Collaborative Research: Elements: A Cyberlaboratory for Randomized Numerical Linear Algebra

现代科学和工程计算需要以超越传统线性代数算法的速度和规模处理数据，这在解决尖端科学和工程问题方面造成了巨大的瓶颈。为了克服这一挑战，线性代数算法正在增加随机化以压缩输入数据，这是一种在理论上显示出巨大前景的技术。不幸的是，这些理论上的进步并没有转化为实际的实施，因为缺乏一个网络基础设施，使快速和可重复的原型，这样的算法。为了解决这一问题，该项目创建了一个创新的网络基础设施，以实现这些随机线性代数算法的快速实施和可重复比较。此外，该项目可以在昂贵的软件开发之前轻松测试科学计算中的随机线性代数算法。因此，该项目准备支持尖端计算科学和工程问题的解决方案。此外，该项目利用网络基础设施提供关于随机线性代数理论和实现的公共教育模块。该项目开发了一个以线性代数问题的算法为重点的随机算法网络基础设施。该项目将我们的随机线性代数算法的创新理论模块化映射到计算内核，这些内核可以很容易地组合和扩展，以快速开发用于特定科学计算的新颖，定制的方法。此外，这种网络基础设施包括一个可重复测试算法的框架，并在部署之前对代码进行基准测试。这种网络基础设施通过直接解决气候应用中的尖端数据问题来展示其力量。该项目强调最佳科学软件实践，以开发可持续的、社区参与的和有影响力的网络基础设施。该奖项由NSF高级网络基础设施办公室颁发，并得到数学科学部的联合支持。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Modern scientific and engineering computations require processing data at speeds and scales that overwhelm traditional linear algebra algorithms, which creates a substantial bottleneck in solving cutting-edge scientific and engineering problems. To overcome this challenge, linear algebra algorithms are being augmented with randomization to compress input data, a technique that has shown tremendous promise in theory. Unfortunately, these theoretical advances have not transformed into practical implementations because of a lack of a cyberinfrastructure that enables rapid and reproducible prototyping of such algorithms. To address this deficit, this project creates an innovative cyberinfrastructure to enable rapid implementation and reproducible comparison of these randomized linear algebra algorithms. Additionally, this project enables easily testing randomized linear algebra algorithms in scientific computations prior to expensive software development. Thus, this project is poised to support the solution of cutting-edge computational science and engineering problems. Moreover, this project utilizes the cyberinfrastructure to deliver publicly accessible educational modules on randomized linear algebra theory and implementation.This project develops a cyberinfrastructure for randomized algorithms with a focus on algorithms for linear algebra problems. This project maps our innovative theoretical modularization of randomized linear algebra algorithms to computational kernels, which can be readily composed and extended to rapidly develop novel, tailored methods for specific scientific computations. Moreover, this cyberinfrastructure includes a framework for reproducibly testing algorithms, and enables benchmarking codes prior to deployment. This cyberinfrastructure demonstrates its power by directly addressing cutting-edge data problems in climate applications. The project emphasizes best scientific software practices to develop a sustainable, community-engaging and impactful cyberinfrastructure.This award by the NSF Office of Advanced Cyberinfrastructure is jointly supported by the Division of Mathematical Sciences.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.