Forward　modeling　of　seismic　waves　using　physics-informed　neural　networks　(PINNs)　has　attracted　much　attention.　However,　a　notable　challenge　arises　when　modeling　seismic　wave　propagation　in　large　domains　(i.e.,　a　half-space),　PINNs　may　encounter　the　issue　of　＂soft　constraint　failure＂.　To　address　this　problem,　we　propose　a　novel　framework　called　physics-constrained　neural　networks　(PCNNs)　specifically　designed　for　modeling　seismic　wave　propagation　in　a　half-space.　The　method　of　images　is　incorporated　to　effectively　implement　the　free　stress　boundary　conditions　of　the　Earth＇s　surface,　leading　to　the　successful　propagation　of　plane　waves　and　cylindrical　waves　in　a　half-space.　We　analyze　the　training　dynamics　of　neural　networks　when　solving　two-dimensional　(2D)　wave　equations　from　the　neural　tangent　kernel　(NTK)　perspective.　An　adaptive　training　algorithm　is　introduced　to　mitigate　the　unbalanced　gradient　flow　dynamics　of　the　different　components　of　the　loss　function　of　PINNs/PCNNs.　Furthermore,　to　tackle　the　complex　behavior　of　seismic　waves　in　layered　media,　a　sequential　training　strategy　is　considered　to　enhance　network　scalability　and　solution　accuracy.　The　results　of　numerical　experiments　demonstrate　the　accuracy　and　effectiveness　of　our　approach.　©　2023　Elsevier　Ltd