Probing the Higgs portal to a strongly-interacting dark sector at the FCC-ee

collisions. The ensuing strong dynamics may lead to semi-visible jet final states, containing both visible and invisible particles. We investigate semi-visible jets with different fractions of invisible states, and enriched in leptons and photons. When the invisible component is large, selections based on kinematic features, such as the missing energy in the event, already provide good signal-to-background discrimination. For smaller invisible fractions, the reduced missing energy makes these signals more similar to Standard Model events, and we therefore employ a graph neural network jet tagger exploiting differences in jet substructure. This machine learning strategy improves sensitivity and enhances the discovery prospects of Higgs boson-induced semi-visible jets at the Future Circular Collider. Our results show that the proposed strategy can effectively probe a wide parameter space for the models considered, and a variety of signatures, constraining the Higgs boson exotic branching ratios into dark quarks at the permille-level.