A parameterized LSTM deep neural network framework to model unsteady flow problems

We propose a deep learning framework that can predict the space-time evolution of complex flow problems across a range of parametric regimes. Our approach is based on a Proper Orthogonal Decomposition (POD) for dimensionality reduction combined with a Long-Short Term Memory (LSTM) deep learning neural network for the temporal modeling of dynamical systems. The specific contributions of our work are focused on the LSTM architecture, where the problem parameters, such as those governing flow, body shape, or body kinematics, are considered independent inputs to the LSTM deep learning neural network. This enables the LSTM network to predict different flow states within a wide problem space as defined by the parametrization, and/or switch dynamically between them. We demonstrate the benefits of this approach on the 2D modeling of flow past a flapping ellipse and show that our approach is capable of real-time modeling flow patterns across a set of kinematic parameters.