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Model reduction based global optimization for large-scale steady state nonlinear systems
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  • Min Tao,
  • Panagiotis Petsagkourakis,
  • Jie Li,
  • Constantinos Theodoropoulos
Min Tao
University of Manchester
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Panagiotis Petsagkourakis
University College London
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Jie Li
University of Manchester
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Constantinos Theodoropoulos
University of Manchester
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Abstract

Many engineering processes can be accurately modeled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimization. In this work, a model reduction methodology combining principal component analysis (PCA) and artificial neural networks (ANNs) is employed to construct a reduced surrogate model, which is then utilized by advanced deterministic global optimization algorithms to compute global optimal solutions with theoretical guarantees. However, the optimization framework is still time-consuming due to the high non-convexity of the activation functions inside the reduced ANN structure. To further enhance the capability of our optimization framework, two alternative strategies have been proposed. The first one is a piecewise-affine reformulation while the second one is based on deep rectifier neural networks with ReLU activation function. The performances of the two improved frameworks is demonstrated through two illustrative case studies.

Peer review status:UNDER REVIEW

25 Jun 2021Submitted to AIChE Journal
28 Jun 2021Assigned to Editor
28 Jun 2021Submission Checks Completed
07 Jul 2021Reviewer(s) Assigned