Stokes flow in repeated unit cell structures is extensively studied in applications for many natural and engineering processes. However, for large number of cells, resolving all scales can be prohibitively expensive using traditional numerical methods. To make the problem tractable, these methods often rely on volume-averaged approximation, resulting in accuracy issues. To address this, we propose a novel data-driven component model reduction approach that is constrained by the first-principle physics equation. This method employs reduced order modeling (ROM) to identify crucial physics modes in small-scale unit components and projects them onto the governing physics equation, creating a reduced model with essential physics details. We incorporate discontinuous Galerkin domain decomposition (DG-DD), enabling large-scale system construction without data at such vast scales. Applying this approach to incompressible Stokes flow equation, we achieve nearly 100 times faster solutions with a relative error of ~1%, even at scales 1000 times larger than the original problem.