Michele Giuliano Carlino
ONERA/INRIA – 🇫🇷 Bordeaux (France)
Collocation-based reduced-order modelling: from explicit dynamics to implicit and stationary problems
Collocation-based reduced-order models (cROMs) provide a model reduction framework in which the high-fidelity discretisation is retained at a selected subset of computational cells, while the remaining solution is reconstructed through a reduced representation. This creates a direct connection between reduced modelling, hyper-reduction and the underlying high-fidelity numerical scheme, while allowing existing simulation routines to be largely reused.
In this talk, I will introduce the main principles of the cROM framework and discuss their application to different classes of problems. I will first consider explicit time-dependent problems, with particular attention to transport-dominated dynamics and adaptive collocation strategies following the evolution of coherent structures.
I will then discuss recent developments towards implicit and stationary problems, where the interaction between hyper-reduction and nonlinear solution procedures raises additional questions concerning residual and Jacobian approximation and conditioning. Some of the results presented in this part are preliminary and will be used to highlight open methodological questions and ongoing research directions. The workshop will therefore also provide an opportunity to discuss these observations, compare them with related approaches, and exchange ideas on possible theoretical and computational developments.