In this work, we present an equation-based parametrized Reduced Order Model (ROM) enhanced with data-driven machine learning techniques to improve its accuracy. Our focus lies on a Proper Orthogonal Decomposition (POD)-Galerkin approach, in the under-resolved or marginally-resolved regime, namely where the number of retained modes is insufficient to fully capture the system dynamics. In such cases, we seek to recover the influence of the truncated modes by incorporating additional closure or correction terms directly into the reduced equations. Similar closure strategies have been explored in non-parametrized settings, for instance by modeling the closure as a quadratic function of the reduced coefficients (e.g., [1, 2, 3, 4]). Our approach extends this framework to a parametrized context by leveraging machine learning (in particular, Deep Operator Networks) to learn these closure terms. We assess the proposed method on several benchmark problems featuring different parameters and flow behaviors: the periodic turbulent flow past a circular cylinder, the unsteady turbulent flow in a lid-driven cavity, and the geometrically parametrized backstep flow. In all test cases and different modal regimes, the machine learning-augmented ROM significantly outperforms the standard ROM in terms of flow reconstruction accuracy. [1] Xie, X., Mohebujjaman, M., Rebholz, L. G., & Iliescu, T. (2018). Data-driven filtered reduced order modeling of fluid flows. SIAM Journal on Scientific Computing, 40(3), B834-B857. [2] Mohebujjaman, M., Rebholz, L. G., & Iliescu, T. (2019). Physically constrained data-driven correction for reduced-order modeling of fluid flows. International Journal for Numerical Methods in Fluids, 89(3), 103-122. [3] Ivagnes, A., Stabile, G., Mola, A., Iliescu, T., & Rozza, G. (2023). Pressure data-driven variational multiscale reduced order models. Journal of Computational Physics, 476, 111904. [4] Ivagnes, A., Stabile, G., Mola, A., Iliescu, T., & Rozza, G. (2023). Hybrid data-driven closure strategies for reduced order modeling. Applied Mathematics and Computation, 448, 127920.