Recent advances in hardware development have significantly improved simulation methods such as finite element method (FEM) and computational fluid dynamics (CFD). However, when dealing with high-fidelity simulations, computational cost is still a limiting factor, especially for scenarios that require real-time results. To address this challenge, the numerical methods community has developed several Reduced Order Models (ROM) techniques that allow that provide fast results with minimal loss of accuracy. Deep Learning (DL) helps to enhance these techniques, enabling real-time predictions for complex systems. In the present work, we propose a DL approach to estimate the evolution of velocity and pressure fields for flow-past a cylinder with varying. To promote generalization and physical consistency of the prediction, we introduce two biases are introduced to our method: an inductive bias and a geometrical bias. The inductive bias is applied by the GENERIC (General Equation of Non-Equilibrium Reversible-Irreversible Coupling) formalism [1], an extension of the Hamiltonian formalism for non-conservative systems. To apply the geometrical bias, we rely on graph neural networks (GNNs) [2], which learn local relationships between nodes in a graph, thus enabling generalization across different geometries. This approach also allows the method to deal with unstructured data, meaning that the simulation mesh can be treated as the input for the network. The combination of both biases leads to methods that are less data-hungry and provide thermodynamically-consistent predictions. Our network architecture is based on Thermodynamics-Informed Graph Neural Networks (TIGNNs) [3]. The method is tested on various geometries and input velocities, therefore varying the Reynolds number, and is compared with two additional methods. The first one is a Vanilla-GNN, which introduces the geometrical bias but relies solely on data. The second combines the use of an Autoencoder (AE) and a Structure Preserving Neural Network (SPNN)[4], obtaining a ROM for predicting the dynamical evolution of the flow.