Nowadays, artificial intelligence systems seem to be breakthrough tools for the efficient management of modern transportation networks. One of the key challenges for decision makers in this area is to predict or estimate dynamic flows in real time in case of emergency situations that affect the capacity of network elements. It is generally accepted that the problem of flow assignment is an optimization problem with a nonlinear objective function and linear constraints, which requires special optimization methods for solving. However, the execution of the optimization algorithm takes a certain time, which may exceed acceptable levels, for example, for real-time decision making. We developed neural network models to estimate the flow assignment in a transportation network under dynamically changing values of travel demand and capacities of arcs. We used solutions of the nonlinear optimization problem of equilibrium flow assignment under various demand models to generate datasets for training and testing. Our computational study leads to the conclusion that heterogeneous graph neural networks is well suited for flow assignment estimation in our case. We believe that our findings can provide new insights for transportation engineers.