Reliable Molecular Dynamics: Uncertainty quantification using interval analysis in molecular dynamics simulation

In molecular dynamics (MD) simulation, atomic interaction is characterized by the interatomic potential as the input of simulation models. The interatomic potentials are derived experimentally or from first principles calculations. Therefore they are inherently imprecise because of the measurement error or model-form error. 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 locations and velocities of particles are not assumed to be precisely known as in traditional MD. Instead, they are represented as intervals in order to capture the input uncertainty associated with the atomistic model. The advantage of the new mechanism is the significant reduction of computational cost from traditional sensitivity analysis when assessing the effects of input uncertainty. A formalism of generalized interval is incorporated in R-MD, as an intrusive uncertainty quantification method, to model the propagation of uncertainty during the simulation. Error generating functions associated with embedded atomic method (EAM) interatomic potentials are developed to capture the bounds of input variations to demonstrate interval interatomic potentials. Four different uncertainty propagation schemes are proposed to capture the uncertainty of the output. An example of uniaxial tensile loading of single-crystal aluminum is used to demonstrate the R-MD mechanism. (C) 2016 Elsevier B.V. All rights reserved.