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

TL;DR

This paper introduces two deep learning hybrid reduced order models, POD-RNN and CRAN, for predicting unsteady fluid flows, demonstrating their effectiveness on benchmark problems with CRAN outperforming POD-RNN in complex scenarios.

Contribution

The paper presents novel hybrid deep learning models, POD-RNN and CRAN, for efficient unsteady flow prediction, with CRAN showing superior performance on complex flow problems.

Findings

CRAN outperforms POD-RNN in complex flow scenarios.

Both models perform satisfactorily on simple flow problems.

CRAN's scalability enables advanced applications like pressure force prediction.

Abstract

In this paper, we present two deep learning-based hybrid data-driven reduced order models for the prediction of unsteady fluid flows. 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 POD basis vectors. This model is referred as POD-RNN. The second model, referred to as convolution recurrent autoencoder network (CRAN), employs convolutional neural networks (CNN) 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 flow past a side-by-side cylinder are selected as the test problems to assess the efficacy of these models. For the problem of flow past a single cylinder, the performance of both the models is satisfactory, with CRAN being a bit overkill. However, it completely outperforms the POD-RNN model for a more complicated problem of flow past side-by-side cylinders. Owing to the scalability of CRAN, we briefly introduce an observer-corrector method for the 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 CRAN. This motivates us to further explore the application of CRAN models for the prediction of fluid flows.