Despite increasing computational resources many high-dimensional applications are impractical for model inversions. In this paper, two methods are presented that are promising for high-dimensional model inversion. The methods draw on proper orthogonal decomposition (POD) and yield reduced models that describe a truncated behavior of the original model. We utilize POD differently for the two methods, which differ in efficiency and implementation. The first method (RIGM) applies a POD to an existing partial differential equation; the second method (RISM) applies it to an autoregressive formulation of a discrete model. Both methods were applied to several synthetic cases and a real-world case with synthetic measurements and by comparing them to classic inverse methodologies (i.e., the method of finite differences and the adjoint method). The two POD methods appeared to be computationally robust and more efficient for a wide range of prior estimates. Moreover, the implementation of an adjoint for the RISM method is easy.