  This work describes and validates an approach for autonomously bifurcating
turbulent combustion manifolds to divide regression tasks amongst specialized
artificial neural networks (ANNs). This approach relies on the mixture of
experts (MoE) framework, where each neural network is trained to be specialized
in a given portion of the input space. The assignment of different input
regions to the experts is determined by a gating network, which is a neural
network classifier. In some previous studies, it has been demonstrated that
bifurcation of a complex combustion manifold and fitting different ANNs for
each part leads to better fits or faster inference speeds. However, the manner
of bifurcation in these studies was based on heuristic approaches or clustering
techniques. In contrast, the proposed technique enables automatic bifurcation
using non-linear planes in high-dimensional turbulent combustion manifolds that
are often associated with complex behavior due to different dominating physics
in various zones. The proposed concept is validated using 4-dimensional (4D)
and 5D flamelet tables, showing that the errors obtained with a given network
size, or conversely the network size required to achieve a given accuracy, is
considerably reduced. The effect of the number of experts on inference speed is
also investigated, showing that by increasing the number of experts from 1 to
8, the inference time can be approximately reduced by a factor of two.
Moreover, it is shown that the MoE approach divides the input manifold in a
physically intuitive manner, suggesting that the MoE framework can elucidate
high-dimensional datasets in a physically meaningful way.
