Gradient-based Constrained Optimization Using a Database of Linear Reduced-Order Models

TL;DR

This paper introduces a model reduction-based methodology that accelerates gradient-based constrained optimization involving PDEs by using a database of linear reduced-order models and an efficient interpolation scheme.

Contribution

It presents a novel offline database construction of PROMs and a real-time interpolation method for sensitivities, enhancing efficiency in nonlinear aerodynamic shape optimization.

Findings

Demonstrated significant computational speed-ups.

Validated approach on realistic aerodynamic problems.

Achieved accurate sensitivity interpolation for unsampled parameters.

Abstract

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.