Embedded discrepancy operators in reduced models of interacting species

In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain critical populations are truly consequential). Thus it is common to use greatly reduced models, in which only the interactions among the species of interest are retained. However, reduction introduces a model error, or discrepancy, which typically is not well characterized. In this work, we explore the use of an embedded and statistically calibrated discrepancy operator to represent model error. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information, and calibrated over many scenarios. These qualities of the discrepancy model---interpretability, physical-consistency, and robustness to different scenarios---are intended to support reliable predictions under extrapolative conditions.