A Deep Learning based Approach to Reduced Order Modeling for Turbulent Flow Control using LSTM Neural Networks

TL;DR

This paper presents a novel deep learning approach using LSTM neural networks to develop reduced order models for turbulent flow control, offering a data-driven alternative to traditional physics-based methods.

Contribution

It introduces the use of LSTM networks for ROM in turbulence, incorporating the Hurst Exponent to analyze non-stationary data, advancing data-driven flow modeling techniques.

Findings

LSTM networks effectively model temporal turbulence dynamics.

Hurst Exponent provides insights into non-stationary flow data.

Deep learning-based ROM offers a promising alternative to traditional methods.

Abstract

Reduced Order Modeling (ROM) for engineering applications has been a major research focus in the past few decades due to the unprecedented physical insight into turbulence offered by high-fidelity CFD. The primary goal of a ROM is to model the key physics/features of a flow-field without computing the full Navier-Stokes (NS) equations. This is accomplished by projecting the high-dimensional dynamics to a low-dimensional subspace, typically utilizing dimensionality reduction techniques like Proper Orthogonal Decomposition (POD), coupled with Galerkin projection. In this work, we demonstrate a deep learning based approach to build a ROM using the POD basis of canonical DNS datasets, for turbulent flow control applications. We find that a type of Recurrent Neural Network, the Long Short Term Memory (LSTM) which has been primarily utilized for problems like speech modeling and language translation, shows attractive potential in modeling temporal dynamics of turbulence. Additionally, we introduce the Hurst Exponent as a tool to study LSTM behavior for non-stationary data, and uncover useful characteristics that may aid ROM development for a variety of applications.