Model order reduction is a pervasive and necessary activity in materials research. However, even though reduced order models are never perfect, their “imperfection” is almost never accounted for. In this talk, I will give an example of how the quality of an inference in materials research may be improved by accounting for the imperfection of a reduced order model. The example will consider inference of the properties of a substrate based on the behavior of a phase separating thin film deposited on the substrate.