemistry, materials science, and many related fields. More specifically, topics considered include: (1) reduced scaling methods for electronic structure theory, which will extend the system size of the simulation; (2) efficient sampling algorithms for metastable systems, which will bridge the temporal scales; and (3) algorithms that go beyond Born-Oppenheimer approximation, which will give a more accurate account of quantum effects in classical dynamics. The educational objectives of this proposal are to prepare and train students for interdisciplinary research and to disseminate knowledge from graduate and undergraduate students to high school students and the general public in the U.S. and abroad.

从头算模拟已经成为物理、化学、材料科学和许多相关领域广泛使用的科学工具，但模拟的范围受到计算复杂性的限制。为了超越当前在现实和预测从头算模拟方面的能力，有必要解决当前的瓶颈。该项目旨在极大地扩大从头算模拟的范围，并为基于电子结构理论的预测方法开辟主要的新领域，这在今天是不可能的。这项研究是多学科的交叉。该项目将计算数学中最先进的技术与化学和材料科学中出现的具有挑战性的问题联系起来。综合研究计划将汇集思想和技术，不仅有助于推进应用领域，而且有可能开辟新的数学研究领域。本项目的研究目标是创新和分析基于电子结构理论和计算统计力学的先进计算数学的高效算法，这将极大地推进从头算模拟在化学、材料科学和许多相关领域的应用范围。更具体地说，考虑的主题包括：(1)电子结构理论的降尺度方法，这将扩展模拟的系统规模；(2)亚稳态系统的有效采样算法，它将跨越时间尺度；(3)超越玻恩-奥本海默近似的算法，这将更准确地描述经典动力学中的量子效应。该提案的教育目标是为跨学科研究做好准备和培养学生，并将研究生和本科生的知识传播给美国和国外的高中生和公众。