Active Manifold and Model Order Reduction to Accelerate Multidisciplinary Analysis and Optimization

One approach we have proposed in the past to deal with this issue is the concept of a quadrature rule in hyperspace. This involves computing a projection on selected elements of a mesh, rather than the entire mesh, in order to speed up the process. Similar to a Gauss rule in calculus, only a few points are needed to evaluate the function at those points. The weights for the selected elements must be positive and determined using machine learning techniques based on solution snapshots. Once training is complete, the original projection is transformed into a hyperreduced projection, providing the desired advantages.

For example, in a CFD application using a large-scale mesh over the NASA Common Research Model, hyperreduction focuses on a small set of elements, as shown in color.