Verifiability of the Data-Driven Variational Multiscale Reduced Order Model

Birgul Koc (1) , Changhong Mou (2) , Honghu Liu (3) , Zhu Wang (4) , Gianluigi Rozza (5) , Traian Iliescu (3)

1 IFPEN - IFP Energies nouvelles
2 University of Wisconsin-Madison
3 Virginia Tech [Blacksburg]
4 University of South Carolina [Columbia]
5 SISSA MathLab [Trieste]

In this paper, we focus on the mathematical foundations of reduced order model (ROM) closures. First, we extend the verifiability concept from large eddy simulation to the ROM setting. Specifically, we call a ROM closure model verifiable if a small ROM closure model error (i.e., a small difference between the true ROM closure and the modeled ROM closure) implies a small ROM error. Second, we prove that the data-driven ROM closure studied here (i.e., the data-driven variational multiscale ROM) is verifiable. Finally, we investigate the verifiability of the data-driven variational multiscale ROM in the numerical simulation of the one-dimensional Burgers equation and a two-dimensional flow past a circular cylinder at Reynolds numbers Re=100 and Re=1000.

Mots clés: Reduced order Model; Variational Multiscale; Data-Driven Model; Verifiability

Domaines: Sciences de l'environnement; Sciences de l'ingénieur [physics]

Birgul Koc, Changhong Mou, Honghu Liu, Zhu Wang, Gianluigi Rozza, et al.. Verifiability of the Data-Driven Variational Multiscale Reduced Order Model. Journal of Scientific Computing, 2022, 93 (2), pp.54. ⟨10.1007/s10915-022-02019-y⟩. ⟨hal-03854187⟩