用主成分分析降维重构参数空间，提升模型效率
A new methodology to decompose a parametric domain using reduced order data manifold in machine learning
- 通过迭代PCA将高维数据流形压缩为低维流形
- 提出两种逆投影重建方法，实现低维到原空间映射
- 在谐波传输问题中优于传统神经网络等元模型
本文提出一种基于迭代主成分分析（iterative PCA）的参数域分解新方法。首先利用迭代PCA将高维数据流形降维至低维流形；随后，开发两种方法重构逆投影算子，实现从低维成分向原始空间的逆映射；进而，基于低维流形设计详细的参数域划分策略。最后，通过谐波传输问题的数值实验，验证了该方法在计算效率与精度上均优于经典元模型（如神经网络）。
原文摘要 · Abstract (English)
We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold. Moreover, two approaches are developed to reconstruct the inverse projector to project from the lower data component to the original one. Afterward, we provide a detailed strategy to decompose the parametric domain based on the low dimension manifold. Finally, numerical examples of harmonic transport problem are given to illustrate the efficiency and effectiveness of the proposed method comparing to the classical meta-models such as neural networks.
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