Quantifying Sampling Noise and Parametric Uncertainty in Atomistic-to-Continuum Simulations Using Surrogate Models

We present a methodology to assess the predictive fidelity of multiscale simulations byincorporating uncertainty in the information exchanged between the components of anatomistic-to-continuum simulation. We account for both the uncertainty due to finitesampling in molecular dynamics (MD) simulations and the uncertainty in the physicalparameters of the model. Using Bayesian inference, we represent the expensive atomisticcomponent by a surrogate model that relates the long-term output of the atomisticsimulation to its uncertain inputs. We then present algorithms to solve for the variablesexchanged across the atomistic-continuum interface in terms of polynomial chaos expansions(PCEs). We consider a simple Couette flow where velocities are exchanged between theatomistic and continuum components, while accounting for uncertainty in the atomisticmodel parameters and the continuum boundary conditions. Results show convergence of thecoupling algorithm at a reasonable number of iterations. The uncertainty in the obtainedvariables significantly depends on the amount of data sampled from the MD simulations andon the width of the time averaging window used in the MD simulations.