Progress variable optimization: Effects on the manifold topology and reduced-order modeling

Reduced-order models (ROMs) replace computationally expensive simulations of high-dimensional systems with cheaper surrogates. ROMs can be used to design, optimize, and control energy systems of industrial and engineering relevance, including reacting flows, electrochemical processes, thermal systems, and multiphysics energy devices. In reacting flow simulation, a common way to build a ROM is to project the original high-dimensional state–space onto a low-dimensional manifold, typically defined by a set of heuristic parameters being linear combinations of the original state variables. While encoder–decoder neural network architectures have been proposed to automatically define and optimize the manifold parameterization, the literature lacks in-depth understanding of how optimized parameterizations improve the accuracy of ROMs compared to heuristic parameterizations. In this paper, we investigate the endcoder–decoder architecture in details, for an application involving hydrogen combustion system. We show that the introduction of a trainable scaling layer prior to the encoder and a log-transformation of the highly nonlinear decoded QoIs leads to an improved representation of key quantities of interest (QoIs) and facilites the regression of the QoIs during ROM simulation compared with heuristic parameterizations. Moreover, we demonstrate that sparsifying the parameter definition is possible with no major impact on the manifold topology. We show how improvements in manifold parameterization lead to improved numeric simulations of reacting systems.