Active learning-based domain adaptive localized polynomial chaos expansion

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F23%3APU150238" target="_blank" >RIV/00216305:26110/23:PU150238 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/abs/pii/S0888327023006362?dgcid=author" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0888327023006362?dgcid=author</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ymssp.2023.110728" target="_blank" >10.1016/j.ymssp.2023.110728</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Active learning-based domain adaptive localized polynomial chaos expansion

Popis výsledku v původním jazyce

The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to as domain adaptive localized polynomial chaos expansion (DAL-PCE). The approach utilizes sequential decomposition of the input random space into smaller sub-domains approximated by low-order polynomial expansions. This allows the approximation of functions with strong nonlinearities, discontinuities, and/or singularities that often appear in dynamical systems. Decomposition of the input random space and local approximations alleviates the Gibbs phenomenon for these types of problems and confines error to a very small vicinity near the non-linearity. The global behavior of the surrogate model is therefore significantly better than existing methods, as shown in numerical examples, including an engineering dynamical system exhibiting discontinuous response. The whole process is driven by an active learning routine that uses the recently proposed Theta criterion to assess local variance contributions (Novak et al., 2021). The proposed approach balances both exploitation of the surrogate model and exploration of the input random space and thus leads to efficient and accurate approximation of the original mathematical model. The numerical results show the superiority of the DAL-PCE in comparison to (i) a single global polynomial chaos expansion and (ii) the recently proposed stochastic spectral embedding (SSE) method (Marelli et al., 2021) developed as an accurate surrogate model and which is based on a similar domain decomposition process. This method represents a general framework upon which further extensions and refinements can be based and which can be combined with any technique for non-intrusive polynomial chaos expansion construction.

Název v anglickém jazyce

Active learning-based domain adaptive localized polynomial chaos expansion

Popis výsledku anglicky

The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to as domain adaptive localized polynomial chaos expansion (DAL-PCE). The approach utilizes sequential decomposition of the input random space into smaller sub-domains approximated by low-order polynomial expansions. This allows the approximation of functions with strong nonlinearities, discontinuities, and/or singularities that often appear in dynamical systems. Decomposition of the input random space and local approximations alleviates the Gibbs phenomenon for these types of problems and confines error to a very small vicinity near the non-linearity. The global behavior of the surrogate model is therefore significantly better than existing methods, as shown in numerical examples, including an engineering dynamical system exhibiting discontinuous response. The whole process is driven by an active learning routine that uses the recently proposed Theta criterion to assess local variance contributions (Novak et al., 2021). The proposed approach balances both exploitation of the surrogate model and exploration of the input random space and thus leads to efficient and accurate approximation of the original mathematical model. The numerical results show the superiority of the DAL-PCE in comparison to (i) a single global polynomial chaos expansion and (ii) the recently proposed stochastic spectral embedding (SSE) method (Marelli et al., 2021) developed as an accurate surrogate model and which is based on a similar domain decomposition process. This method represents a general framework upon which further extensions and refinements can be based and which can be combined with any technique for non-intrusive polynomial chaos expansion construction.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20102 - Construction engineering, Municipal and structural engineering

Projekt

<a href="/cs/project/GA22-00774S" target="_blank" >GA22-00774S: Pravděpodobnostní posouzení v mostním inženýrství za užití náhradního metamodelu (MAPAB)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

MECHANICAL SYSTEMS AND SIGNAL PROCESSING

ISSN

0888-3270

e-ISSN

1096-1216

Svazek periodika

204

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

22

Strana od-do

„“-„“

Kód UT WoS článku

001140284200001

EID výsledku v databázi Scopus

2-s2.0-85171334875