  In this study, a fast and stable machine-learned hybrid algorithm implemented
in TensorFlow for the integration of stiff chemical kinetics is introduced.
Numerical solutions to differential equations are at the core of computational
fluid dynamics calculations. As the size and complexity of the simulations
grow, so does the need for computational power and time. Many efforts have been
made to implement stiff chemistry solvers on GPUs but have not been highly
successful because of the logical divergence in traditional stiff solver
algorithms. Because of these constrains, a novel Explicit Stabilized
Variable-load (STEV) solver has been developed. Overstepping due to the
relatively large time steps is prevented by introducing limits to the maximum
changes of chemical species per time step. To prevent oscillations, a discrete
Fourier transform is introduced to dampen ringing. In contrast to conventional
explicit approaches, a variable-load approach is used where each cell in the
computational domain is advanced with its unique time step. This approach
allows cells to be integrated simultaneously while maintaining warp convergence
but finish at different iterations and be removed from the workload. To improve
the computational performance of the introduced solver, specific thermodynamic
quantities of interest were estimated using shallow neural networks in place of
polynomial fits, leading to an additional 10% savings in clock time with
minimal training and implementation requirements. However ML specific hardware
could increase the time savings to as much as 28%. While the complexity of
these particular machine learning models is not high by modern standards, the
impact on computational efficiency should not be ignored. The results show a
dramatic decrease in total chemistry solution time (over 200 times) while
maintaining a similar degree of accuracy.
