Nonlinear model order reduction of engineering turbulence using data-assisted neural networks

Conducting repeated high-fidelity simulations of complex turbulent flows entails substantial computational costs in engineering applications. Reduced-order modeling (ROM) seeks to derive low-dimensional representations from full-order numerical systems, thereby facilitating rapid forecasting of future flow states. This study presents a novel data-assisted computational framework that employs deep neural networks for nonlinear ROM of engineering turbulent flows. Specifically, the Stacked Auto-Encoder (SAE) network is utilized for nonlinear dimensionality reduction and feature extraction; the resulting latent features subsequently serve as inputs to the Long Short-Term Memory (LSTM) network for predictive ROM of turbulent fluid dynamics. A comparative analysis is conducted between SAE and proper orthogonal decomposition regarding dimensionality reduction, and the performance of LSTM in time-series forecasting is also evaluated against dynamic mode decomposition, where two different training strategies are applied for LSTM within the reduced-order latent space. The proposed SAE-LSTM-based ROM approach is tested on two typical turbulent flow problems for non-intrusive model order reduction. The results demonstrate that the constructed surrogate models possess significant capability in predicting the evolution of turbulent flows by preserving essential nonlinear characteristics inherent in fluid dynamics. This innovative method shows great promise in addressing computational challenges associated with high-resolution numerical modeling applied to complex large-scale flow problems.