A general adaptive modeling algorithm for selection and validation of coarsegrained models of atomistic systems is presented. A Bayesian framework is developed to address uncertainties in parameters, data, and model selection. Algorithms for computing output sensitivities to parameter variances, model evidence and posterior model plausibilities for given data, and for computing what are referred to as Occam Categories in reference to a rough measure of model simplicity, make up components of the overall approach. Computational results are provided for representative applications.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.