On the Statistical Calibration of Physical Models

Sargsyan, Khachik; Najm, Habib N.; Ghanem, Roger

doi:10.1002/kin.20906

Cited by 107 publications

(138 citation statements)

References 79 publications

(119 reference statements)

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“…For optimal utilization of the method, all relevant sources of uncertainties for each of the data types should be considered in the interpretation of the data. These include both “parametric uncertainties” (quantitative uncertainties in the model description due to uncertainties in the model parameters) and “structural uncertainties” (qualitative uncertainties in the model description due to assumptions/limitations of the model itself, also termed “model inadequacy” or “model discrepancy error” ).…”

Section: Multiscale Informatics Approachmentioning

confidence: 99%

Harnessing the Combined Power of Theoretical and Experimental Data through Multiscale Informatics

Burke

2016

Int J of Chemical Kinetics

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Monumental, recent and rapidly continuing, improvements in the capabilities of ab initio theoretical kinetics calculations provides reason to believe that progress in the field of chemical kinetics can be accelerated through a corresponding evolution of the role of theory in kinetic modeling and its relationship with experiment. The present article reviews and provides additional demonstrations of the unique advantages that arise when theoretical and experimental data across multiple scales are considered on equal footing, including the relevant uncertainties of both, within a single mathematical framework. Namely, the multiscale informatics framework simultaneously integrates information from a wide variety of sources and scales: ab initio electronic structure calculations of molecular properties, rate constant determinations for individual reactions, and measured global observables of multireaction systems. The resulting model representation consists of a set of theoretical kinetics parameters (with constrained uncertainties) that are related through elementary kinetics models to rate constants (with propagated uncertainties) that in turn are related through physical models to global observables (with propagated uncertainties). An overview of the approach and typical implementation is provided along with a brief discussion of the major uncertainties (parametric and structural) in theoretical kinetics calculations, kinetic models for complex chemical mechanisms, and physical models for experiments. Higher levels of automation in all aspects, including closed‐loop autonomous mixed‐experimental‐and‐computational model improvement, are advocated for facilitating scalability of the approach to larger systems with reasonable human effort and computational cost. The unique advantages of combining theoretical and experimental data across multiple scales are illustrated through a series of examples. Previous results demonstrating the utility of simultaneous interpretation of theoretical and experimental data for assessing consistency in complex systems and for reliable, physics‐based extrapolation of limited data are briefly summarized. New results are presented to demonstrate the high predictive accuracy of multiscale informed models for both small (molecular properties) and large (global observables) scales. These new results provide examples where the optimization yields physically realistic parameter adjustments and where physical model uncertainties in experiments are larger than kinetic model uncertainties. New results are also presented to demonstrate the utility of the multiscale informatics approach for design of experiments and theoretical calculations, accounting for both theoretical and experimental existing knowledge as well as relevant parametric and structural uncertainties in interpreting potential new data. These new results provide examples where neglecting structural uncertainties in design of experiments results in failure to identify the most worthwhile experiment. Further progress in the c...

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Section: Multiscale Informatics Approachmentioning

confidence: 99%

Harnessing the Combined Power of Theoretical and Experimental Data through Multiscale Informatics

Burke

2016

Int J of Chemical Kinetics

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“…In this context, the parameters

bold-italicθ = {C_{μ_{ε}}, C_{ε}}

, the data

scriptD

is represented by z ={ f k , i | i = 1,…, N t }, while

bold-italicx = {f_{_{P}}, f_{_{D}}}

are independent variables. In general, the discrepancy between model predictions and the data can be formalized as

bold-italicz = m (bold-italicx; bold-italicθ) + ε_{z}

Here, the model

m (bold-italicx; bold-italicθ) = C_{μ_{ε}} f_{_{P}} - C_{ε} f_{_{D}}

and ε z is the discrepancy between the data and the model, that is, a consequence of the model only being an approximation of the true process and any imperfections in the measurement process.…”

Section: Model Calibrationmentioning

confidence: 99%

“…The likelihood, expressed as

L_{scriptD} ({bold-italicα}_{1}, {bold-italicα}_{2}) = p (bold-italicz | {bold-italicα}_{1}, {bold-italicα}_{2}, {bold-italicx}_{bold-italica}),

is the multivariate density for z ={ f k , i | i = 1,…, N t }. Generally, this multivariate density has been shown to be degenerate . Instead, we approximate this density with a product of marginal densities corresponding to each data point

L_{scriptD} ({bold-italicα}_{1}, {bold-italicα}_{2}) = \prod_{i = 1}^{N_{t}} p (f_{k, i} | {bold-italicα}_{1}, {bold-italicα}_{2}, {bold-italicx}_{bold-italica}),

Given that germs ξ 1 and ξ 2 in Equation are normal RVs and that the model, in Equation , is linear, the marginal densities p ( f k , i | α 1 , α 2 , x a ) are normal, with mean and variance given by

\begin{matrix} μ_{f} & = α_{10} f_{_{P}}^{a} - α_{11} f_{_{D}}^{a} \\ σ_{f}^{2} & = {(α_{20} f_{_{P}}^{a} - α_{21} f_{_{D}}^{a})}^{2} + {(α_{22} f_{_{D}}^{a})}^{2} \end{matrix}

…”

Section: Model Calibrationmentioning

confidence: 99%

See 1 more Smart Citation

Uncertainty quantification in LES of channel flow

Safta

Blaylock

Templeton

et al. 2016

Numerical Methods in Fluids

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Summary In this paper, we present a Bayesian framework for estimating joint densities for large eddy simulation (LES) sub‐grid scale model parameters based on canonical forced isotropic turbulence direct numerical simulation (DNS) data. The framework accounts for noise in the independent variables, and we present alternative formulations for accounting for discrepancies between model and data. To generate probability densities for flow characteristics, posterior densities for sub‐grid scale model parameters are propagated forward through LES of channel flow and compared with DNS data. Synthesis of the calibration and prediction results demonstrates that model parameters have an explicit filter width dependence and are highly correlated. Discrepancies between DNS and calibrated LES results point to additional model form inadequacies that need to be accounted for. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Often, the impact of one uncertainty source is studied, but in order to make credible predictions, the greater effort required to aggregate multiple sources is necessary. Previously at Sandia, many pieces of the full rollup problem have been considered independently: the rollup of information from multiple validation points to the prediction conditions of interest [7], embedding model discrepancy into model parameter uncertainties during calibration to make better extrapolative predictions [8], and calibration of model parameters from multiple levels of model complexity using Bayesian networks [9]. Other methods of integrating uncertainty from different sources (i.e.…”

Section: Vvuq Workflow Applied To Applicationmentioning

confidence: 99%