# PGD-based advanced nonlinear multiparametric regressions for constructing metamodels at the scarce-data limit

arXiv: https://arxiv.org/abs/2103.05358 · HTML: https://mlsanity.com/paper/2103.05358/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [Convergence bounds for nonlinear least squares and applications to tensor recovery](https://mlsanity.com/paper/2108.05237/) (2021)
- [Generative Parametric Design (GPD): A framework for real-time geometry generation and on-the-fly multiparametric approximation](https://mlsanity.com/paper/2512.11748/) (2025)

## Abstract (arXiv)

Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding multi-parametric solutions can be viewed as a sort of computational vademecum that, once computed offline, can be then used in a variety of real-time engineering applications including optimization, inverse analysis, uncertainty propagation or simulation based control. Sometimes, these multi-parametric problems can be solved by using advanced model order reduction -- MOR -- techniques. However, when the solution of these multi-parametric problems becomes cumbersome, one possibility consists in solving the problem for a sample of the parametric values, and then creating a regression from all the computed solutions, to finally infer the solution for any choice of the problem parameters. However, addressing high-dimensionality at the low data limit, ensuring accuracy and avoiding overfitting constitutes a difficult challenge. The present paper aims at proposing and discussing different PGD-based advanced regressions enabling the just referred features.