Fine-grained　crowd　distribution　forecasting　benefits　smart　transportation　operations　and　management,　such　as　public　transport　dispatch,　traffic　demand　prediction,　and　transport　emergency　response.　Considering　the　co-evolutionary　patterns　of　crowd　distribution,　the　interactions　among　places　are　essential　for　modelling　crowd　distribution　variations.　However,　two　issues　remain.　First,　the　lack　of　sampling　design　in　passive　big　data　acquisition　makes　the　spatial　interaction　characterizations　of　less　crowded　places　insufficient.　Second,　the　multi-order　spatial　interactions　among　places　can　help　forecasting　crowd　distribution　but　are　rarely　considered　in　the　existing　literature.　To　address　these　issues,　a　novel　crowd　distribution　forecasting　method　with　multi-order　spatial　interactions　was　proposed.　In　particular,　a　weighted　random　walk　algorithm　was　applied　to　generate　simulated　trajectories　for　improving　the　interaction　characterizations　derived　from　sparse　mobile　phone　data.　The　multi-order　spatial　interactions　among　contextual　non-adjacent　places　were　modelled　with　an　embedding　learning　technique.　The　future　crowd　distribution　was　forecasted　via　a　graph-based　deep　neural　network.　The　proposed　method　was　verified　using　a　real-world　mobile　phone　dataset,　and　the　results　showed　that　both　the　multi-order　spatial　interactions　and　the　trajectory　data　enhancement　algorithm　helped　improve　the　crowd　distribution　forecasting　performance.　The　proposed　method　can　be　utilized　for　capturing　fine-grained　crowd　distribution,　which　supports　various　applications　such　as　intelligent　transportation　management　and　public　health　decision　making.　©　2022　Elsevier　Ltd