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

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.