The growth of computational resources in the past decades has expanded the application of Computational Fluid Dynamics (CFD) from the traditional fields of aerodynamics and hydrodynamics to a number of new areas. Examples range from the heat and fluid flows in nuclear reactor vessels and in data centers to the turbulence flows through wind turbine farms and coastal vegetation plants. However, in these new applications complex structures are often exist (e.g., rod bundles in reactor vessels and turbines in wind farms), which makes fully resolved, first-principle based CFD modeling prohibitively expensive. This obstacle seriously impairs the predictive capability of CFD models in these applications. On the other hand, a limited amount of measurement data is often available in the systems in the above-mentioned applications. In this work we propose a data-driven, physics-based approach to perform full field inversion on the effects of the complex structures on the flow. This is achieved by assimilating observation data and numerical model prediction in an iterative Ensemble Kalman method. Based on the inversion results, the velocity and turbulence of the flow field can be obtained. A major novelty of the present contribution is the non-parametric, full field inversion approach adopted, which is in contrast to the inference of coefficient in the ad hoc models often practiced in previous works. The merits of the proposed approach are demonstrated on the flow past a porous disk by using both synthetic data and real experimental measurements. The spatially varying drag forces of the porous disk on the flow are inferred. The proposed approach has the potential to be used in the monitoring of complex system in the above mentioned applications.