A parametric LSTM neural network for predicting flow field dynamics across a design space

We develop a data-driven reduced-order model (ROM) to robustly predict the dynamics of fluid flows across a parametric design space. Our approach extends a long-short-term memory (LSTM) neural network with a new design gate, which enables the network to distinguish dynamic patterns associated with different design parameters. We first compare this parametric LSTM (pLSTM) with traditional LSTMs trained on a Van der Pol oscillator, where the design parameter is the nonlinear damping coefficient. The results show that pLSTM can provide accurate and robust predictions, whereas LSTMs fail to predict the correct dynamics when evaluated outside the immediate training data. Next, we use the pLSTM to predict the two-dimensional incompressible flow past a heaving and pitching ellipse. The pLSTM is trained with simulated flow field data compressed to a latent space, here defined through a proper orthogonal decomposition. The pLSTM can successfully predict the long-time dynamics of the flow field for unseen heaving/pitching kinematic parameters, while showing exceptional robustness to noise in the initial states. Taken together, the proposed pLSTM approach offers a three-aspect ROM approach (space, time and design space) to benefit prediction, optimization and control problems across parametric flow regimes.