In molecular dynamics (MD) simulation, the two main sources of uncertainty are the interatomic potential functions and thermal fluctuation. The accuracy of the interatomic potential functions plays a vital role toward the reliability of MD simulation prediction. Reliable molecular dynamics (R-MD) is an interval-based MD simulation platform, where atomistic positions and velocities are represented as Kaucher (or generalized) intervals to capture the uncertainty associated with the interatomic potentials. The advantage of this uncertainty quantification (UQ) approach is that the uncertainty effect can be assessed on-the-fly with only one run of simulation, and thus the computational time for UQ is significantly reduced. In this paper, an extended interval statistical ensemble is introduced to quantify the uncertainty associated with the system control variables, such as temperature and pressure at each time-step. This method allows for quantifying and propagating the uncertainty in the system as MD simulation advances. An example of interval isothermal-isobaric (NPT) ensemble is implemented to demonstrate the feasibility of applying the intrusive UQ technique toward MD simulation.
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