Assessment of unsteady flow predictions using hybrid deep learning based reduced-order models

Abstract

In this paper, we present two deep learning-based hybrid data-driven reduced-order models for prediction of unsteady fluid flows. These hybrid models rely on recurrent neural networks (RNNs) to evolve low-dimensional states of unsteady fluid flow. The first model projects the high-fidelity time series data from a finite element Navier–Stokes solver to a low-dimensional subspace via proper orthogonal decomposition (POD). The time-dependent coefficients in the POD subspace are propagated by the recurrent net (closed-loop encoder–decoder updates) and mapped to a high-dimensional state via the mean flow field and the POD basis vectors. This model is referred to as POD-RNN. The second model, referred to as the convolution recurrent autoencoder network (CRAN), employs convolutional neural networks (instead of POD) as layers of linear kernels with nonlinear activations, to extract low-dimensional features from flow field snapshots. The flattened features are advanced using a recurrent (closed-loop manner) net and up-sampled (transpose convoluted) gradually to high-dimensional snapshots. Two benchmark problems of the flow past a cylinder and the flow past side-by-side cylinders are selected as the unsteady flow problems to assess the efficacy of these models. For the problem of the flow past a single cylinder, the performance of both the models is satisfactory and the CRAN model is found to be overkill. However, the CRAN model completely outperforms the POD-RNN model for a more complicated problem of the flow past side-by-side cylinders involving the complex effects of vortex-to-vortex and gap flow interactions. Owing to the scalability of the CRAN model, we introduce an observer-corrector method for calculation of integrated pressure force coefficients on the fluid–solid boundary on a reference grid. This reference grid, typically a structured and uniform grid, is used to interpolate scattered high-dimensional field data as snapshot images. These input images are convenient in training the CRAN model, which motivates us to further explore the application of the CRAN-based models for prediction of fluid flows.

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

“…2020; Xu & Duraisamy 2020; Bukka et al. 2021). Since a few studies have also recently recognized the challenges of the current form of CNN-AE for turbulence (Brunton, Hemati & Taira 2020; Fukami et al.…”

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

“…Such hybrid architectures consider spatio-temporal domain knowledge and achieve data-driven time series predictions. Recently proposed POD-based DL-ROMs are the POD-CNN by Miyanawala and Jaiman 40 , the POD-RNN by Bukka et al 7 , the POD-enhanced autoencoders by Fresca and Manzoni 17 . These hybrid architectures have been demonstrated for 2D bluff body flows with and without fluid-structure interaction.…”

“…Many promising approaches have been established in the research community for a synergistic coupling of deep learning and physics-based models 7,9 . These models are trained to represent a full or partial parametrization of a forward process to reduce computational costs while emulating physical laws.…”

“…Likewise, Snachez et al 51 and Pfaff et al 46 utilized graph neural networks to represent the state of a physical system as nodes in a graph and compute the dynamics by learning messagepassing signals. The third category in the physics-based deep learning involves the development of the hybrid DL-ROMs that take into account the spatial and temporal domain knowledge in neural networks 7,17,19,40 . We refer to such DL-ROM frameworks as physics-based because they incorporate physical interpretability via proper orthogonal decomposition and its variants.…”

Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models

“…This latter defines a sparse representation through a linear combination of selected functions, and has been used for data-driven forecasting in fluid dynamics [49]. RNNs have been considered in [50,51] to evolve lowdimensional states of unsteady flows, exploiting either POD or a convolutional recurrent autoencoder to extract low-dimensional features from snapshots. DL algorithms have also been used in [52] to describe the reduced trial manifold where the approximation is sought, then relying on a minimum residual formulation to derive the ROM-hence, still requiring the assembling and the solution of a ROM as in traditional POD-Galerkin ROMs.…”