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SUMMARY:Truly Predictive Reduced Order Modeling for Complex Multi-scale\, 
 Multi-physics Problems - Karthik Duraisamy (University of Michigan)
DTSTART:20230515T141500Z
DTEND:20230515T151500Z
UID:TALK200620@talks.cam.ac.uk
DESCRIPTION:This talk will begin with a brief discussion of existing appro
 aches in data-driven modeling\, and sets the context for the term &lsquo\;
 truly predictive&rsquo\; models. Challenges involved in the predictive mod
 eling of complex multi-scale\, multi-physics systems will be discussed. Th
 e main part of the talk will present advances towards the development of e
 ffective projection-based reduced order models (ROMs).&nbsp\; As a represe
 ntative application\, we consider combustion dynamics in a rocket engine\,
  which is characterized by a complex coupling between chemical reactions\,
  heat release\, hydrodynamics and acoustics.&nbsp\;&nbsp\;\n- Improving ro
 bustness and consistency: A structure-preserving transformation of the sta
 te variables is used along with a discretely consistent least squares form
 ulation to yield symmetrized model operators in both explicit and implicit
  time integration settings. The resulting reduced order model is well-cond
 itioned and globally stable. Local stability is promoted via limiters that
  enforce physical realizability.&nbsp\;&nbsp\;\n- Accomplishing true predi
 ctivity: Dimension reduction approaches based on static manifolds - linear
  or non-linear - are not effective in predictive modeling of multi-scale p
 roblems with significant transport effects. To address this issue\, we pre
 sent an adaptive formulation in which the basis vectors and sampling point
 s are adapted online using a novel non-local procedure\, leading to ROMs t
 hat are demonstrated to be predictive in future state and parametric probl
 ems with negligible off-line training.&nbsp\; Opportunities for further im
 provement are also highlighted.&nbsp\;&nbsp\;\n- Promoting tractability vi
 a ROM networks :&nbsp\; ROMs are used to enable computations of problems f
 or which full order models are not affordable. In particular\, we develop 
 a multi-fidelity framework in which component-level ROMs are trained on sm
 all domains\, and integrated to enable full-system predictions in an affor
 dable manner.&nbsp\; This training method is shown to enhance predictive c
 apabilities and robustness of the resulting ROMs\, and the ability of thes
 e models to capture emergent phenomena is highlighted.
LOCATION:Seminar Room 2\, Newton Institute
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