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Heterogeneous aerial access networks (AANs), comprising a hierarchical model of a low Earth orbit (LEO) satellite constellation and multiple high-altitude platforms (HAPs), provide a radio access medium from the sky to enhance the service experience of ground terminals (GTs) in remote areas. In this scenario, aerial edge caching addresses the challenge of delivering on-demand content requests to GTs. Although existing caching schemes for AANs have improved caching efficiency, they often overlook important concerns related to privacy preservation and overhead. This paper proposes an intelligent, proactive content-caching scheme to maximize cache efficiency while ensuring privacy preservation for GTs. The proposed caching scheme employs hierarchical federated learning (HierFL) that involves GTs, HAPs, and LEO satellites in heterogeneous AANs. In particular, the proposed HierFL-based proactive …