This work introduces a methodology to develop reduced-order models (ROM) of combustion systems that addresses the challenges of nonlinearity and high dimensionality by combining soft clustering techniques with dimensionality-reduction and nonlinear regression. Clustering is routinely used to partition data into localized regions, allowing ROMs to better represent the system response within each zone. To avoid discontinuities at cluster interfaces, a soft clustering is introduced to allow for overlapping regions, resulting in smoother and more consistent predictions. The use of soft clustering provides an additional degree of flexibility compared to traditional hard-clustered ROM formulations. In each cluster, a local reduced-order model is built using Proper Orthogonal Decomposition to reduce the dimensionality, and Gaussian Process Regression to estimate the input–output relationship. The approach is validated using a dataset of 80 one-dimensional NH3/H2 laminar flames and a stagnation-point reverse-flow combustor fueled with the same mixture, using a dataset of 175 two-dimensional axisymmetric RANS simulations. Results demonstrate a significant improvement in predictive accuracy over traditional global and local reduced-order model approaches, with soft clustering enhancing model performance and reducing sharp gradients at cluster boundaries. This research contributes to the development of efficient reduced-order model frameworks for practical combustion systems, supporting the design and implementation of sustainable energy technologies.
Novelli et al. (Mon,) studied this question.