Autoencoder

Deep learning

Physics

Iterative method

Reynolds number

Mathematics

Mechanics

Algorithm

Mathematical optimization

Geodesy

Recurrent neural network

Krylov subspace

Benchmark (surveying)

Artificial intelligence

Turbulence

Geography

Solver

Flow (mathematics)

Computer science

Applied mathematics

Artificial neural network

Physics of Fluids

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.

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