Proper orthogonal decomposition and physical field reconstruction with artificial neural networks (ANN) for supercritical flow problems
Feng Sun, Gongnan Xie, Jian Song, Christos N. Markides
Abstract
The development of mathematical models, and the associated numerical simulations, are challenging in higher-dimensional systems featuring flows of supercritical fluids in various applications. In this paper, a data-driven methodology is presented to achieve system order reduction, and to identify important physical information within the principal flow features. Firstly, a new hybrid neural network based on radial basis function (RBF) and multi-layer perceptron (MLP) methods, namely RBF-MLP, is tested to achieve a highly nonlinear approximation. When provided with 1000 nonlinear test samples, this model provides an excellent prediction accuracy with a maximum regression coefficient (R) of 0.99 and a minimum root mean square error (RMSE) below 1%. Furthermore, the model is also proven to be flexible enough to capture accurately the turbulent fluctuation characteristics, even at significant nonlinear buoyancy conditions. Secondly, the high-dimensional buoyancy data is collected and integrated into a matrix database. Subsequently, a proper orthogonal decomposition (POD) approach is employed to reduce the high-dimensional database, and to obtain a set of low-dimensional POD basis-spanned space, which defines a reduced-order system with low-dimensional basis vectors. The results reveal that the first five order modes contain dominant flow features, accounting for 93% of the total mode energy, which can be selected to reconstruct the physical flow field. Thirdly, a new data-driven POD-ANN model is established to construct the nonlinear mapping between the full-field buoyancy data and decomposed basis vectors. It is also demonstrated that the POD-ANN model reconstructs the principal flow features accurately and reliably. This POD-ANN model can be used to provide new insights for reduced-order modelling and for reconstructing physical fields of higher-dimensional nonlinear flow cases.