Abstract de conférence
| Résumé : | Dimensionality reduction techniques are used in turbulent combustion to find low- dimensional manifolds (LDMs) in high-dimensional reacting systems. This approach allows for building reduced-order models (ROMs), where only the low-dimensional parameters are transported in combustion simulations. We achieve a substantial reduction in the number of parameters needed to visualize, describe and predict complex systems, but some topological properties of LDMs can hinder their practical application. For instance, ROMs often require training a nonlinear regression model to predict physical quantities of interest from the reduced representation. The current literature points to the many difficulties in accurate reconstruction of minor species that exhibit large gradients, and also of the projected source terms of the state variables that are needed to close the system of transport equations for the reduced parameters. In this talk, we delineate the outstanding challenges that remain in ROM of turbulent combustion. We focus on the topological issues that the LDMs present. We discuss our recent advances in characterizing manifold quality, generating improved manifold topologies and improving nonlinear regression performance. We demonstrate novel quantitative tools for characterizing the quality of LDMs from the perspective of non-uniqueness and steep gradients in the physical quantities of interest. We show applications of the manifold assessment tools in optimization algorithms that yield improved manifolds. We discuss novel local kernel regression models that achieve better predictive performance than the current state-of-the- art models. |
