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

Abstract

A computational framework for efficiently solving multidisciplinary analysis and optimization (MDAO) problems in relatively high-dimensional design parameter spaces is presented. It relies on hyperreduced projection-based reduced-order models (HPROM)s; and a new concept of active manifold (AM) that mitigates the curse of dimensionality during the training of the HPROMs. 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. Additionally, the presented computational framework blends the idea of global HPROMs as surrogate models of nonlinear partial differential equation (PDE)-based objective and/or constraint functions with that of a database of local, linear PROMs for approximating a linear PDE-based constraint function. The framework 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, one of the constraint functions 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 computational framework proposed for realistic MDAO problems and its ability to significantly reduce solution time.