Data-Driven Methods and Reduced-Order Modeling

Reduced-order modeling is an active area of research by which simplified models of experimental or numerical data can be generated that are faithful to the behavior of the unerlying system. These methods are based on Galerkin projection, which is motivated by variational methods, or some other method of weighted residuals and allow for the projection of any governing differential equation onto an appropriate set of basis vectors or functions. These basis vectors or functions can be obtained using proper-orthogonal decomposition (POD) or one of its extensions or alternatives. Galerkin projection and POD are applied to continuous and discrete data sets.