The　imposition　of　boundary　conditions　is　an　essential　step　in　solving　the　definite　problem　of　partial　differential　equations.　When　the　definite　problem　of　partial　differential　equations　is　resolved　by　neural　network,　the　original　problem　should　be　transformed　to　its　corresponding　constructive　variational　problem,　and　the　loss　function　is　a　functional　consisting　of　the　governing　equations　and　the　boundary　conditions.　If　the　boundary　conditions　are　imposed　by　the　classical　penalty　function　method　and　its　improvements,　the　value　of　the　penalty　factor　will　affect　the　solution　accuracy　and　the　computational　efficiency.　If　the　boundary　conditions　are　directly　imposed　by　the　Lagrange　multiplier　method,　the　computational　results　may　deviate　from　the　optimal　solution　of　the　original　problem.　To　overcome　these　limitations,　the　generalized　multiplier　method　is　employed　in　the　imposition　of　boundary　conditions.　The　predicted　solution　of　the　original　problem　is　obtained　from　the　neural　network.　The　generalized　multiplier　method　is　used　to　construct　the　loss　function　of　the　neural　network　and　calculate　the　loss.　The　gradient　descent　method　is　utilized　to　perform　parameter　optimization.　Afterwards,　the　loss　function　is　calculated.　The　penalty　factor　and　multiplier　are　updated,　and　the　resolution　is　repeated　till　the　loss　is　acceptable.　The　results　of　numerical　examples　verify　that　the　proposed　method　has　better　solution　accuracy,　higher　computational　efficiency　and　more　stable　solution　process　than　those　neural　networks　in　which　the　boundary　conditions　are　applied　by　the　classical　penalty　function　method,　L1　exact　penalty　function　method,　and　Lagrange　multiplier　method.　©　2023　Tsinghua　University.　All　rights　reserved.