Estimation of an improved surrogate model in uncertainty quantification by neural networks

Benedict Götz (), Sebastian Kersting () and Michael Kohler ()
Additional contact information
Benedict Götz: Technische Universität Darmstadt
Sebastian Kersting: Technische Universität Darmstadt
Michael Kohler: Technische Universität Darmstadt

Annals of the Institute of Statistical Mathematics, 2021, vol. 73, issue 2, No 2, 249-281

Abstract: Abstract Quantification of uncertainty of a technical system is often based on a surrogate model of a corresponding simulation model. In any application, the simulation model will not describe the reality perfectly, and consequently the surrogate model will be imperfect. In this article, we combine observed data from the technical system with simulated data from the imperfect simulation model in order to estimate an improved surrogate model consisting of multilayer feedforward neural networks, and we show that under suitable assumptions, this estimate is able to circumvent the curse of dimensionality. Based on this improved surrogate model, we show a rate of the convergence result for density estimates. The finite sample size performance of the estimates is illustrated by applying them to simulated data. The practical usefulness of the newly proposed estimates is demonstrated by using them to predict the uncertainty of a lateral vibration attenuation system with piezo-elastic supports.

Keywords: Curse of dimensionality; Density estimation; Imperfect models; $$L_1$$ L 1 error; Neural networks; Surrogate models; Uncertainty quantification (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-020-00748-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:aistmt:v:73:y:2021:i:2:d:10.1007_s10463-020-00748-1

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-020-00748-1

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().