Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

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Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison (2011, background): “…have appeared in the literature (Aubry et al. 1988; Podvin & Lumley 1998; Podvin 2001; Rempfer & Fasel 1994; Rempfer 1996; Cazemier et al. 1998; Ma & Karniadakis 2002; Sirisup & Karniadakis 2004; Buffoni et al. 2006; Noack et al. 2002, 2003, 2005, 2008; Ullmann & Lang 2010; Hay et al. 2009, 2010).”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “In [58, 59] the parametric sensitivities of the POD modes were computed and added to the snapshot set, which improved the validity of the reduced solutions away from the parametric snapshots.”
On the use of modal derivatives for nonlinear model order reduction (2016, methodology): “Similar methods have also been presented for enhancement of POD reduction in the context of fluid dynamics [28].”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “One can also include sensitivity information in the snapshot set [127, 131].”