Model Order Reduction for Multidisciplinary Design Analysis and Optimization in Higher-Dimensional Parameter Spaces
Speaker: Gabriele Boncoraglio, Stanford University
Presentation
Abstract
Optimization problems constrained by partial differential equations (PDEs) arise in many engineering applications, including design and optimal control. Even though the state of the numerical solution of PDEs has reached impressive levels of maturity, it remains a computationally intensive process. The problem is aggravated in the many-query scenario that is typical of PDE-constrained optimization, as the governing PDEs need to be repeatedly solved for various configurations. This situation is further complicated when the design parameter space D is high-dimensional. Projection-based model order reduction (PMOR) methods significantly reduce computational cost by generating low-dimensional, projection-based reduced-order models (PROMs) that can be processed in near real-time, while preserving most of the accuracy of the underlying PDE-based high-dimensional models. However, optimization in a high-dimensional parameter space D raises two issues. First, the training of PROMs in such a space is typically computationally intensive, as it involves sampling the solution of each concerned PDE at a large number of parameter points in D, thereby suffering the curse of dimensionality. Second, constructing a single, global PROM that is robust in the entirety of D leads in general to a larger dimension than desired for accelerating the optimization process.
This talk addresses both challenges outlined above. It introduces the method of active manifold (AM) as a superior alternative to the method of active subspace (AS), whose capabilities are limited by the underlying affine approximation. It also presents an adaptive sampling approach that first predicts the region Dv ∁ D that will be visited by the optimization procedure using a low-cost approach, then trains the PROMs only in this region of the design parameter space. Finally, the talk will introduce the concept of piecewise-global PROMs that achieves robustness within Dv at a lower dimensionality than standard global PROMs. Most importantly, it will demonstrate the feasibility and benefits of the proposed PROM-based computational framework for realistic multidisciplinary design analysis and optimization problems of relevance to aeronautics.
Biography
