  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.
