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We propose an enhanced adaptive sampling method for heterogeneous multiscale simulations with stochastic data. Our multi-scale approach is based on the heterogeneous multi-scale method for two-dimensional hyperbolic conservation laws. A finite-volume scheme integrates the macro-scale differential equations for elastodynamics, which are supplemented by momentum and energy fluxes evaluated at the micro-scale. Therefore, light-weight MD simulations have to be launched for every volume element.
Our adaptive sampling scheme replaces costly micro-scale simulations with fast table lookup and prediction. The key-value database Redis serves as plain table lookup and with locality aware hashing we gather input data for our prediction scheme. For the latter we use ordinary kriging, which estimates an unknown value at a certain location by using weighted averages of the neighboring points. We find that our enhanced adaptive scheme significantly improves simulation performance about a factor of $10-25$, while retaining high accuracy for various choices of the algorithm parameters. With further development, adaptive sampling could be a promising tool for dynamical studies of defects such as interstitials, vacancies, and phase boundaries. |