Edge　devices　(EDs)　carry　limited　energy,　but　6th　generation　mobile　networks　(6G)　communication　will　consume　more　energy.　The　unmanned　aerial　vehicle　(UAV)-aided　wireless　communication　network　can　provide　communication　links　to　EDs　without　a　signal.　However,　with　the　time-lag　system,　the　EDs　cannot　dynamically　adjust　the　emission　energy　because　the　dynamic　UAV　coordinates　cannot　be　accurately　acquired.　In　addition,　the　fixed　emission　energy　makes　the　EDs　have　poor　endurance.　To　address　this　challenge,　in　this　paper,　we　propose　a　deep　learning-based　energy　optimization　algorithm　(DEO)　to　dynamically　adjust　the　emission　energy　of　the　ED　so　that　the　received　energy　of　the　mobile　relay　UAV　is,　as　much　as　possible,　equal　to　the　sensitivity　of　the　receiver.　Specifically,　the　edge　server　provides　the　computing　platform　and　uses　deep　learning　(DL)　to　predict　the　location　information　of　the　relay　UAV　in　dynamic　scenarios.　Then,　the　ED　emission　energy　is　adjusted　according　to　the　predicted　position.　It　enables　the　ED　to　communicate　reliably　with　the　mobile　relay　UAV　at　minimum　energy.　We　analyze　the　performance　of　a　variety　of　predictive　networks　under　different　time-delay　systems　through　experiments.　The　results　show　that　the　Weighted　Mean　Absolute　Percentage　Error　(WMAPE)　of　this　algorithm　is　0.54%,　0.80%　and　1.15%　under　the　effect　of　a　communication　delay　of　0.4　s,　0.6　s　and　0.8　s,　respectively.　©　2022　by　the　authors.　Licensee　MDPI,　Basel,　Switzerland.