Quantum　control　plays　an　irreplaceable　role　in　practical　use　of　quantum　computers.　However,　some　challenges　have　to　be　overcome　to　find　more　suitable　and　diverse　control　parameters.　We　propose　a　promising　and　generalizable　average-fidelity-based　machine-learning-inspired　method　to　optimize　the　control　parameters,　in　which　a　neural　network　with　periodic　feature　enhancement　is　used　as　an　ansatz.　In　the　implementation　of　a　single-qubit　gate　by　cat-state　nonadiabatic　geometric　quantum　computation　via　reverse　engineering,　compared　with　the　control　parameters　in　the　simple　form　of　a　trigonometric　function,　our　approach　can　yield　significantly　higher-fidelity　(＞99.99%)　phase　gates,　such　as　the　pi/8　gate　(T　gate).　Single-qubit　gates　are　robust　against　systematic　noise,　additive　white　Gaussian　noise,　and　decoherence.　We　numerically　demonstrate　that　the　neural　network　possesses　the　ability　to　expand　the　model　space.　With　the　help　of　our　optimization,　we　provide　a　feasible　way　to　implement　cascaded　multiqubit　gates　with　high　quality　in　a　bosonic　system.　Therefore,　the　machine-learning-inspired　method　may　be　feasible　in　quantum　optimal　control　of　nonadiabatic　geometric　quantum　computation.