TY - JOUR

T1 - Interval uncertainty propagation by a parallel Bayesian global optimization method

AU - Dang, Chao

AU - Wei, Pengfei

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Beer, Michael

N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC). Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194). Marcos Valdebenito acknowledges the support by ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271. Chao Dang, Pengfei Wei and Michael Beer also would like to appreciate the support of Sino-German Mobility Program under grant number M-0175.

PY - 2022/8

Y1 - 2022/8

N2 - This paper is concerned with approximating the scalar response of a complex computational model subjected to multiple input interval variables. Such task is formulated as finding both the global minimum and maximum of a computationally expensive black-box function over a prescribed hyper-rectangle. On this basis, a novel non-intrusive method, called ‘triple-engine parallel Bayesian global optimization’, is proposed. The method begins by assuming a Gaussian process prior (which can also be interpreted as a surrogate model) over the response function. The main contribution lies in developing a novel infill sampling criterion, i.e., triple-engine pseudo expected improvement strategy, to identify multiple promising points for minimization and/or maximization based on the past observations at each iteration. By doing so, these identified points can be evaluated on the real response function in parallel. Besides, another potential benefit is that both the lower and upper bounds of the model response can be obtained with a single run of the developed method. Four numerical examples with varying complexity are investigated to demonstrate the proposed method against some existing techniques, and results indicate that significant computational savings can be achieved by making full use of prior knowledge and parallel computing.

AB - This paper is concerned with approximating the scalar response of a complex computational model subjected to multiple input interval variables. Such task is formulated as finding both the global minimum and maximum of a computationally expensive black-box function over a prescribed hyper-rectangle. On this basis, a novel non-intrusive method, called ‘triple-engine parallel Bayesian global optimization’, is proposed. The method begins by assuming a Gaussian process prior (which can also be interpreted as a surrogate model) over the response function. The main contribution lies in developing a novel infill sampling criterion, i.e., triple-engine pseudo expected improvement strategy, to identify multiple promising points for minimization and/or maximization based on the past observations at each iteration. By doing so, these identified points can be evaluated on the real response function in parallel. Besides, another potential benefit is that both the lower and upper bounds of the model response can be obtained with a single run of the developed method. Four numerical examples with varying complexity are investigated to demonstrate the proposed method against some existing techniques, and results indicate that significant computational savings can be achieved by making full use of prior knowledge and parallel computing.

KW - Bayesian global optimization

KW - Gaussian process

KW - Infill sampling criterion

KW - Interval uncertainty propagation

KW - Parallel computing

UR - http://www.scopus.com/inward/record.url?scp=85127826831&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2022.03.031

DO - 10.1016/j.apm.2022.03.031

M3 - Article

AN - SCOPUS:85127826831

VL - 108

SP - 220

EP - 235

JO - Applied mathematical modelling

JF - Applied mathematical modelling

SN - 0307-904X

ER -