Computational Steering increases the understanding of relationships between the output of a simulation and its parametrized input. Steering relies on a running simulation which delivers results to a visualization system. However, many simulation codes cannot deliver the required interactive results. This work investigates the use of surrogate models to augment computational steering approaches. Based on the sparse grid method, we present a distributed system that is able to deliver approximate simulation snapshots from a central repository, at interactive rates, even for very large data sets. Combined with visual analytics, we present a novel integrated workflow for the fast investigation of parametrized simulations. The suitability of the method is demonstrated with various applications.