Gradient-based constrained optimization using a database of linear reduced-order models

JOURNAL OF COMPUTATIONAL PHYSICS

卷:423

Article

Choi, Youngsoo¹  Boncoraglio, Gabriele²  Anderson, Spenser²  Amsallem, David^3,5  Farhat, Charbel^2,3,4 

[1] Lawrence Livermore Natl Lab, Computat Engn Div, Livermore, CA 94550 USA

[2] Stanford Univ, Dept Aeronaut & Astronaut, Stanford, CA 94305 USA

[3] Stanford Univ, Dept Mech Engn, Stanford, CA 94305 USA

[4] Stanford Univ, Inst Computat & Math Engn, Stanford, CA 94305 USA

[5] Facebook, Menlo Pk, CA 94025 USA

关键词: Constrained optimization;    Flutter;    Gradient-based optimization;    Interpolation on a matrix manifold;    Model reduction;    Parameter sampling;   

DOI  :  10.1016/j.jcp.2020.109787

来源: Elsevier

【 摘 要 】

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential Equation (PDE). A key component of this methodology is the construction, during an offline phase, of a database of pointwise, linear, Projection-based Reduced-Order Models (PROM)s associated with a design parameter space and the linear PDE(s). A parameter sampling procedure based on an appropriate saturation assumption is proposed to maximize the efficiency of such a database of PROMs. A real-time method is also presented for interpolating at any queried but unsampled parameter vector in the design parameter space the relevant sensitivities of a PROM. The practical feasibility, computational advantages, and performance of the proposed methodology are demonstrated for several realistic, nonlinear, aerodynamic shape optimization problems governed by linear aeroelastic constraints. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free