Subsurface models with uncertainty quantification

A method and apparatus for modeling a subsurface region, including: obtaining a training set of geologically plausible models for the subsurface region; training an autoencoder with the training set; extracting a decoder from the trained autoencoder, wherein the decoder comprises a geologic-model-generating function; using the decoder within a data-fitting objective function to replace output-space variables of the decoder with latent-space variables, wherein a dimensionality of the output-space variables is greater than a dimensionality of the latent-space variables; and performing an inversion by identifying one or more minima of the data-fitting objective function to generate a set of prospective latent-space models for the subsurface region; and using the decoder to convert each of the prospective latent-space models to a respective output-space model. A method and apparatus for making one or more hydrocarbon management decisions based on the estimated uncertainty.