Towards Graph Foundation Models for Dynamics in Complex Networked Systems: Lessons from Super-Spreader Identification in Multilayer Networks

Network dynamics --- including spreading, influence maximisation, and epidemic modelling --- remain largely confined to the transductive paradigm, where models are trained on a single network and cannot be reused on unseen graphs without retraining. We argue that inductive cross-network generalisation is a necessary prerequisite for Graph Foundation Models (GFMs) in this domain and identify four design desiderata they must satisfy. As a proof of concept, \textit{ts-net} (TopSpreadersNetwork), trained solely on synthetic multilayer networks (MLNs), demonstrates zero-shot generalisation to real-world MLNs of varying size and layer count, outperforming classical heuristics and transductive baselines on three of four metrics. Based on \textit{ts-net}'s performance, we further outline five open challenges towards building GFMs for network dynamics: scale, many-layer generalisation, self-supervised pretraining, cross-task transfer, and node-attribute integration.