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

A computational framework is proposed for efficiently solving multidisciplinary analysis and optimization (MDAO) problems in a relatively high-dimensional design parameter space. It relies on projection-based reduced-order models (PROMs) and a new concept of an active manifold (AM) to mitigate the curse of dimensionality during the training of the PROMs. The AM is discovered using a deep convolutional autoencoder for dimensionality reduction: it is proposed as a superior alternative to the concept of active subspace whose capabilities are limited by the associated affine approximation. The computational framework also blends the concept of a global PROM as a surrogate model of a nonlinear partial differential equation (PDE)-based behavior function with that of a database of local, linear PROMs for approximating a linear PDE-based behavior function. It is demonstrated for the solution of a flexible instance of NASA's Common Research Model for transport aircraft, where the objective function pertains to aerodynamics, the constraint relates to flutter, and the design space contains 58 structural and shape parameters. The obtained results illustrate the potential of the AM concept for mitigating the aforementioned curse of dimensionality. They also demonstrate the feasibility of the proposed computational framework for realistic MDAO problems and its ability to reduce solution time.