Some aspects of combined equation- and data-driven modeling for turbulent flows

Significant recent progress has been made in flow modeling using both equation-driven and data-driven techniques. We focus here on the intersection of these two approaches, using data to complete the details of known flow dynamics. In turbulent flows, nonlinear effects can prevent linear data-driven techniques such as dynamic mode decomposition (Schmid, 2010) and data-driven resolvent analysis (Hermann et al, 2021) from identifying the correct underlying linear operator governing the dynamics. In this talk we will review some of the aspects of learning and exploiting linear and nonlinear dynamics from equations and from data recently explored by the authors.