PCAfold 2.0—Novel tools and algorithms for low-dimensional manifold assessment and optimization

Journal Article · 02 July 2023 · SoftwareX

DOI: https://doi.org/10.1016/j.softx.2023.101447 · OSTI ID:2424309

Zdybał, Kamila  ^[1]; Armstrong, Elizabeth ^[2]; Parente, Alessandro ^[1]; Sutherland, James C. ^[2]

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1. Université Libre de Bruxelles, Brussels (Belgium); BRITE: BRussels Institute for Thermal-fluid systems and clean Energy (Belgium)
2. University of Utah, Salt Lake City, UT (United States)

We describe an update to our open-source Python package, PCAfold, designed to help researchers generate, analyze and improve low-dimensional data manifolds. In the current version, PCAfold 2.0, we introduce novel tools and algorithms for assessing and optimizing low-dimensional manifolds. This includes a method that generates a “map” of local feature sizes that can help pinpoint researchers to problematic regions on a manifold. We introduce a novel cost function that characterizes the quality of a manifold topology with a single number. We develop two algorithms for feature selection based on principal component analysis (PCA) that use the cost function as an objective function to minimize. We introduce a quantity of interest (QoI)-aware dimensionality reduction strategy where data projections are computed using an artificial neural network and are directly optimized towards representing various projection-independent and projection-dependent QoIs. We also introduce an implementation of partition of unity networks (POUnets) for efficient reconstruction of QoIs from low-dimensional manifolds based on combining neural network classification with localized polynomial regression. Our software can be broadly applicable in all domains of science and engineering that aim to reduce data dimensionality, as well as in the fundamental research on representation learning.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: European Union’s Horizon 2020 research and innovation program; National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0003525
• OSTI ID: 2424309
• Journal Information: SoftwareX, Journal Name: SoftwareX Journal Issue: C Vol. 23; ISSN 2352-7110
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English