Scientific Machine Learning is transforming traditional engineering industries by enhancing the efficiency of existing technologies and accelerating innovation, particularly in modeling chemical reactions. Despite recent advancements, the issue of solving stiff chemically reacting problems within computational fluid dynamics remains a significant issue. In this study we propose a novel approach utilizing a multi-layer-perceptron mixer architecture (MLP-Mixer) to model the time-series of stiff chemical kinetics. We evaluate this method using the ROBER system, a benchmark model in chemical kinetics, to compare its performance with traditional numerical techniques. This study provides insight into the industrial utility of the recently developed MLP-Mixer architecture to model chemical kinetics and provides motivation for such neural architecture to be used as a base for time-series foundation models.

We utilize neural operators to learn the solution propagator for the challenging chemical kinetics equation. Specifically, we apply the deep operator network (DeepONet) along with its extensions, such as the autoencoder-based DeepONet and the newly proposed Partition-of-Unity (PoU-) DeepONet to study a range of examples, including the ROBERS problem with three species, the POLLU problem with 25 species, pure kinetics of the syngas skeletal model for $CO/H_2$ burning, which contains 11 species and 21 reactions and finally, a temporally developing planar $CO/H_2$ jet flame (turbulent flame) using the same syngas mechanism. We have demonstrated the advantages of the proposed approach through these numerical examples. Specifically, to train the DeepONet for the syngas model, we solve the skeletal kinetic model for different initial conditions. In the first case, we parametrize the initial conditions based on equivalence ratios and initial temperature values. In the second case, we perform a direct numerical simulation of a two-dimensional temporally developing $CO/H_2$ jet flame. Then, we initialize the kinetic model by the thermochemical states visited by a subset of grid points at different time snapshots. Stiff problems are computationally expensive to solve with traditional stiff solvers. Thus, this work aims to develop a neural operator-based surrogate model to solve stiff chemical kinetics. The operator, once trained offline, can accurately integrate the thermochemical state for arbitrarily large time advancements, leading to significant computational gains compared to stiff integration schemes.