  Within the scope of reacting flow simulations, the real-time direct
integration (DI) of stiff ordinary differential equations (ODE) for the
computation of chemical kinetics stands as the primary demand on computational
resources. Meanwhile, as the number of transport equations that need to be
solved increases, the computational cost grows more substantially, particularly
for those combustion models involving direct coupling of chemistry and flow
such as the transported probability density function model. In the current
study, an integrated Graphics Processing Unit-Artificial Neural Network
(GPU-ANN) framework is introduced to comply with heavy computational costs
while maintaining high fidelity. Within this framework, a GPU-based solver is
employed to solve partial differential equations and compute thermal and
transport properties, and an ANN is utilized to replace the calculation of
reaction rates. Large eddy simulations of two swirling flames provide a robust
validation, affirming and extending the GPU-ANN approach's applicability to
challenging scenarios. The simulation results demonstrate a strong correlation
in the macro flame structure and statistical characteristics between the
GPU-ANN approach and the traditional Central Processing Unit (CPU)-based solver
with DI. This comparison indicates that the GPU-ANN approach is capable of
attaining the same degree of precision as the conventional CPU-DI solver, even
in more complex scenarios. In addition, the overall speed-up factor for the
GPU-ANN approach is over two orders of magnitude. This study establishes the
potential groundwork for widespread application of the proposed GPU-ANN
approach in combustion simulations, addressing various and complex scenarios
based on detailed chemistry, while significantly reducing computational costs.
