Model reduction, machine learning based global optimisation for
large-scale steady state nonlinear systems
Abstract
Many engineering processes can be accurately modelled using partial
differential equations (PDEs), but high dimensionality and non-convexity
of the resulting systems pose limitations on their efficient
optimisation. In this work, a model reduction, machine-learning
methodology combining principal component analysis (PCA) and artificial
neural networks (ANNs) is employed to construct a reduced surrogate
model, which can then be utilised by advanced deterministic global
optimisation algorithms to compute global optimal solutions with
theoretical guarantees. However, such optimisation would still be
time-consuming due to the high non-convexity of the activation functions
inside the reduced ANN structures. To develop a
computationally-efficient optimization framework, we propose two
alternative strategies: The first one is a piecewise-affine
reformulation of the nonlinear ANN activation functions, while the
second one is based on deep rectifier neural networks with ReLU
activation function. The performance of the proposed framework is
demonstrated through three illustrative case studies.