Prediction using numerical simulations, a Bayesian framework for uncertainty quantification and its statistical challenge

J. Glimm, Y. Lee, K. Q. Ye, D. H. Sharp

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Uncertainty quantification is essential in using numerical models for prediction. While many works focused on how the uncertainty of the inputs propagate to the outputs, the modeling errors of the numerical model were often overlooked. In our Bayesian framework, modeling errors play an essential role and were assessed through studying numerical solution errors. The main ideas and key concepts will be illustrated through an oil reservoir case study. In this study, inference on the input has to be made from the output. Bayesian analysis is adopted to handle this inverse problem, then combine it with the forward simulation for prediction. The solution error models were established based on the scale-up solutions and fine-grid solutions. As the central piece of our framework, the robustness of these error models is fundamental. In addition to the oil reservoir computer codes, we will also discuss the modelling of solution error of shock wave physics. Although the framework itself is simple, there is many statistical challenges which include optimal dimension of the error model, trade-off between sample size and the solution accuracy. These challenges are also discussed.

Original languageEnglish (US)
Title of host publication4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003
EditorsNii O. Attoh-Okine, Bilal M. Ayyub
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages380-385
Number of pages6
ISBN (Electronic)0769519970, 9780769519975
DOIs
StatePublished - 2003
Event4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003 - College Park, United States
Duration: Sep 21 2003Sep 24 2003

Publication series

Name4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003

Other

Other4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003
CountryUnited States
CityCollege Park
Period9/21/039/24/03

Keywords

  • Analytical models
  • Bayesian methods
  • Computational modeling
  • Computer errors
  • Hydrocarbon reservoirs
  • Inverse problems
  • Numerical models
  • Numerical simulation
  • Petroleum
  • Uncertainty

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Control and Optimization
  • Modeling and Simulation

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  • Cite this

    Glimm, J., Lee, Y., Ye, K. Q., & Sharp, D. H. (2003). Prediction using numerical simulations, a Bayesian framework for uncertainty quantification and its statistical challenge. In N. O. Attoh-Okine, & B. M. Ayyub (Eds.), 4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003 (pp. 380-385). [1236189] (4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISUMA.2003.1236189