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

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

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

2 Citations (Scopus)

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
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages380-385
Number of pages6
ISBN (Print)0769519970, 9780769519975
DOIs
StatePublished - 2003
Externally publishedYes
Event4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003 - College Park, United States
Duration: Sep 21 2003Sep 24 2003

Other

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

Fingerprint

Uncertainty Quantification
Error Model
Modeling Error
Numerical Simulation
Prediction
Computer simulation
Scale-up
Output
Bayesian Analysis
Shock Waves
Inverse Problem
Sample Size
Trade-offs
Numerical models
Physics
Numerical Solution
Robustness
Grid
Uncertainty
Modeling

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

Cite this

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

Prediction using numerical simulations, a Bayesian framework for uncertainty quantification and its statistical challenge. / Glimm, J.; Lee, Y.; Ye, Qian K.; Sharp, D. H.

4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003. Institute of Electrical and Electronics Engineers Inc., 2003. p. 380-385 1236189.

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

Glimm, J, Lee, Y, Ye, QK & Sharp, DH 2003, Prediction using numerical simulations, a Bayesian framework for uncertainty quantification and its statistical challenge. in 4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003., 1236189, Institute of Electrical and Electronics Engineers Inc., pp. 380-385, 4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003, College Park, United States, 9/21/03. https://doi.org/10.1109/ISUMA.2003.1236189
Glimm J, Lee Y, Ye QK, Sharp DH. Prediction using numerical simulations, a Bayesian framework for uncertainty quantification and its statistical challenge. In 4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003. Institute of Electrical and Electronics Engineers Inc. 2003. p. 380-385. 1236189 https://doi.org/10.1109/ISUMA.2003.1236189
Glimm, J. ; Lee, Y. ; Ye, Qian K. ; Sharp, D. H. / Prediction using numerical simulations, a Bayesian framework for uncertainty quantification and its statistical challenge. 4th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2003. Institute of Electrical and Electronics Engineers Inc., 2003. pp. 380-385
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