On reduced-order modeling of gas–solid flows using deep learning

Reduced-order models (ROMs) have been extensively employed to understand complex systems efficiently and adequately. In this study, a novel parametric ROM framework is developed to produce Eulerian–Lagrangian simulations. This study employs two typical parametric strategies to reproduce the physical phenomena of a gas–solid flow by predicting the adequate dynamics of modal coefficients in the ROM: (i) based on the radial-basis function (RBF) interpolation, termed ROM-RBF and (ii) based on a long–short term memory (LSTM) neural network, termed ROM-LSTM. In the ROM, an advanced technique, namely, Lanczos-based proper orthogonal decomposition (LPOD), is employed to efficiently transform numerical snapshots into the modal coefficients. Validation tests are conducted in a typical gas–solid flow system such as a spouted bed. The coherent structures of the gas–solid flows are shown to be captured by the LPOD technique. Besides, in comparison with the high-fidelity simulations, our proposed ROMs are shown to simulate the gas–solid flows by significantly reducing the calculation time by several orders of magnitude and faithfully predicting the macroscopic properties. In particular, compared to the ROM-RBF, the ROM-LSTM can capture the flow fields more accurately within the gas–solid flows.