Critical Point Extraction from Multivariate Functional Approximation

TL;DR

This paper introduces CPE-MFA, a novel framework for extracting critical points directly from multivariate functional approximation models, enabling scalable topological data analysis of large, high-dimensional scientific data.

Contribution

It presents the first method to extract critical points from MFA models without discretization, facilitating continuous topological analysis at scale.

Findings

Enables critical point extraction directly from MFA models.

Supports high-dimensional, large-scale data analysis.

Facilitates scalable topological data analysis.

Abstract

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.