Physics-based, non-intrusive modeling comprises a promising solution to dynamics prediction for systems with partially known physical laws, for which data are available, either through experimental campaigns or proprietary software simulations. Non-intrusive, reduced-order modeling methods are specifically interesting, as they allow for high computational efficiency by projecting the system dynamics onto a basis of reduced dimension. The inferred reduced-order models are highly accurate for a wide class of dynamical systems. From a different perspective, a recent line of work has focused on the inference of phyiscs-informed, full-order models (FOMs) which govern system dynamics. This approach is motivated by the sparsity of polynomial operators in spatially discretized partial differential equations. Exploiting sparsity creates the potential for computation and storage of otherwise intractable, non-intrusive FOMs. Under this perspective, the inferred model is independent of a projection basis, which could in turn allow for dynamical predictions beyond the span of the training data. Nonetheless, this capability comes at a significant offline and online computational cost. In this work we investigate the potential of leveraging the capabilities of localized, sparse FOM inference and the high computational efficiency of a non-intrusive ROM, via domain decomposition for systems with localized, slow singular value decay. Assuming state access, the spatial domain is decomposed into two subdomains where the system dynamics exhibit slow and fast singular value decay, respectively. By inferring a full-order model on the former subdomain, we aspire to capture phenomena with slow singular value decay, such as advection-dominated dynamics. Employing a ROM for the latter subdomain considerably restricts the involved com-putational cost for the overall system inference, while retaining prediction accuracy over the span of the training data. Approaches for deriving the coupled, domain-decomposed, non-intrusive FOM/ROM system are discussed. Finally, we present numerical results forlinear and nonlinear systems which arise in fluid dynamics problems.