High-fidelity models are expensive for numerical simulations, especially in multi-query scenarios, thus reduced-order modeling has been introduced to provide computationally cheap surrogates. Such reduced-order models are constructed offline based on a collection of snapshot data, that are of low dimensions and can be efficiently simulated at an online stage. Although the reduced-order modeling has achieved many successes, its efficacy could degrade when the problem of interest has a slowly decaying Kolmogorov n-width. In this talk, we consider incompressible fluid flows and introduce data-driven closure methods to overcome this challenge, which provides nonlinear surrogate models of better stability and accuracy.