Regularized regressions for parametric models based on separated representations

Sancarlos, Abel ; Champaney, Víctor ; Cueto, Elías (Universidad de Zaragoza) ; Chinesta, Francisco

Resumen: 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, solving these multi-parametric problems can be very costly. In that case, one possibility consists in solving the problem for a sample of the parametric values and creating a regression from all the computed solutions. The solution for any choice of the parameters is then inferred from the prediction of the regression model. 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 advanced regressions based on the proper generalized decomposition (PGD) enabling the just referred features. In particular, new PGD strategies are developed adding different regularizations to the s-PGD method. In addition, the ANOVA-based PGD is proposed to ally them.

Idioma: Inglés

DOI: 10.1186/s40323-023-00240-4

Año: 2023

Publicado en: Advanced modeling and simulation in engineering sciences 10 (2023), 4 [26 pp.]
ISSN: 2213-7467

Factor impacto CITESCORE: 6.8 - Applied Mathematics (Q1) - Engineering (miscellaneous) (Q1) - Modeling and Simulation (Q1) - Computer Science Applications (Q2)

Factor impacto SCIMAGO: 0.741 - Engineering (miscellaneous) (Q1) - Modeling and Simulation (Q2) - Applied Mathematics (Q2) - Computer Science Applications (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/T24-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI/PID2020-113463RB-C31/AEI/10.13039/501100011033

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Mec.Med.Cont. y Teor.Est. (Dpto. Ingeniería Mecánica)