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)是基于代数拓扑学的方法，用于从大数据集中提取重要的拓扑特征，其应用范围从天文到生物学、社会科学和人工智能(AI)。然而，随着数据仪表化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日益增长的需求，高效的并行TDA软件至关重要。为了满足这一需求，本项目的PI与领域专家、软件开发人员和高性能计算研究人员合作，为各种TDA应用开发了一个开源的GPU加速软件工具，目的是提高计算效率，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：(1)设计和实现增强的算法，以高效地并行计算并最大限度地减少数据移动；(2)使我们的TDA软件能够在异构计算平台上运行；(3)设计一个吸引非GPU编程用户并允许与其他用户级TDA软件工具集成的图形用户界面；以及(4)通过人工智能和机器学习领域的最先进应用程序来测试和评估我们的开源软件。这些发展将为TDA应用程序提供及时的硬件加速解决方案，使跨学科的科学家和数据分析师更容易访问TDA，并推动TDA社区和行业的科学发现。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。

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.