Elements: Sustained Innovation and Service by a GPU-accelerated Computation Tool for Applications of Topological Data Analysis

拓扑数据分析（TDA）和持久同调（PH）是一种强大的基于代数拓扑的方法，用于从大型数据集中提取重要的拓扑特征，其应用范围从天文学到生物学、社会科学和人工智能（AI）。然而，随着数据仪器和生成式数据生产的快速发展，TDA任务变得越来越复杂和计算密集型。因此，为了跟上硬件加速软件不断发展的技术趋势和对快速拓扑数据分析的不断增长的需求，一个高效的并行TDA软件是至关重要的。为了满足这一需求，该项目的pi与领域专家、软件开发人员和高性能计算研究人员合作，开发了用于各种TDA应用的开源gpu加速软件工具。该项目的目标是提高计算效率，并确保gpu加速计算工具的持续创新和服务。该项目的具体目标有四个方面：(1)设计和实现有效并行计算和最小化数据移动的增强算法；(2)在异构计算平台上启用我们的TDA软件；(3)设计图形用户界面，吸引非gpu编程用户，并允许与其他用户级TDA软件工具集成；(4)通过最先进的人工智能和机器学习应用测试和评估我们的开源软件。这些发展将为TDA应用提供及时的硬件加速解决方案，使各个学科的科学家和数据分析师更容易使用TDA，并推动TDA社区和行业的科学发现。该奖项反映了美国国家科学基金会的法定使命，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。

Topological data analysis (TDA) and persistent homology (PH) are powerful algebraic topology-based methods for extracting significant topological features in large datasets, with diverse applications ranging from astronomy to biology, social sciences, and artificial intelligence (AI). However, with the rapid advancement of data instrumentation and generative data production, TDA tasks have become increasingly complex and computationally intensive. Thus, to keep up with the ever-evolving technological trends of hardware-accelerated software and increasing demand for fast topological data analytics, a highly efficient parallel TDA software is crucial. To address this need, the PIs of this project develop an open-source GPU-accelerated software tool for various TDA applications, in collaboration with domain experts, software developers, and high-performance computing researchers.The objective of this project is to enhance the computing efficiency and ensure sustained innovation and service of the GPU-accelerated computation tool. The specific goals of the project are fourfold: (1) to design and implement enhanced algorithms that efficiently parallelize computations and minimize data movement; (2) to enable our TDA software on a heterogeneous computing platform; (3) to design a graphical user interface that attracts non-GPU programming users and allows integration with other user-level TDA software tools; and (4) to test and evaluate our open-source software through state-of-the-art applications in AI and machine learning. These developments will provide timely hardware-acceleration solutions for TDA applications, make TDA more accessible to scientists and data analysts across disciplines, and advance scientific discoveries in the TDA community and industries.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.