CA-Based Interpretable Knowledge Representation and Analysis of Geometric Design Parameters
This work addresses a specific challenge in CAD engineering for improved simulation and optimization, but it is incremental as it builds on existing PCA methods.
The paper tackles the problem of estimating original design parameters from PCA-based compact representations of complex geometries in CAD applications, showing that a recent modification yields identical results to standard PCA and establishing conditions for accurate, interpretable parameter recovery.
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.