Details
| Original language | English |
|---|---|
| Article number | 113035 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 365 |
| Early online date | 11 Apr 2020 |
| Publication status | Published - 15 Jun 2020 |
Abstract
Probabilistic integration is a Bayesian inference technique for numerical integration, and has received much attention in the community of scientific and engineering computations. The most appealing advantages are the ability to improve the integration accuracy by making full use of the spatial correlation information among the design points, and the treatment of discretization error as a source of epistemic uncertainty being explicitly propagated to the integration results. This paper aims to develop an adaptive algorithm for further improving the efficiency and accuracy of the probabilistic integration when it is applied to the time-consuming computer simulators. A learning function is first extracted from the posterior variance of the integration and is shown to be especially useful for identifying the design point, by adding which to the training data set, the most reduction of the posterior variance of integration can be achieved. Based on this learning function, an adaptive experiment design algorithm is then developed for actively producing optimal design points. Results of the experiment tests and engineering application show that, with the same number of design points, the developed design strategy always produce more accurate and robust integration results, than the three kinds of commonly used random sampling design strategies (i.e., Monte Carlo design, Latin-hypercube design and Sobol sequence).
Keywords
- Bayesian inference, Epistemic uncertainty, Experiment design, Gaussian Process Regression, Kernel function, Probabilistic integration
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 365, 113035, 15.06.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Adaptive experiment design for probabilistic integration
AU - Wei, Pengfei
AU - Zhang, Xing
AU - Beer, Michael
N1 - Funding Information: This work is supported by the National Natural Science Foundation of China (NSFC 51905430). The first author is also supported by the Alexander von Humboldt Foundation of Germany and the Top International University Visiting Program for Outstanding Young Scholars of Northwestern Polytechnical University, China.
PY - 2020/6/15
Y1 - 2020/6/15
N2 - Probabilistic integration is a Bayesian inference technique for numerical integration, and has received much attention in the community of scientific and engineering computations. The most appealing advantages are the ability to improve the integration accuracy by making full use of the spatial correlation information among the design points, and the treatment of discretization error as a source of epistemic uncertainty being explicitly propagated to the integration results. This paper aims to develop an adaptive algorithm for further improving the efficiency and accuracy of the probabilistic integration when it is applied to the time-consuming computer simulators. A learning function is first extracted from the posterior variance of the integration and is shown to be especially useful for identifying the design point, by adding which to the training data set, the most reduction of the posterior variance of integration can be achieved. Based on this learning function, an adaptive experiment design algorithm is then developed for actively producing optimal design points. Results of the experiment tests and engineering application show that, with the same number of design points, the developed design strategy always produce more accurate and robust integration results, than the three kinds of commonly used random sampling design strategies (i.e., Monte Carlo design, Latin-hypercube design and Sobol sequence).
AB - Probabilistic integration is a Bayesian inference technique for numerical integration, and has received much attention in the community of scientific and engineering computations. The most appealing advantages are the ability to improve the integration accuracy by making full use of the spatial correlation information among the design points, and the treatment of discretization error as a source of epistemic uncertainty being explicitly propagated to the integration results. This paper aims to develop an adaptive algorithm for further improving the efficiency and accuracy of the probabilistic integration when it is applied to the time-consuming computer simulators. A learning function is first extracted from the posterior variance of the integration and is shown to be especially useful for identifying the design point, by adding which to the training data set, the most reduction of the posterior variance of integration can be achieved. Based on this learning function, an adaptive experiment design algorithm is then developed for actively producing optimal design points. Results of the experiment tests and engineering application show that, with the same number of design points, the developed design strategy always produce more accurate and robust integration results, than the three kinds of commonly used random sampling design strategies (i.e., Monte Carlo design, Latin-hypercube design and Sobol sequence).
KW - Bayesian inference
KW - Epistemic uncertainty
KW - Experiment design
KW - Gaussian Process Regression
KW - Kernel function
KW - Probabilistic integration
UR - http://www.scopus.com/inward/record.url?scp=85082999201&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2020.113035
DO - 10.1016/j.cma.2020.113035
M3 - Article
AN - SCOPUS:85082999201
VL - 365
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 113035
ER -