Verifiability of the Data-Driven Variational Multiscale Reduced Order Model

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