A new methodology to decompose a parametric domain using reduced order data manifold in machine learning
This work addresses parametric domain decomposition for computational modeling, offering a potentially more efficient alternative to existing methods, though it appears incremental in its approach.
The authors tackled the problem of parametric domain decomposition by developing a methodology using iterative principal component analysis to reduce high-dimensional manifolds to lower dimensions, with numerical examples on a harmonic transport problem showing improved efficiency and effectiveness compared to classical meta-models like neural networks.
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.