Deep Convolutional Recurrent Autoencoders for Flow Field Prediction

Abstract

In this paper, an end-to-end nonlinear model reduction methodology is presented based on the convolutional recurrent autoencoder networks. The methodology is developed in the context of overall data-driven reduced order model framework proposed in the paper. The basic idea behind the methodology is to obtain the low dimensional representations via convolutional neural networks and evolve these low dimensional features via recurrent neural networks in time domain. The high dimensional representations are constructed from the evolved low dimensional features via transpose convolutional neural networks. With an unsupervised training strategy, the model serves as an end to end tool which can evolve the flow state of the nonlinear dynamical system. The convolutional recurrent autoencoder network model is applied on the problem of flow past bluff bodies for the first time. To demonstrate the effectiveness of the methodology, two canonical problems namely the flow past plain cylinder and the flow past side-by-side cylinders are explored in this paper. Pressure and velocity fields of the unsteady flow are predicted in future via the convolutional recurrent autoencoder model. The performance of the model is satisfactory for both the problems. Specifically, the multiscale nature and the gap flow dynamics of the side-by-side cylinders are captured by the proposed data-driven model reduction methodology. The error metrics, the normalized squared error and the normalized reconstruction error are considered for the assessment of the data-driven framework.

A twin-decoder structure for incompressible laminar flow reconstruction with uncertainty estimation around 2D obstacles

“…In [14], AEs are used in conjunction with convolutional layers to learn low-dimensional features of fluid systems. In [15] and [16], the authors combine recurrent neural networks with CAE to learn the dynamics of the extracted low dimensional features. Adversely, in the case of supervised learning, AEs are exploited to perform various full-field flow prediction tasks [4][5][6].…”

Learning Wave Propagation with Attention-Based Convolutional Recurrent Autoencoder Net

“…CRAN is a fully data-driven approach in which both the lowdimensional representation of the state and its time evolution are learned using deep learning algorithms. Convolutional recurrent autoencoders have been shown to perform well for unsteady flow and fluidstructure phenomenon [22,27,38]. On the other hand, the ability of current CRAN architecture to learn PDEs with a dominant hyperbolic character relies on learning low-dimensional manifold with convolutional autoencoder and evolving these low-dimensional latent representations in time via RNN-LSTM, which can pose difficulties to generalize for the various physical phenomenon characterized by hyperbolic PDEs.…”

“…As a result, many of these methods are usually not the preferred choice in the engineering community when it comes to reduced-order modeling of hyperbolic PDE systems. To overcome such limitations, nonlinear dimensionality reduction based on neutral networks [20] are explored (e.g., autoencoders), which allow to project the input physical data to a latent low-dimension space and back to the original physical dimension [9,21,22,23,14,24,25]. Instead of the projection, the low-dimensional model in the latent space can be achieved by generating the trainable layers of the encoder and decoder space such that the error function is minimized.…”