Truly Predictive Reduced Order Modeling for Complex Multi-scale, Multi-physics Problems

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• Karthik Duraisamy (University of Michigan)
• Monday 15 May 2023, 15:15-16:15
• Seminar Room 2, Newton Institute.

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DDE - The mathematical and statistical foundation of future data-driven engineering

This talk will begin with a brief discussion of existing approaches in data-driven modeling, and sets the context for the term ‘truly predictive’ models. Challenges involved in the predictive modeling of complex multi-scale, multi-physics systems will be discussed. The main part of the talk will present advances towards the development of effective projection-based reduced order models (ROMs).  As a representative application, we consider combustion dynamics in a rocket engine, which is characterized by a complex coupling between chemical reactions, heat release, hydrodynamics and acoustics.   - 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.   - Accomplishing true predictivity: Dimension reduction approaches based on static manifolds – linear or non-linear – are not effective in predictive modeling of multi-scale problems with significant transport effects. To address this issue, we present an adaptive formulation in which the basis vectors and sampling points are adapted online using a novel non-local procedure, leading to ROMs that are demonstrated to be predictive in future state and parametric problems with negligible off-line training.  Opportunities for further improvement are also highlighted.   - Promoting tractability via ROM networks :  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.  This training method is shown to enhance predictive capabilities and robustness of the resulting ROMs, and the ability of these models to capture emergent phenomena is highlighted.

This talk is part of the Isaac Newton Institute Seminar Series series.

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