Extended Fourier Neural Operators to learn stiff chemical kinetics under unseen conditions

The solution of stiff chemical kinetics is recognized as the computational bottleneck for direct simulations of reacting flows. In this study, we extend the concept of Fourier Neural Operator (FNO) to learn stiff chemical kinetics. Specifically, element and mass conservation are introduced as the physical constraints in the extended FNO (EFNO). In addition, the training data are transformed by a Box-Cox strategy to rectify the skewed distribution of the species in the stiff problems. Finally, balanced loss functions are formulated to address the unbalanced sampling data points in complex reacting flow problems. The EFNO model is leveraged to forecast the temporal evolution of chemical species, utilizing an iterative approach wherein the prediction outcome from the previous time step is employed as anew input for subsequent time step prediction. The results in this work demonstrate the significant use of an EFNO approach to solving stiff chemical dynamics in reacting flow simulations, with a time step size comparable to the typical flow time step size. Its prediction accuracy and generalization ability are evaluated by comparing with the original FNO, Deep Nueral Network (DNN) and DeepONet models, in solving toy problems, zero-dimensional hydrogen autoignition, and a three-dimensional hydrogen/ammonia turbulent jet flame. The EFNO is shown to be highly accurate. More importantly, compared with other deep learning models, it can be generalized to stiff chemical kinetic states under unseen conditions, which the model has never trained for. The great performance of EFNO in terms of accuracy and generalization ability suggests that EFNO is a promising solution algorithm for stiff chemical kinetics problems in reacting flows. Novelty and Significance Statement: The novelty of this work lies in the newly developed extended Fourier neural operators (EFNO) to learn stiff chemical kinetics. Specifically, we for the first time evaluated and tested the performance of Fourier neural operators in solving stiff chemical kinetics. More importantly, we extended the original Fourier neural operators to accurately solve for stiff chemical kinetics problems under unseen conditions, which was a very challenging problem for deep learning methods in the literature. Our results demonstrated that the EFNO model solves chemical kinetics in both simple 0D autoignition and complex 3D turbulent jet flames with great accuracy and generalization ability, even for conditions which the training dataset has never encompassed. This work is significant because it developed a neural operator- based algorithm that can significantly accelerate the stiff chemical kinetic solution process in reacting flow simulations with great accuracy even for unseen initial conditions.