Numerical simulation of multiscale problems characterized by complex microstructures remains a major computational challenge due to strong geometric heterogeneity, scale separation, and the high dimensionality of the underlying models. In this work, we investigate how non-intrusive Model Order Reduction (ROM) techniques can be systematically incorporated within a Domain Decomposition (DD) framework, combining data-driven model reduction and problem localization to construct efficient and scalable solvers while preserving a consistent mathematical formulation at the global level. The proposed formulation builds on the complementary strengths of the two methodologies. On the one hand, domain decomposition techniques confine computational complexity to smaller, independently solvable subproblems, enabling parallelism and localized resolution of heterogeneous features. On the other hand, reduced order modeling provides low-dimensional surrogate representations that significantly accelerate local computations without requiring intrusive modifications of the governing equations or discretization schemes. A key contribution of this work is the introduction of a localization procedure that defines local parametric spaces associated with each subdomain, allowing the training of surrogate models using subdomain-specific data only. The proposed methodology is motivated by mixed-dimensional PDEs, in particular applications to a coupled 3D–1D models of microcirculation. The three-dimensional tissue domain is partitioned into voxels, within which expressive low-dimensional representations are obtained by training local ROMs based on Proper Orthogonal Decomposition (POD) and sparse Mesh-Informed Neural Networks (MINNs) [2] in a supervised learning setting. These local reduced models are coupled through an Optimized Schwarz method with Robin transmission conditions [1], together with iterative updates of the one-dimensional network variables describing vascular flow. Numerical experiments demonstrate that the resulting DD–ROM algorithm converges to a consistent and accurate global solution, effectively combining the scalability of domain decomposition with the computational efficiency of localized reduced models.