An artificial neural network framework for reduced order modeling of transient flows

This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our approach utilizes a training process from full-order scale direct numerical simulation data projected on proper orthogonal decomposition (POD) modes to achieve an artificial neural network (ANN) model with reduced memory requirements. This data-driven ANN framework allows for a nonlinear time evolution of the modal coefficients without performing a Galerkin projection. Our POD-ANN framework can thus be considered an equation-free approach for latent space dynamics evolution of nonlinear transient systems and can be applied to a wide range of physical and engineering applications. Within this framework we introduce two architectures, namely sequential network (SN) and residual network (RN), to train the trajectory of modal coefficients. We perform a systematic analysis of the performance of the proposed reduced order modeling approaches on prediction of a nonlinear wave-propagation problem governed by the viscous Burgers equation, a simplified prototype setting for transient flows. We find that the POD-ANN-RN yields stable and accurate results for test problems assessed both within inside and outside of the database range and performs significantly better than the standard intrusive Galerkin projection model. Our results show that the proposed framework provides a non-intrusive alternative to the evolution of transient physics in a POD basis spanned space, and can be used as a robust predictive model order reduction tool for nonlinear dynamical systems.