To　make　full　use　of　the　handwriting　order　feature　and　global　two-dimensional　structure　feature　of　online　handwritten　mathematical　expression‚　a　dual-mode　recognition　model　based　on　an　encoder-decoder　framework　was　designed　by　combining　online　mode　and　offline　mode.　The　model　can　accept　the　handwritten　mathematical　expression　data　in　the　form　of　one-dimension　coordinate　point　sequence　and　two-dimensional　static　image.　The　model　can　extract　the　handwriting　order　feature　information　from　the　input　coordinate　point　sequence　through　the　online　encoder‚　and　extract　the　two-dimensional　structure　feature　information　from　the　static　image　through　the　offline　encoder‚　so　as　to　fully　retain　the　handwriting　order　feature　and　global　two-dimensional　structure　feature.　In　the　encoder　stage‚　sinusoidal　coding　was　proposed　for　the　online　mode　to　encode　the　input　coordinate　point　sequence　and　supplement　the　stroke　level　information‚　which　can　effectively　avoid　the　loss　of　stroke　information　caused　by　fuzzy　stroke　interval.　For　the　offline　mode‚　the　smooth　attention　mechanism　was　proposed.　By　adopting　the　smooth　window‚　adaptive　adjustment　of　the　receptive　field　of　each　pixel　feature　in　the　feature　map　was　realized‚　which　had　solved　the　problem　that　the　ordinary　attention　mechanism　cannot　filter　the　effective　feature　information　of　handwritten　symbols　with　large　size　differences　at　the　same　time.　It　had　effectively　improved　the　ability　of　the　attention　mechanism　to　capture　the　effective　handwritten　area.　The　experimental　results　show　that　the　accuracy　rate　of　mathematical　expression　recognition　of　the　dual-mode　model　can　reach　58.　76%　‚　and　compared　with　other　recognition　models　in　the　same　field‚　the　dual-mode　model　can　improve　the　accuracy　rate　of　mathematical　expression　recognition　by　1.　56%　-　4.　71%　‚　reaching　a　higher　level.　©　2024　Beijing　University　of　Technology.　All　rights　reserved.