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

Abstract

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.

Prediction of the dynamics of a backward-facing step flow using focused time-delay neural networks and particle image velocimetry data-sets

“…We also mention that, in a future implementation, the Re h number could also be integrated as an input, while the output could include POD coefficients from the different Re h numbers, making it even more useful for flow control purposes [36]. Distributed sensors, upstream and/or downstream, could also help achieve this complicated task.…”

“…In fluid systems, feed-forward artificial NNs have been used for data-driven reduced-order modelling [31,32,33,34,35] with many results showing better field reconstruction than traditional POD methods [36,37]. They were also used by [38] for experimental flow regime identification in multiphase flows.…”

Modeling transient fluid simulations with proper orthogonal decomposition and machine learning

“…More importantly, this is a new extension to prior work which have focused largely on steady‐state scenarios, or on training models to extend a single transient simulation further in time 20,28 . In particular, we evaluate the models' ability to extrapolate to flow simulations across multiple input velocity magnitudes with different temporal evolutions, even when those transient simulations are not included in the training dataset, similar to recent interesting work by San et al 29 …”

Sampling and resolution characteristics in reduced order models of shallow water equations: Intrusive vs nonintrusive

“…The residual between two time steps is then applied to update the current state during prediction. The learning of the residual information was observed to result in a more stabilized performance [105,121] and also improves the accuracy of neural network prediction [122]. Also, it is typical in machine learning community to normalize the input and output data.…”