The direct use of detailed chemical kinetics in combustion simulations is limited by the extremely high computational costs. Recently, Owoyele and Pal (Energy and AI, 2022), proposed the neural ordinary differential equations (NODE) method to accelerate calculations of chemical kinetics and proved its effectiveness in zero-dimensional calculations of hydrogen combustion considering 9 species and 21 reactions. However, its performance for more realistic high-dimensional calculations and more complex kinetic systems remains unexplored. Therefore, this study further applies the method for more complex chemical kinetics of ammonia combustion, especially with optimizations in the data sampling, model training strategies, and model application methods that remedy the problems of versatility and application to more practical simulations. The newly developed NODE models are comprehensively validated in the zero-dimensional calculations of ammonia auto-ignition, one-dimensional calculations of laminar freely-propagating ammonia-premixed flames, and two-dimensional direct numerical simulation (DNS) of ammonia-premixed flames in a temporally evolving jet. Present NODE models focus on seven chemical species, namely NH₃, O₂, H₂, OH, H₂O. N₂, and NO, and the results show that, compared with the results obtained by using detailed chemical kinetics, this method is able to reduce the computational costs of the zero-dimensional auto-ignition reaction to 1/24 while reproducing the ignition delay time for a wide range of initial temperatures and equivalence ratios with relatively good accuracy. Additionally, the method is able to reduce the computational costs of the one-dimensional freely propagating flame and two-dimensional jet flame to 1/4 and 1/38 respectively, while acceptable reproduction of the laminar flame speed and temporal evolution of the gas temperature and mass fractions of the interested species can be achieved.