Data-driven Reduced Order Models for Multi-scale, Multi-physics Systems

Abstract

This talk presents advances towards the development of effective reduced order models (ROMs) for complex multi-scale multi-physics problems. As a representative application, we consider combustion dynamics in a rocket engine, which is characterized by the coupling between heat release, hydrodynamics and acoustics. The first part of the talk is focused on improving robustness and consistency: A structure-preserving transformation of the state variables is used along with a discretely consistent least squares formulation to yield symmetrized model operators in both explicit and implicit time integration settings. The resulting reduced order model is well-conditioned and globally stable. Local stability is promoted via limiters that enforce physical realizability. The second part of the talk is focused on improving accuracy: Dimension reduction approaches based on static linear manifolds are not effective in addressing multi-scale problems with significant convection. To help mitigate this issue, we present formulations using adaptive spaces. Opportunities for further improvement are also highlighted. The last part of the talk discusses tractability : ROMs are used to enable computations of problems for which full order models are not affordable. In particular, we develop a multi-fidelity framework in which component-level ROMs are trained on small domains, and integrated to enable full-system predictions in an affordable manner. In essence, geometry-specific training is replaced by the response generated by perturbing the characteristics at the boundary of the truncated domain. This training method is shown to enhance predictive capabilities and robustness of the resulting ROMs, including conditions outside the training range.