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

arXiv: https://arxiv.org/abs/2505.08497 · HTML: https://mlsanity.com/paper/2505.08497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 13 references that are in the map.
- First posted on arXiv 13 May 2025.

## Builds on (most cited first, 1 of 1)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)

## Abstract (arXiv)

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.