1. Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural Networks
- Author
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Mücke, Nikolaj Takata, Christiansen, Lasse Hjuler, Karup-Engsig, Allan Peter, and Jørgensen, John Bagterp
- Subjects
Mathematics - Numerical Analysis ,Mathematics - Analysis of PDEs ,Mathematics - Optimization and Control - Abstract
Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential equations (PDEs), black-box optimizers are rarely sufficient to get the required online computational speed. In such cases one must resort to customized solvers. This paper present a new solver for nonlinear time-dependent PDE-constrained optimization problems. It is composed of a sequential quadratic programming (SQP) scheme to solve the PDE-constrained problem in an offline phase, a proper orthogonal decomposition (POD) approach to identify a lower dimensional solution space, and a neural network (NN) for fast online evaluations. The proposed method is showcased on a regularized least-square optimal control problem for the viscous Burgers' equation. It is concluded that significant online speed-up is achieved, compared to conventional methods using SQP and finite elements, at a cost of a prolonged offline phase and reduced accuracy., Comment: Accepted for publishing at the 58th IEEE Conference on Decision and Control, Nice, France, 11-13 December, https://cdc2019.ieeecss.org/
- Published
- 2019