Nowadays, artificial intelligence systems appear to be breakthrough tools for efficient management in modern transportation networks. One of the key problems for decision-makers in this sphere is the prediction or estimation of flow assignment. Despite the fact that researchers have already developed numerous approaches to dealing with the flow assignment problem, in many cases there is still a lack of ability to achieve the required speed of estimation. Indeed, the transport flow assignment problem is actually an optimization problem with a non-linear goal function and linear constraints, which requires special optimization techniques to be solved. However, the execution of the optimization algorithm takes a certain time, which can exceed acceptable levels, for instance, for real-time decision-making. We developed machine learning models to estimate flow assignment for a transportation network with multiple origin-destination pairs. We used solutions to the non-linear optimization problem of equilibrium flow assignment under different demand patterns to generate data sets for training and tests. Our computational study leads to the conclusion that the linear regression fits well to estimate flow assignment by travel demand values. We believe our findings can give fresh insights to transportation engineers.