Predictions of turbulent shear flows using deep neural networks

PA Srinivasan, L Guastoni, Hossein Azizpour, PHILIPP Schlatter, Ricardo Vinuesa

Abstract:

In the present work we assess the capabilities of neural networks to predict temporally evolving turbulent flows. In particular, we use the nine-equation shear flow
model by Moehlis et al. [New J. Phys. 6, 56 (2004)] to generate training data
for two types of neural networks: the multilayer perceptron (MLP) and the long
short-term memory (LSTM) network. We tested a number of neural network architectures by varying the number of layers, number of units per layer, dimension of
the input, weight initialization and activation functions in order to obtain the best
configurations for flow prediction. Due to its ability to exploit the sequential nature
of the data, the LSTM network outperformed the MLP. The LSTM led to excellent predictions of turbulence statistics (with relative errors of 0.45% and 2.49%
in mean and fluctuating quantities, respectively) and of the dynamical behavior of
the system (characterized by Poincar´e maps and Lyapunov exponents). This is an
exploratory study where we consider a low-order representation of near-wall turbulence. Based on the present results, the proposed machine-learning framework may
underpin future applications aimed at developing accurate and efficient data-driven
subgrid-scale models for large-eddy simulations of more complex wall-bounded turbulent flows, including channels and developing boundary layers.