Reduced-order modelling of parameterised incompressible and compressible unsteady flow problems using deep neural networks

Abstract

A non-intrusive reduced-order model for nonlinear parametric flow problems is developed. It is based on extracting a reduced-order basis from full-order snapshots via proper orthogonal decomposition and using both deep and shallow neural network architectures to learn the reduced-order coefficients variation in time and over the parameter space. Even though the focus of the paper lies in developing a reduced-order methodology for approximating fluid flow problems, the methodology is generic and can be used for the order reduction of arbitrary time-dependent parametric systems. Since it is non-intrusive, it is independent of the full-order computational method and can be used together with black-box commercial solvers. An adaptive sampling strategy is proposed to increase the quality of the neural network predictions while minimising the required number of parameter samples. Numerical studies are presented for two canonical test cases, namely unsteady incompressible laminar flow around a circular cylinder and transonic inviscid flow around a pitching NACA 0012 aerofoil. Results show that the proposed methodology can be used as a predictive tool for unsteady parameter-dependent flow problems.