A Neural Network-Inspired Matrix Formulation of Chemical Kinetics for Acceleration on GPUs

Abstract

High-fidelity simulations of turbulent flames are computationally expensive when using detailed chemical kinetics. For practical fuels and flow configurations, chemical kinetics can account for the vast majority of the computational time due to the highly non-linear nature of multi-step chemistry mechanisms and the inherent stiffness of combustion chemistry. While reducing this cost has been a key focus area in combustion modeling, the recent growth in graphics processing units (GPUs) that offer very fast arithmetic processing, combined with the development of highly optimized libraries for artificial neural networks used in machine learning, provides a unique pathway for acceleration. The goal of this paper is to recast Arrhenius kinetics as a neural network using matrix-based formulations. Unlike ANNs that rely on data, this formulation does not require training and exactly represents the chemistry mechanism. More specifically, connections between the exact matrix equations for kinetics and traditional artificial neural network layers are used to enable the usage of GPU-optimized linear algebra libraries without the need for modeling. Regarding GPU performance, speedup and saturation behaviors are assessed for several chemical mechanisms of varying complexity. The performance analysis is based on trends for absolute compute times and throughput for the various arithmetic operations encountered during the source term computation. The goals are ultimately to provide insights into how the source term calculations scale with the reaction mechanism complexity, which types of reactions benefit the GPU formulations most, and how to exploit the matrix-based formulations to provide optimal speedup for large mechanisms by using sparsity properties. Overall, the GPU performance for the species source term evaluations reveals many informative trends with regards to the effect of cell number on device saturation and speedup. Most importantly, it is shown that the matrix-based method enables highly efficient GPU performance across the board, achieving near-peak performance in saturated regimes.

Efficient neural network models of chemical kinetics using a latent asinh rate transformation

“…Gas composition and temperature are assumed to be constant during this process. The obtained surface coverages are used in eqn (9) to calculate steady state source terms s ˙i (mol m −2 s −1 ) using the site density Γ which is assumed to be 2.3…”

“…Therefore, there is huge interest in accelerating the kinetic calculations. 1,2,8,9 This can be done by tabulating the kinetics or even a time integration step. 9,10 Latter is often done for gas-phase reactive systems [11][12][13] because the integration of the stiff ODE system resulting from the gasphase kinetics is very time-consuming.…”

Review of Machine Learning for Hydrodynamics, Transport, and Reactions in Multiphase Flows and Reactors

“…However, most of these established models appear to be only valid for specific reaction systems, since the data sets used for training are usually limited to a specific composition space. In addition, recent advancements in GPUs provides a unique pathway for boosting the modeling efficiency of reaction networks by ML, 301 and this important direction deserves more research efforts.…”

Efficient Neural Network Models of Chemical Kinetics Using a Latent asinh Rate Transformation

“…Therefore, there is huge interest in accelerating the kinetic calculations. [1,2,8,9] This can be done by tabulating the kinetics or even a time integration step. [9,10] Latter is often done for gas-phase reactive systems [11][12][13] because the integration of the stiff ODE system resulting from the gas-phase kinetics is very time-consuming.…”

“…[1,2,8,9] This can be done by tabulating the kinetics or even a time integration step. [9,10] Latter is often done for gas-phase reactive systems [11][12][13] because the integration of the stiff ODE system resulting from the gas-phase kinetics is very time-consuming. For heterogeneous catalysis, timescales of surface reactions and the gas phase are usually separable via the steady state approximation.…”