Combustion reduced-order modeling with nonlinear projections

Reduced-order models (ROMs) of high-dimensional combustion systems are used to decrease the computational costs of simulations by reducing the number of equations needed to describe a system. These ROMs are constructed through dimensionality reduction (projections) to re-parameterize the system creating a low-dimensional manifold (LDM) where the corresponding LDM parameters are transported. Projections have typically been obtained through linear methods, such as principal component analysis (PCA) or linear encoder neural networks, as linear projections allow low-dimensional transport equations to be trivially derived. However, as the complexity of reaction mechanisms increases for different fuels, more LDM parameters are needed to provide a LDM with good topological quality. Nonlinear projections achieve better topological quality than linear projections for the same number of LDM parameters, but the derivation of low-dimensional transport equations becomes nontrivial. This work derives low-dimensional laminar flamelet transport equations for nonlinear projections and demonstrates the ability to converge steady solutions and move between dissipation rates on the LDM, and is demonstrated for hydrogen, syngas, and methane flamelets that have been reduced to two latent dimensions.