A method of operating a reservoir simulator can include performing a time step of a reservoir simulation using a spatial reservoir model that represents a subterranean environment that includes a reservoir to generate simulation results for a first time where the simulation results include a front defined by at least in part by a gradient at a position between portions of the spatial reservoir model; predicting a position of the front for a subsequent time step for a corresponding second time using a trained machine model; discretizing the spatial reservoir model locally at the predicted position of the front to generate a locally discretized version of the spatial reservoir model; and performing a time step of the reservoir simulation using the locally discretized version of the spatial reservoir model to generate simulation results for the second time.