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We present a framework to accelerate optimization of problems where the objective function is governed by a nonlinear partial differential equation (PDE) using projection-based reduced-order models (ROMs) and a trust-region (TR) method. To reduce the cost of objective function evaluations by several orders of magnitude, we replace the underlying full-order model (FOM) with a series of hyperreduced ROMs (HROMs) constructed on-the-fly. Each HROM is equipped with an online-efficient a posteriori error estimator, which is used to define a TR. Hyperreduction is performed following a goal-oriented empirical quadrature procedure, which guarantees first-order consistency of the HROM with the FOM at the TR center. This ensures the optimizer converges to a local minimum of the underlying FOM problem. We demonstrate the framework through optimization of a nonlinear thermal fin and pressure-matching inverse design of an airfoil under Euler flow and Reynolds-averaged Navier-Stokes flow. | We present a framework to accelerate optimization of problems where the objective function is governed by a nonlinear partial differential equation (PDE) using projection-based reduced-order models (ROMs) and a trust-region (TR) method. To reduce the cost of objective function evaluations by several orders of magnitude, we replace the underlying full-order model (FOM) with a series of hyperreduced ROMs (HROMs) constructed on-the-fly. Each HROM is equipped with an online-efficient a posteriori error estimator, which is used to define a TR. Hyperreduction is performed following a goal-oriented empirical quadrature procedure, which guarantees first-order consistency of the HROM with the FOM at the TR center. This ensures the optimizer converges to a local minimum of the underlying FOM problem. We demonstrate the framework through optimization of a nonlinear thermal fin and pressure-matching inverse design of an airfoil under Euler flow and Reynolds-averaged Navier-Stokes flow. | ||
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Revision as of 12:40, 23 November 2022
Summary
We present a framework to accelerate optimization of problems where the objective function is governed by a nonlinear partial differential equation (PDE) using projection-based reduced-order models (ROMs) and a trust-region (TR) method. To reduce the cost of objective function evaluations by several orders of magnitude, we replace the underlying full-order model (FOM) with a series of hyperreduced ROMs (HROMs) constructed on-the-fly. Each HROM is equipped with an online-efficient a posteriori error estimator, which is used to define a TR. Hyperreduction is performed following a goal-oriented empirical quadrature procedure, which guarantees first-order consistency of the HROM with the FOM at the TR center. This ensures the optimizer converges to a local minimum of the underlying FOM problem. We demonstrate the framework through optimization of a nonlinear thermal fin and pressure-matching inverse design of an airfoil under Euler flow and Reynolds-averaged Navier-Stokes flow.
Abstract
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Published on 24/11/22
Accepted on 24/11/22
Submitted on 24/11/22
Volume Science Computing, 2022
DOI: 10.23967/eccomas.2022.035
Licence: CC BY-NC-SA license
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