Innovative Numerical Methods for High-Dimensional Applications

高维应用的创新数值方法

基本信息

  • 批准号:
    2012286
  • 负责人:
  • 金额:
    $ 29.31万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2020
  • 资助国家:
    美国
  • 起止时间:
    2020-07-01 至 2024-06-30
  • 项目状态:
    已结题

项目摘要

This project aims to develop efficient numerical algorithms for a class of important systems in science and engineering that are modeled with high-dimensional partial differential equations (PDE) such as the many-body Schrödinger equation. Examples of such systems include many-body quantum mechanics, dynamics of chemical systems, learning and control of complex systems, and spectral methods for high-dimensional data. The numerical solution of high-dimensional PDE has been one of the greatest challenges in computational science and remains a formidable task even with today's computational power and algorithmic advances. Efficient numerical simulations present opportunities for major breakthroughs in scientific understanding. This project will employ modern techniques to develop novel efficient numerical algorithms for such important systems. Graduate students will be trained through involvement in the research.The research project combines mathematical analysis and algorithmic design to make progress in numerical methods for high-dimensional PDE. The research will draw from and further develop ideas and tools from recent advances in computational physics, quantum chemistry, and machine learning. In particular, the project will use modern techniques for large-scale optimization and nonlinear parameterization of high-dimensional functions. Specifically, the PI will (1) develop novel highly efficient coordinate algorithms for large-scale eigenvalue problems, and (2) develop and analyze efficient methods based on neural-network parameterization of the solutions for high-dimensional PDE.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
该项目旨在为科学和工程中的一类重要系统开发有效的数值算法,这些系统是用高维偏微分方程(PDE)建模的,如多体薛定谔方程。这类系统的例子包括多体量子力学、化学系统的动力学、复杂系统的学习和控制,以及高维数据的光谱方法。高维偏微分方程的数值求解一直是计算科学中最大的挑战之一,即使在今天的计算能力和算法的进步仍然是一个艰巨的任务。高效的数值模拟为科学理解的重大突破提供了机会。该项目将采用现代技术为这些重要系统开发新的有效数值算法。本研究计画结合数学分析与演算法设计,在高阶偏微分方程数值方法上取得进展。该研究将借鉴并进一步发展计算物理,量子化学和机器学习的最新进展的想法和工具。特别是,该项目将使用现代技术进行大规模优化和高维函数的非线性参数化。具体而言,PI将(1)开发用于大规模特征值问题的新型高效坐标算法,(2)开发和分析基于高维PDE解的神经网络参数化的高效方法。该奖项反映了NSF的法定使命,通过使用基金会的智力价值和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(25)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Fast Localization of Eigenfunctions via Smoothed Potentials
通过平滑势快速定位特征函数
  • DOI:
    10.1007/s10915-021-01682-x
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    2.5
  • 作者:
    Lu, Jianfeng;Murphey, Cody;Steinerberger, Stefan
  • 通讯作者:
    Steinerberger, Stefan
Fast algorithms of bath calculations in simulations of quantum system-bath dynamics
  • DOI:
    10.1016/j.cpc.2022.108417
  • 发表时间:
    2022-02
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Zhenning Cai;Jianfeng Lu;Siyao Yang
  • 通讯作者:
    Zhenning Cai;Jianfeng Lu;Siyao Yang
Complexity of zigzag sampling algorithm for strongly log-concave distributions
强对数凹分布的锯齿形采样算法的复杂性
  • DOI:
    10.1007/s11222-022-10109-y
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    2.2
  • 作者:
    Lu, Jianfeng;Wang, Lihan
  • 通讯作者:
    Wang, Lihan
On the Global Convergence of Randomized Coordinate Gradient Descent for Nonconvex Optimization
非凸优化的随机坐标梯度下降的全局收敛性
  • DOI:
    10.1137/21m1460375
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    3.1
  • 作者:
    Chen, Ziang;Li, Yingzhou;Lu, Jianfeng
  • 通讯作者:
    Lu, Jianfeng
Random Coordinate Langevin Monte Carlo
  • DOI:
  • 发表时间:
    2020-10
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Zhiyan Ding;Qin Li;Jianfeng Lu;Stephen J. Wright
  • 通讯作者:
    Zhiyan Ding;Qin Li;Jianfeng Lu;Stephen J. Wright
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Jianfeng Lu其他文献

Filling dynamics and phase change of molten salt in cold receiver pipe during initial pumping process
初始泵送过程中冷接收管内熔盐的充填动力学和相变
span style=background-color:#ffffff;color:#000000;Lead Methylammonium Triiodide Perovskite-Based Solar Cells: An Interfacial Charge-Transfer Investigation/span
三碘化甲基铵钙钛矿太阳能电池:界面电荷转移研究
  • DOI:
  • 发表时间:
    2014
  • 期刊:
  • 影响因子:
    8.4
  • 作者:
    Xiaobao Xu;Hua Zhang;Kun Cao;Jin Cui;Jianfeng Lu;Xianwei Zeng;Yan Shen;Mingkui Wang
  • 通讯作者:
    Mingkui Wang
Toward Quality-Aware Reverse Auction-based Incentive Mechanism for Federated Learning
面向联邦学习的基于质量意识的反向拍卖激励机制
DETECTION OF CRONOBACTER IN INFANT FORMULA AND PHYLOGENETIC ANALYSIS ON α-GLUCOSIDASE GENES
婴儿配方奶粉中克罗诺杆菌的检测及α-葡萄糖苷酶基因的系统发育分析
  • DOI:
    10.1111/j.1745-4565.2010.00283.x
  • 发表时间:
    2011
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Y. Ye;Qingping Wu;Jumei Zhang;Jianfeng Lu;Lin Lin
  • 通讯作者:
    Lin Lin
Multiplicity and stability of boiling on a thin cylinder with heat generation
薄壁圆筒上沸腾的多重性和稳定性

Jianfeng Lu的其他文献

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{{ truncateString('Jianfeng Lu', 18)}}的其他基金

Innovation of Numerical Methods for High-Dimensional Partial Differential Equations
高维偏微分方程数值方法的创新
  • 批准号:
    2309378
  • 财政年份:
    2023
  • 资助金额:
    $ 29.31万
  • 项目类别:
    Standard Grant
EAGER: QAC-QSA: Resource Reduction in Quantum Computational Chemistry Mapping by Optimizing Orbital Basis Sets
EAGER:QAC-QSA:通过优化轨道基集减少量子计算化学绘图中的资源
  • 批准号:
    2037263
  • 财政年份:
    2020
  • 资助金额:
    $ 29.31万
  • 项目类别:
    Standard Grant
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
  • 批准号:
    1454939
  • 财政年份:
    2015
  • 资助金额:
    $ 29.31万
  • 项目类别:
    Continuing Grant
Mathematical Problems for Electronic Structure Models
电子结构模型的数学问题
  • 批准号:
    1312659
  • 财政年份:
    2013
  • 资助金额:
    $ 29.31万
  • 项目类别:
    Continuing Grant

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Numerical Methods for Partial Differential Equations: Algorithms and Software on Innovative Computer Architectures
偏微分方程的数值方法:创新计算机架构的算法和软件
  • 批准号:
    RGPIN-2015-05648
  • 财政年份:
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    Discovery Grants Program - Individual
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  • 批准号:
    1939692
  • 财政年份:
    2017
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    $ 29.31万
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    Studentship
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