7 - Reliable molecular dynamics simulations for intrusive uncertainty quantification using generalized interval analysis

Abstract

The major source of uncertainty in molecular dynamics (MD) simulation is the interatomic potential function. The interatomic potentials are derived experimentally or from first-principles calculations, and they inherit the measurement error or model-form error in quantum calculation. Nonintrusive uncertainty quantification (UQ) approaches have been applied to estimate the prediction errors of MD simulation. In these approaches, the MD simulation is treated as a black box, thus high computational cost is involved in sampling. In this work, a reliable molecular dynamics (R-MD) mechanism is developed to extend the predictive capability of MD given the input uncertainty. In R-MD, the interatomic potentials are represented as interval-valued functions in order to capture the input uncertainty and imprecision. The advantage of the intrusive UQ approach is the significant reduction of computational cost from traditional sensitivity analysis when assessing the effects of input uncertainty. The interval versions of Lennard-Jones and embedded atomic method (EAM) potentials are developed. Error generating functions associated with EAM potentials are devised to capture the bounds of input variations. Four different computational schemes for uncertainty propagation in R-MD are proposed. An example of uniaxial tensile loading of single-crystal aluminum is used to demonstrate the R-MD framework.