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

Reduced Order Models are a specific technique that can be applied to any type of representation, such as regression-based or model-based. The Basic Version involves Projection Based Model Order Reduction (PMOR), which is a method that results in a projection-based reduced-order model. The emphasis on projection is important because it provides a clear understanding of starting from a high-fidelity model and projecting it onto a lower-dimensional subspace. This technique is specific and has a community dedicated to it.

In the modern age of data and machine learning, it is crucial to recognize that physics-based machine learning methods are essential for model reduction. The process begins with a semi-discrete or discrete computational model with parameters. The goal is to approximate the solution accurately in a lower-dimensional space. This involves creating a hypothesis, building a representation, and using data-driven learning to construct a reduced basis. The final step is to minimize a loss function by finding generalized coordinates that minimize the residual.

Overall, the process of building a projection-based reduced-order model incorporates elements of machine learning, including hypothesis formulation, representation building, data-driven learning, and loss function minimization.