Gradient-enhanced surrogate modeling based on proper orthogonal decomposition

A new method for enhanced surrogate modeling of complex systems by exploiting gradient information is presented. The technique combines the proper orthogonal decomposition (POD) and interpolation methods capable of fitting both sampled input values and sampled derivative information like Kriging (aka spatial Gaussian processes). In contrast to existing POD-based interpolation approaches, the gradient-enhanced method takes both snapshots and partial derivatives of snapshots of the associated full-order model (FOM) as an input. It is proved that the resulting predictor reproduces these inputs exactly up to the standard POD truncation error. Hence, the enhanced predictor can be considered as (approximately) first-order accurate at the snapshot locations. The technique applies to all fields of application, where derivative information can be obtained efficiently, for example via solving associated primal or adjoint equations. This includes, but is not limited to Computational Fluid Dynamics (CFD). The method is demonstrated for an academic test case exhibiting the main features of reduced-order modeling of partial differential equations.