TY - JOUR

T1 - Efficient estimation of space varying parameters in numerical models using non-intrusive subdomain reduced order modeling

AU - Xiao, Cong

AU - Leeuwenburgh, Olwijn

AU - Lin, Hai Xiang

AU - Heemink, Arnold

PY - 2021

Y1 - 2021

N2 - A reduced order modeling algorithm for the estimation of space varying parameter patterns in numerical models is proposed. In this approach domain decomposition is applied to construct separate approximations to the numerical model in every subdomain. We introduce a new local parameterization that decouples the computational cost of the algorithm from the number of global principal components and therefore provides attractive scaling for models with a very large number of uncertain parameter patterns. By defining uncertain parameter patterns only in the various subdomains the number of full order simulation required for the derivation of the reduced order models can be reduced drastically. To avoid non-smoothness at the boundaries of the subdomains, the optimal local parameters patterns are projected onto global parameter patterns. The computational effort of the new methodology hardly increases when the number of parameter patterns increases. The number of training models depends primarily on the maximum number of local parameters in a subdomain, which can be decreased by refining the domain decomposition. We apply the new algorithm to a large-scale reservoir model parameter estimation problem. In this application 282 parameters could be estimated using only 90 full order model runs.

AB - A reduced order modeling algorithm for the estimation of space varying parameter patterns in numerical models is proposed. In this approach domain decomposition is applied to construct separate approximations to the numerical model in every subdomain. We introduce a new local parameterization that decouples the computational cost of the algorithm from the number of global principal components and therefore provides attractive scaling for models with a very large number of uncertain parameter patterns. By defining uncertain parameter patterns only in the various subdomains the number of full order simulation required for the derivation of the reduced order models can be reduced drastically. To avoid non-smoothness at the boundaries of the subdomains, the optimal local parameters patterns are projected onto global parameter patterns. The computational effort of the new methodology hardly increases when the number of parameter patterns increases. The number of training models depends primarily on the maximum number of local parameters in a subdomain, which can be decreased by refining the domain decomposition. We apply the new algorithm to a large-scale reservoir model parameter estimation problem. In this application 282 parameters could be estimated using only 90 full order model runs.

KW - Adjoint model

KW - Domain decomposition

KW - Model reduction

KW - Parameter estimation

UR - http://www.scopus.com/inward/record.url?scp=85091952956&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2020.109867

DO - 10.1016/j.jcp.2020.109867

M3 - Article

AN - SCOPUS:85091952956

VL - 424

SP - 1

EP - 30

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 109867

ER -