This work introduces a novel and efficient approach for solving inverse problems using Physics-Informed Neural Networks (PINNs)\cite{pinns1,conte_pinns}, with a specific focus on the Navier--Stokes equations. We propose an automated framework based on DeepXDE \cite{deepxde}, a specialized library that incorporates physical constraints directly into neural network architectures to enhance solution quality and convergence properties. The proposed methodology addresses the challenging inverse problem of parameter identification. Rather than relying on conventional numerical discretizations, our approach leverages the expressivity of neural networks to simultaneously learn flow fields and unknown parameters while enforcing physical conservation laws. We present comparative analyses between our PINN-based implementation and traditional numerical methods, demonstrating the advantages of our approach in terms of computational efficiency and solution accuracy for these challenging inverse problems. The methodology is validated through a series of numerical experiments addressing diverse inverse problems in computational fluid dynamics, ranging from incompressible Navier--Stokes flows to other relevant flow regimes. This research contributes to the emerging paradigm at the intersection of computational fluid dynamics and machine learning, offering new perspectives for solving computationally intensive inverse flow problems efficiently. \\ This work is supported by the research grant DSTE372---Risoluzione numerica di problemi differenziali anomali (RNPDA).