Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant length scales. Here a class of coarse-grained stochastic processes and corresponding Monte Carlo simulation methods, describing computationally feasible mesoscopic length scales, are derived directly from microscopic lattice systems. It is demonstrated below that the coarse-grained stochastic models can capture large-scale structures while retaining significant microscopic information. The requirement of detailed balance is used as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or computer time per executive event compared to microscopic Monte Carlo simulations.
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