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With a new approach of driving force application, the relationship between grain boundary migration rate and driving force was found to be nonlinear as to be expected from rate theory for extremely large applied driving forces in molecular dynamics simulations. By evaluating grain boundary mobility non-linearly, the simulated mobilities at different temperatures reveal that grain boundary migration is a thermally activated process. For a series of <110> twist grain boundaries, the resultant mobilities demonstrate that high-angle grain boundaries move much faster than low-angle grain boundaries.