用PCA还原几何设计参数，让降维后的模型更可解释。
PCA-Based Interpretable Knowledge Representation and Analysis of Geometric Design Parameters
- 基于主成分分析提取几何变化模式，构建紧凑表示
- 发现改进版PCA与标准PCA结果一致，无实质提升
- 给出参数反推的可行条件，适合需可解释性的设计场景
在众多基于计算机辅助设计（CAD）的应用中，复杂几何形状由大量设计参数定义，导致高维设计空间，给仿真、优化和设计探索等下游任务带来挑战。为此常采用主成分分析（PCA）等降维方法，识别几何变化的主要模式，实现几何的紧凑表达。尽管经典PCA在紧凑表示方面表现优异，但无法直接恢复生成几何所对应的原始设计参数。本文研究从PCA表示中估计设计参数的问题。通过分析近期针对本领域提出的PCA改进方法，我们发现其结果实际上与标准PCA完全一致。进一步探讨该方法的局限性，并提出在特定条件下可实现准确且可解释的参数估计。借助专门实验，深入考察了PCA各阶段对几何形态的影响及可能的变化。
原文摘要 · Abstract (English)
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.
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