Deep neural networks for the construction of reduced order models of compressible flows

Abstract

In this work, we present a numerical methodology for construction of reduced order models of compressible flows which combines flow modal decomposition via proper orthogonal decomposition and regression analysis using deep feedforward neural networks. The framework is implemented in the context of the sparse identification of non-linear dynamics algorithm recently proposed in the literature. The method is tested on the reconstruction of a canonical nonlinear oscillator and the compressible flow past a cylinder. Results demonstrate that the technique provides accurate and stable reconstructions of the full order model beyond the training window of the deep feedforward neural network, demonstrating the robustness of the current reduced order model