Bayesian learning methods for potential energy parameter inference in coarse-grained models of atomistic systems

Abstract

The present work addresses issues related to the derivation of reduced models of atomistic systems, their statistical calibration, and their relation to atomistic models of materials. The reduced model, known in the chemical physics community as a coarse-grained model, is calibrated within a Bayesian framework. Particular attention is given to developing likelihood functions, assigning priors on coarse-grained model parameters, and using data from molecular dynamics representations of atomistic systems to calibrate coarse-grained models such that certain physically relevant atomistic observables are accurately reproduced. The developed Bayesian framework is then applied in three case studies of increasing complexity and practical application. A freely jointed chain model is considered first for illustrative purposes. The next example entails the construction of a coarse-grained model for a liquid heptane system, with the explicit design goal of accurately predicting a vapor-liquid transfer free energy. Finally, a coarse-grained model is developed for an alkylthiophene polymer that has been shown to have practical use in certain types of photovoltaic cells. The development therein employs Bayesian decision theory to select an optimal CG potential energy function. Subsequently, this model is subjected to validation tests in a prediction scenario that is relevant to the performance of a polyalkylthiophene-based solar cell.