Calibration and validation of coarse-grained models of atomic systems: application to semiconductor manufacturing

Farrell, Kathryn; Oden, J. Tinsley

doi:10.1007/s00466-014-1028-y

Cited by 15 publications

(11 citation statements)

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“…Let π(θ) be any prior probability density on the parameters θ (computed, for instance, using the maximum entropy method of Jaynes [12], as described for CG models in [3]); then the posterior density satisfies,…”

Section: Model Misspecification and Statistical Analysismentioning

confidence: 99%

“…[12] for discussion of the ideas) and was introduced to the best of our knowledge in [18]. The development of algorithms involving Bayesian plausibilities to study model selection in CG models of complex atomic system is discussed in [3,20]. It has been demonstrated, the most plausible model in a set will, under stated assumptions, involve parameters that minimize the D KL −distance between the model and the so-called truth parameters.…”

Section: Plausibility-d Kl Theorymentioning

confidence: 99%

“…It has been demonstrated, the most plausible model in a set will, under stated assumptions, involve parameters that minimize the D KL −distance between the model and the so-called truth parameters. Whether that "best" model is valid for the intended purpose depends on tolerances set of error in key observables, the QoIs of the validation scenario (see [3]). …”

Section: Plausibility-d Kl Theorymentioning

confidence: 99%

“…The use of coarse-grained (CG) approximations has been prevalent in molecular dynamics (MD) simulations for many decades Comprehensive reviews of a large segment of the literature on CG models was recently given by Noid [1] and Li et al [2], and an application to semiconductor nano-manufacturing is discussed in Farrell et al [3]. The issue of central importance in developing CG models is the accuracy with which they approximate key features of the atomistic system.…”

mentioning

confidence: 99%

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Estimation of error in observables of coarse-grained models of atomic systems

Oden

Farrell

Faghihi

2015

Adv. Model. and Simul. in Eng. Sci.

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Background: The use of coarse-grained approximations of atomic systems is the most common methods of constructing reduced-order models in computational science. However, the issue of central importance in developing these models is the accuracy with which they approximate key features of the atomistic system. Many methods have been proposed to calibrate coarse-grained models so that they qualitatively mimic the atomic systems, but these are often based on heuristic arguments. Methods: A general framework for deriving a posteriori estimates of modeling error in coarse-grained models of key observables in atomistic systems is presented. Such estimates provide a new tool for model validation analysis. The connection of error estimates with relative information entropy of observables and model predictions is explained for so-called misspecified models. The relationship between model plausibilities and Kullback-Leibler divergence between the true parameters and model predictions is summed up in several theorems. Results: Numerical examples are presented in this paper involving a family of coarsegrained models of a polyethylene chain of united atom monomers. Numerical results suggest that the proposed methods of error estimation can be very good indications of the error inherent in coarse-grained models of observables in the atomistic systems. Also, new theorems relating the Kullback-Leibler divergence between model predictions and observations to measures of model plausibility are presented. Conclusions: A formal structure for estimating errors produced by coarse-graining atomistic models is presented. Numerical examples confirm that the estimates are in agreement with exact errors for a simple class of materials. Errors measured in the D KL -divergence can be related to computable model plausibilities. The results should provide a powerful framework for assessing the validity and accuracy of coarse-grained models.

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Section: Model Misspecification and Statistical Analysismentioning

confidence: 99%

Section: Plausibility-d Kl Theorymentioning

confidence: 99%

Section: Plausibility-d Kl Theorymentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Estimation of error in observables of coarse-grained models of atomic systems

Oden

Farrell

Faghihi

2015

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…It was certainly known to Schwarz [26], who developed easily implemented approximations to model evidence that lead to the Bayesian information criterion (BIC) in analogy to information-theoretic approaches. More recently, the use of such Bayesian probability approaches for model selection were advocated by Beck and Yuen [5], Hawkins-Daarud et al [13], and Farrell et al [10,11]; see also [24].…”

Section: Model Selectionmentioning

confidence: 99%