Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural Networks

Nikolaj Takata Mucke, Lasse Hjuler Christiansen, Allan Peter Engsig-Karup, John Bagterp Jørgensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


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.
Original languageEnglish
Title of host publicationProceedings of 2019 IEEE 58th Conference on Decision and Control
Publication date2019
ISBN (Print)9781728113982
Publication statusPublished - 2019

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