CDS&E: Collaborative Research: Hierarchical Kernel Matrices for Scientific and Data Applications

CDS

• 批准号: 2003683
• 负责人: Edmond Chow
• 金额: $ 31.6万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2003683&HistoricalAwards=false
• 关键词: CDS& Collaborative; Research; Hierarchical; Kernel

Kernel matrices in machine learning and scientific computing describe the relationships between collections of points which may represent various types of information. The increasing size of data sets in various disciplines and the increasing computational capability of computer hardware make it essential that our algorithms and software for kernel matrices are scalable, and that the time it takes for their execution grows linearly or close to linearly, with the problem size. Otherwise, such large-scale data problems may not be tractable. This project addresses the scaling bottlenecks associated with handling the kernel matrix by exploiting a hierarchical structure that is often found in these matrices. By accelerating computations with kernel matrices, this research enables large-scale data analysis and scientific simulation in diverse areas such as uncertainty quantification, integral equation problems, particle simulations, and geostatistics. High-performance software implementing the newly developed methods will be developed in an open-source environment.This project specifically addresses high-dimensional problems, the use of specialized kernel functions in machine learning, and the high initial computational cost of constructing a hierarchical representation for a kernel matrix. New methods developed will be applied to large-scale cases in a scientific application and a machine learning application: Brownian dynamics and Gaussian process regression. In machine learning, the new methods will complement existing large-scale approaches for Gaussian processes. High-performance software will address specific scaling challenges in constructing hierarchical matrices.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.

机器学习和科学计算中的核矩阵描述了可能代表各种类型信息的点集合之间的关系。不同学科的数据集的大小不断增加，计算机硬件的计算能力不断增加，这使得我们的核矩阵算法和软件具有可伸缩性，并且执行它们所需的时间随着问题的大小线性或接近线性地增长。否则，如此大规模的数据问题可能难以处理。该项目通过利用经常在这些矩阵中发现的层次结构来解决与处理内核矩阵相关的扩展瓶颈。通过加速核矩阵的计算，这项研究使不同领域的大规模数据分析和科学模拟成为可能，如不确定性量化、积分方程式问题、粒子模拟和地质统计学。实现新开发的方法的高性能软件将在开放源代码环境中开发。该项目专门解决高维问题，在机器学习中使用专门的核函数，以及构建核矩阵的分层表示的高初始计算成本。开发的新方法将在一个科学应用程序和一个机器学习应用程序中应用于大规模案例：布朗动力学和高斯过程回归。在机器学习中，新方法将补充现有的针对高斯过程的大规模方法。高性能软件将解决构建分层矩阵中的特定扩展挑战。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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

A hierarchical matrix approach for computing hydrodynamic interactions

• DOI: 10.1016/j.jcp.2021.110761
• 发表时间: 2021-10-14
• 期刊: JOURNAL OF COMPUTATIONAL PHYSICS
• 影响因子: 4.1
• 作者: Xing，Xin;Huang，Hua;Chow，Edmond
• 通讯作者: Chow，Edmond