2024/08/23 by Guanqun Ma, David Lenz, Ma, Guanqun +7 · 1 citation
Decision Sciences · Engineering · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Probabilistic and Robust Engineering Design #Scientific Measurement and Uncertainty Evaluation #Tribology and Lubrication Engineering
paper · pdf · doi:10.48550/arxiv.2408.13193
openalex publication_date 2024/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Advances in high-performance computing require new ways to represent large-scale scientific data to support data storage, data transfers, and data analysis within scientific workflows. Multivariate functional approximation (MFA) has recently emerged as a new continuous meshless representation that approximates raw discrete data with a set of piecewise smooth functions. An MFA model of data thus offers a compact representation and supports high-order evaluation of values and derivatives anywhere in the domain. In this paper, we present CPE-MFA, the first critical point extraction framework designed for MFA models of large-scale, high-dimensional data. CPE-MFA extracts critical points directly from an MFA model without the need for discretization or resampling. This is the first step toward enabling continuous implicit models such as MFA to support topological data analysis at scale.