Methods for creating and using space-time surrogate models of subsurface regions, such as subsurface regions containing at least one hydrocarbon formation. The created surrogate models are explicit models that may be created from implicit models, such as computationally intensive full-physics models. The space-time surrogate models are parametric with respect to preselected variables, such as space, state, and/or design variables, while also indicating responsiveness of the preselected variables with respect to time. In some embodiments, the space-time surrogate model may be parametric with respect to preselected variables as well as to time. Methods for updating and evolving models of subsurface regions are also disclosed.