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

A standard procedure today combines a sequential design of experiments with active learning and iterative sampling. This procedure is guided by an understanding of the residual, which serves as an indicator for most applications. Each time a new point is sampled, the training accuracy achieved so far is taken into account with respect to previous points.

The procedure can be used to build a global reduced order basis that is accurate across the entire parameter domain, or to build a database of local reduced order bases and models that are trained at specific parameter points but can be interpolated between. Interpolation on a matrix manifold is used to preserve the structure and constraints of what is being interpolated.

In the generic case, a two-dimensional parameter space with components mu one and mu two is considered. An initial point is selected to build a RAM or reduced order basis, followed by iterations where random candidate points are generated and evaluated using the initial RAM. The point with the highest residual is then selected based on the residual indicator.