This paper discusses a physics-informed methodology aimed at reconstructing efficiently the fluid state of a system. Herein, the generation of an accurate reduced order model of two-dimensional unsteady flows from data leverages on sparsity-promoting statistical learning tech-niques. The cornerstone of the approach is l1 regularised regression, resulting in sparsely-connected models where only the important quadratic interactions between modes are retained. The original dynamical behaviour is reproduced at low computational costs, as few quadratic inter-actions need to be evaluated. The approach has two key features. First, interactions are selected sys-tematically as a solution of a convex optimisation problem and no a priori assumptions on the physics of the flow are required. Second, the presence of a regularisation term improves the predic-tive performance of the original model, generally affected by noise and poor data quality. Test cases are for two-dimensional lid-driven cavity flows, at three values of the Reynolds number for which the motion is chaotic and energy interactions are scattered across the spectrum. It is found that:(A) the sparsification generates models maintaining the original accuracy level but with a lower number of active coefficients;this becomes more pronounced for increasing Reynolds numbers suggesting that extension of these techniques to real-life flow configurations is possible; (B) sparse models maintain a good temporal stability for predictions. The methodology is ready for more complex applications without modifications of the underlying theory, and the integration into a cyber-physical model is feasible.