Acceleration of nonlinear POD models: A neural network approach

This paper presents a way of accelerating the evaluation and simulation of nonlinear POD models by using feedforward neural networks. Traditionally, Proper Orthogonal Decomposition (POD) and Galerkin projection have been employed to reduce the high-dimensionality of the discretized systems used to approximate Partial Differential Equations (PDEs). Although a large model-order reduction can be obtained with these techniques, the computational saving is small when we are dealing with nonlinear or Linear Time Variant (LTV) models. If we approximate the nonlinear vector function of the POD models by means of a feedforward neural network like a Multi-Layer Perceptron (MLP), then we can speed up the simulation of the POD models given that the on-line evaluation of this kind of networks can be done very fast. This is the approach that is presented in this paper.