Weather　forecasting　has　become　a　popular　research　topic　recently,　which　mainly　benefits　from　the　development　of　spatio-temporal　neural　networks　to　effectively　extract　useful　patterns　from　weather　data.　Generally,　the　weather　changes　in　the　meteorological　system　are　governed　by　physical　principles.　However,　it　is　challenging　for　spatio-temporal　methods　to　capture　the　physical　knowledge　of　meteorological　dynamics.　To　address　this　problem,　we　propose　in　this　paper　a　spatio-temporal　Transformer　network　with　physical　knowledge　distillation　(PKD-STTN)　for　weather　forecasting.　First,　the　teacher　network　is　implemented　by　a　differential　equation　network　that　models　weather　changes　by　the　potential　energy　in　the　atmosphere　to　reveal　the　physical　mechanism　of　atmospheric　movements.　Second,　the　student　network　uses　a　spatio-temporal　Transformer　that　concurrently　utilizes　three　attention　modules　to　comprehensively　capture　the　semantic　spatial　correlation,　geographical　spatial　correlation,　and　temporal　correlation　from　weather　data.　Finally,　the　physical　knowledge　of　the　teacher　network　is　transferred　to　the　student　network　by　inserting　a　distillation　position　encoding　into　the　Transformer.　Notice　that　the　output　of　the　teacher　network　is　distilled　to　the　position　encoding　rather　than　the　output　of　the　student　network,　which　can　largely　utilize　physical　knowledge　without　influencing　the　feature　extraction　process　of　Transformers.　Experiments　on　benchmark　datasets　show　that　the　proposed　method　can　effectively　utilize　physical　principles　of　weather　changes　and　has　obvious　performance　advantages　compared　with　several　strong　baselines.　©　2024　ACM.