PIECEWISE-GLOBAL NONLINEAR MODEL ORDER REDUCTION FOR PDE-CONSTRAINED OPTIMIZATION IN HIGH-DIMENSIONAL PARAMETER SPACES

作     者：Boncoraglio, Gabriele Farhat, Charbel 

作者机构：Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA Stanford Univ Dept Mech Engn Stanford CA 94305 USA Stanford Univ Inst Computat & Math Engn Stanford CA 94305 USA 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：2022年第44卷第4期

页      面：A2176-A2203页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Boeing Company Office of Naval Research [N00014-17-1-2749] Air Force Office of Scientific Research [FA9550-20-1-0358] 

主　　题：active subspace gradient-based optimization hyperreduction nonlinear model reduction parameter sampling PDE-constrained optimization 

摘      要：This paper introduces the concept of a database of piecewise-global, nonlinear, projection-based reduced-order models and intertwines it with that of an active subspace. The result is a computational framework for accelerating the solution of optimization problems in a design parameter space of a relatively large dimension. On the algorithmic side, the scope of this framework includes multistart, gradient-based optimization methods and hyperreduced nonlinear models. On the application side, it includes multi-objective and global optimization problems, as well as nonlinear, PDE-based constraints. The potential of the proposed computational framework for optimization is demonstrated using aerodynamic shape optimization problems associated with two different flight systems: the flying wing aircraft mAEWing2, and the NASA Common Research Model (CRM) for transport aircraft.