On Model Error and Statistical Calibration of Physical Models

Habib Najm
Sandia National Laboratories

Existing methods for representation of model error in the statistical
calibration of computational models typically rely on convolving model
predictions of select observables with statistical data and model error terms.
This strategy is successful in providing a statistical correction to model
predictions in a manner that interpolates observations with meaningful
uncertainty estimation between points. However, this approach faces a number of
challenges when applied in the context of calibration of physical models, where,
e.g. auxiliary physical constraints are in force, the model is intended for use
outside the calibration regime, and other non-observable model output
predictions are of interest. Further, the commonly used additive combination of
model and data errors presents challengs for the disambiguation of the two
sources of uncertainty.

I will outline a calibration strategy that addresses these challenges. The key
idea is to embed statistical model error terms inside the model, and not on
observable model outputs. In this manner, model error terms can be placed in
targeted model components where specific approximations were made. This allows
the analyst, e.g. to examine the utility of corrections to one or other suspect
model components, to identify the model component where model improvements are
relevant for agreement with the data. Our hitherto developments embed model
error in specific model parameters, thereby rendering the statistical
calibration, at least partly, a density estimation problem. Employing a Bayesian
framework, we employ different likelihood constructions, depending on whether
there is data noise or not. In particular, for noise free data, as in the case
of model-to-model calibration, we rely on approximate Bayesian computation.

I will illustrate the use of this construction on simple model problems, with
and without data noise, and for calibration of a simplified chemical model for
methane-air kinetics against another, more complex, model. Select parameters are
encumbered by model error, which translates to uncertainty in predictive model
outputs. In cases where there is data noise, the method is seen to enable
disambiguation of data and model errors, allowing clear estimation of
uncertainty in model predictions resulting from model error.

Presentation (PDF File)

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