A new methodology to decompose a parametric domain using reduced order data manifold in machine learning

TL;DR

This paper introduces a novel methodology for decomposing parametric domains in machine learning by leveraging iterative principal component analysis to reduce data manifold dimensions and reconstruct inverse projectors, demonstrated through harmonic transport problems.

Contribution

The paper presents a new approach combining iterative PCA and inverse projector reconstruction for efficient parametric domain decomposition in machine learning.

Findings

Effective reduction of high-dimensional manifolds to lower dimensions.

Improved decomposition strategy for parametric domains.

Enhanced performance over classical meta-models like neural networks.

Abstract

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.