Coordinating emergency responses in extreme environments, such as wildfires, requires resilient and high-bandwidth communication backbones. While autonomous aerial swarms can establish ad-hoc networks to provide this connectivity, the high risk of individual node attrition in these settings often leads to network fragmentation and mission-critical downtime. To overcome this challenge, we introduce and formalize the problem of Robust Task Networking Under Attrition (RTNUA), which extends connectivity maintenance in multi-robot systems to explicitly address proactive redundancy and attrition recovery. We then introduce Physics-Informed Robust Employment of Multi-Agent Networks ($Φ$IREMAN), a topological algorithm leveraging physics-inspired potential fields to solve this problem. In our evaluations, $Φ$IREMAN consistently outperforms baselines, and is able to maintain greater than $99.9\%$ task uptime despite substantial attrition in simulations with up to 100 tasks and 500 drones, demonstrating both effectiveness and scalability.

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