When using simulations for decision making, no matter the domain, the uncertainty of the simulations' output is an important concern. This uncertainty is traditionally estimated by propagating input uncertainties forward through the simulation model. However, this approach requires extensive data collection before the output uncertainty can be estimated. In the worst case scenario, the output may even prove too uncertain to be usable, possibly requiring multiple revisions of the data collection step. To reduce this expensive process, we propose a method for inverse uncertainty propagation using Gaussian processes. For a given bound on the output uncertainty, we estimate the input uncertainties that minimize the cost of data collection and satisfy said bound. That way, uncertainty requirements for the simulation output can be used for demand driven data acquisition. We evaluate the efficiency and accuracy of our approach with several examples.