This　chapter　introduces　both　the　fundamentals　and　advanced　formulations　of　artificial　neural　network　(ANN)　techniques　for　parametric　electromagnetic　(EM)　modeling　and　optimization.　ANN　is　an　information　handling　system　whose　design　was　enlightened　by　the　investigation　into　the　human　brain’s　capacity　to　learn　from　observations　and　to　summarize　through　abstraction.　ANN　is　an　acknowledged　tool　for　parametric　EM　modeling　and　optimization,　that　is,　using　geometric　parameters　as　variables　to　represent　the　EM　behavior.　Direct　methods　for　EM　design　optimization　are　generally　computationally　expensive　and　require　repeated　EM　evaluations　due　to　constantly　changing　geometry.　ANN　has　become　an　effective　method　for　EM　parametric　modeling　by　learning　the　relationship　between　EM　conducts　and　geometric　parameters.　The　ANN　after　training　can　quickly　solve　the　EM　behavior　of　microwave　devices　when　the　geometric　parameters　change　repeatedly.　If　a　neural　network　has　multiple　hidden　layers,　it　is　defined　as　a　deep　neural　network.　In　modeling　highly　complicated　sophisticated　relationships,　such　as　modeling　with　high-dimensional　filters　with　numerous　input　variables,　deep　neural　networks　can　do　better　than　shallow　neural　networks　(neural　networks　with　only　a　few　hidden　layers).　Exploiting　the　availability　of　prior　knowledge　for　parametric　EM　modeling,　knowledge-based　neural　networks　(KBNNs)　have　been　exploited.　Compared　with　traditional　ANN,　KBNN　can　achieve　identical　modeling　precision　with　fewer　training　data　and　offer　preferable　extrapolation,　thus　accelerating　model　development　and　improving　the　generalization　ability　of　parametric　EM　modeling　and　optimization.　A　progressive　knowledge-based　modeling　method,　combining　neural　networks　and　transfer　functions　(neuro-transfer　functions　or　neuro-　transfer　function　[　TF　s]),　has　been　exploited　for　parametric　modeling　of　EM　responses.　Since　an　appropriate　equivalent　circuit　model/experience　model　may　not　be　exploitable　in　certain　cases,　the　neuro-TF　approach　is　capable　of　using　the　transfer　function　as　the　prior　knowledge.　The　ANN-based　parametric　EM　models　can　be　further　utilized　as　surrogate　models　for　EM　optimizations.　The　exploration　of　ANN　techniques　for　parametric　EM　modeling　and　optimization　is　a　hot　topic　and　continues　to　be　an　open　and　strategic　direction.　©　2023　by　The　Institute　of　Electrical　and　Electronics　Engineers,　Inc.