1. A method for causing a computer processor to assist with creating a space-time surrogate model of a subsurface region, the method comprising: (a) providing non-transitory computer readable instructions to the computer processor to cause the computer processor to generate a surrogate model of a full-physics model of a subsurface region for preselected variables at a first time value within a range of time values within at least a portion of the full-physics model and determining a corresponding surrogate model coefficient for the first time value; (b) repeating step (a) n times for n additional time values that are different than the first time value, wherein n is an integer greater than 1, wherein the first time value and the n additional time values define the range of time values and creates a matrix of surrogate model coefficients over the range of time values; (c) generating a time-varying function related to at least a portion of the matrix of surrogate model coefficients; and (d) thereafter, creating an explicit space-time surrogate model of the at least a portion of the full physics model based on (1)the surrogate models produced by the generating and the repeating and (2) the generated at least one time-varying function, wherein the created explicit space-time surrogate model is parametric for at least the preselected variables and also indicates changes in the preselected variables over at least the range of time values.