 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. Solving the equations in parallel can dramatically reduce the time to solution. While traditionally done on CPUs, unlocking the massive number of computational cores on GPUs is highly desirable. 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 algorithms like CVODE or LSODE. This study will demonstrate a machine learned hybrid algorithm implemented in TensorFlow for stiff problems and the speed gains relative to the traditional LSODE solver used in the Multiphase Flow with Interphase eXchanges (MFiX) Computational Fluid Dynamics (CFD) code. The results will show a dramatic decrease in total simulation time while maintaining the same degree of accuracy.
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.
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In this study, a fast and stable machine-learned hybrid algorithm implemented in TensorFlow for the integration of stiff chemical kinetics is introduced.
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Solving the equations in parallel can dramatically reduce the time to solution. While traditionally done on CPUs, unlocking the massive number of computational cores on GPUs is highly desirable.
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algorithms like CVODE or LSODE. This study will demonstrate a machine learned hybrid algorithm implemented in TensorFlow for stiff problems and the speed gains relative to the traditional LSODE solver used in the Multiphase Flow with Interphase eXchanges (MFiX) Computational Fluid Dynamics (CFD) code. The results will
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
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simulation time while maintaining the same
chemistry solution time (over 200 times) while maintaining a similar