PCA-Based Interpretable Knowledge Representation and Analysis of Geometric Design Parameters

TL;DR

This paper explores how PCA can be used to interpret and estimate original design parameters from high-dimensional geometric representations in CAD applications, addressing limitations and conditions for accurate parameter recovery.

Contribution

It analyzes a PCA modification for geometric parameter estimation, compares it to standard PCA, and identifies conditions for reliable, interpretable results.

Findings

PCA can be used to recover design parameters under certain conditions

The studied PCA modification yields results identical to standard PCA

Limitations of PCA in parameter estimation are identified and discussed

Abstract

In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and design exploration tasks. Therefore, dimension reduction methods such as principal component analysis (PCA) are used. The PCA identifies dominant modes of geometric variation and yields a compact representation of the geometry. While classical PCA excels in the compact representation part, it does not directly recover underlying design parameters of a generated geometry. In this work, we deal with the problem of estimating design parameters from PCA-based representations. Analyzing a recent modification of the PCA dedicated to our field of application, we show that the results are actually identical to the standard PCA. We investigate limitations of this approach and present reasonable conditions under which accurate, interpretable parameter estimation can be obtained. With the help of dedicated experiments, we take a more in-depth look at every stage of the PCA and the possible changes of the geometry during these processes.