This work aims to develop a Physics-Informed Machine Learning method for efficiently solving inverse problems, with a focus on parameter identification for flood models, a critical task for improving forecast accuracy. More precisely, we propose a method to infer spatially-distributed physical parameters (e.g., friction or infiltration coefficients) using PINNs (see Boulenc et al [1]). The approach incorporates a physical residual term in the loss function, corresponding to the residuals of the 2D Shallow Water Equations with a hydrological forcing term (rainfall and infiltration). Additionally, a data discrepancy term is included in the loss function, based on observations of free surface height and mass flow rate at various locations within the computational domain. These observations are generated from a reference solution obtained using the Dassflow software for twin experiments, before considering real data. The PINN parameters and the physical parameters are then optimized by minimizing the weighted sum of the physical residual and data discrepancy terms. The training involves a pre-training step where only the data discrepancy term is minimized, followed by an alternating minimization strategy between the PINN parameters and the physical parameters. To address high-frequency components in the solution and optimization challenges, a Fourier Features embedding and an adaptive weighting scheme for the loss terms are used. To illustrate the performance of this method, several test cases will be discussed, some based on real-world data. Overall, the proposed method appears efficient and robust. Moreover, it is simple to implement (non-intrusive) compared to more traditional Variational Data Assimilation approaches (see e.g., Monnier [2]), making it a viable strategy to further enhance for rapid flood forecasts. [1] H. Boulenc, R. Bouclier, P.-A. Garambois and J. Monnier. Spatially-distributed parameter identification by physics-informed neural networks illustrated on the shallow-water equations. Submitted. [2] J. Monnier. Data Assimilation. Inverse Problems, Assimilation, Control, Learning. Lectures notes, November 2021. URL https://hal.science/hal-03040047.