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

When running the Active manifold technique, it reduces the dimensionality of the parameter space from 58 to 10. This means going from millions to a more manageable number. The greedy procedure is used to avoid uniform sampling, allowing for effective handling of dimension 10 instead of dimension 58. Optimization problems can be solved relatively quickly in green.

By examining one optimal design solution, it is clear that the green and red results closely match except for a small variation, which is acceptable when reducing the model. In contrast, the blue results from Data regression with neural networks are not as close to the red and would require more training to match.

Considering the cost, using the Active manifold on the high dimensional model takes about 800 hours, while using it on the hyper-reduced order model only takes 84 hours. This includes all steps such as detecting the Active manifold, building and training models, and running online simulations. The speedup factor can be one to two orders of magnitude.

In a different example involving Aeroelasticity and flutter, the speedup factor was slightly more than one order of magnitude. Viscous problems are expected to be more computationally intensive. The first viscous problem tackled using this approach was suggested by Boeing Research Technology.