<p>The <i>p</i>-hub median problem is central to location science, with multiple applications in network design. Given a set of nodes, each of them sends and receives some flow to and from the other nodes. Among these nodes, <i>p</i> have to be selected to serve as hubs, which act as switching points for directing the flow. These hubs are interconnected with direct links to form a complete subnetwork, while every non-hub node is linked to one of these selected hubs. The <i>p</i>-hub median problem typically arises in the modeling of air traffic, disaster management, logistics, and telecommunications networks, among others. In a world driven by dynamic data, situations may arise in which the same <i>p</i>-hub median problem must be solved for multiple instances with varying flows. While solving each instance exactly from scratch may require long computational times, learning from a training set of previously solved instances can help predict near-optimal solutions for new ones in which the flows have been changed. In this setting, we propose two heuristics to address the <i>p</i>-hub median location problem with single allocation and unconstrained hub capacity: one for problems in which all hub links are activated, allowing flow exchange between every pair of hubs, and another for problems in which flow exchanges between hubs are limited because not all hub links are activated. For the case where all hubs exchange flow with each other, the set of nodes acting as hubs is predicted using a machine learning approach. In the case where flow exchanges between hubs are limited, both the hubs and the activated connections between hubs are predicted using machine learning. Both heuristics include carefully designed strategies to restore feasibility. Our extensive computational results demonstrate the effectiveness of the proposed heuristics, both in terms of the good quality of the solutions, which are near-optimal, and in their ability to produce them in record time when compared to state-of-the-art approaches.</p>