Structural Uncertainty Modeling and Predictive Validation of Unobserved Quantities

Current state-of-the-art strategies in calibrating models rely on the Kennedy and O’Hagan framework based on the external discrepancy, which fall short in providing a comprehensive uncertainty representation that can support reliable predictions of unobserved quantities of interest (QoI) and usually yield biased estimates of physical parameters. The proposed internal discrepancy representation is based on the fact that physics-based models are constructed using a set of highly reliable conservative laws (mass, momentum, energy). This formulation exploits the source of the model error to develop reliable calibration and predictive validation methodologies. This approach removes the constraints associated with the external discrepancy approach: (1) its stochastic solution satisfies physical constraints, (2) it reduces inference bias and under-estimation of uncertainty, and (3) it provides reliable extrapolated predictions for the QoI.

  • T. A. Oliver, G. Terejanu, C. S. Simmons, and R. D. Moser, “Validating Predictions of Unobserved Quantities,” Computer Methods in Applied Mechanics and Engineering, vol. 283, pp. 1310-1335, 2015. doi:10.1016/j.cma.2014.08.023
    [BibTeX] [Download PDF]
    @article{OliverJ_CMAME_2015,
    title = {{Validating Predictions of Unobserved Quantities}},
    journal = {{Computer Methods in Applied Mechanics and Engineering}},
    volume = {283},
    number = {0},
    pages = {1310 - 1335},
    year = {2015},
    issn = {0045-7825},
    doi = {10.1016/j.cma.2014.08.023},
    url = {http://www.sciencedirect.com/science/article/pii/S004578251400293X},
    author = {Todd A. Oliver and Gabriel Terejanu and Christopher S. Simmons and Robert D. Moser},
    keywords = {Extrapolative predictions},
    keywords = {Validation},
    keywords = {Model discrepancy},
    keywords = {Bayesian inference},
    }

  • G. Terejanu, “From Model Calibration and Validation to Reliable Extrapolations,” in IMAC-XXXIV Conference and Exposition on Structural Dynamics, Orlando, Florida, 2016.
    [BibTeX]
    @CONFERENCE{TerejanuP_IMAC_2016,
    author = {Gabriel Terejanu},
    title = {{From Model Calibration and Validation to Reliable Extrapolations}},
    booktitle = {{IMAC-XXXIV Conference and Exposition on Structural Dynamics, Orlando, Florida}},
    year = {2016},
    month= {January},
    }

  • R. D. Moser, G. Terejanu, T. A. Oliver, and C. S. and Simmons, “Validating the Prediction of Unobserved Quantities,” The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, Technical Report 12-32, 2012.
    [BibTeX]
    @techreport{MoserT_2012,
    author = {Robert D. Moser and Gabriel Terejanu and Todd A. Oliver and and Christopher S. Simmons},
    title = {{Validating the Prediction of Unobserved Quantities}},
    type = {Technical Report},
    number = {12-32},
    institution = {The Institute for Computational Engineering and Sciences, The University of Texas at Austin},
    address = {Austin, Texas 78712},
    month = {Aug.},
    year = {2012},
    }