Although　numerous　models　have　been　proposed　to　predict　the　intensity　of　human　activities　in　urban　areas,　two　major　issues　hamper　the　performance　of　existing　models:　(1)　fail　to　incorporate　appropriate　prior　knowledge　instrumental　for　improving　accuracy　and　interpretability;　(2)　fail　to　integrate　probabilistic　and　deterministic　predictions　to　achieve　complementary　strengths,　namely　uncertainty　quantification　and　high　predictive　accuracy.　To　address　these　challenges,　we　proposed　a　prior-enhanced　dual-mode　spatiotemporal　graph　neural　network　(PED-STGNN)　to　support　both　probabilistic　and　deterministic　predictions.　Specifically,　we　introduced　a　hypergraph　node-to-vector　(hypernode2vec)　method　to　capture　the　multivariate　functional　similarity　prior　derived　from　complex　and　multivariate　relations　between　urban　regions.　This　functional　similarity　characterizes　urban　systems　more　precisely　than　existing　methods　relying　on　first-order　pairwise　relations.　It　improves　accuracy　and　interpretability　while　enabling　spatial　modeling　of　higher-order　multivariate　relations　beyond　first-order　pairwise　relations.　We　also　designed　a　plug-and-play　probabilistic　prediction　module　that　enables　switches　between　probabilistic　and　deterministic　modes.　Experiments　based　on　the　human　activity　intensity　in　Fuzhou,　China,　demonstrated　the　advantages　in　accuracy,　interpretability　and　multi-scenario　applicability.