Rajeev Jaiman

Indu Kant Deo, Rui Gao, Rajeev Jaiman

There is a critical need for efficient and reliable active flow control strategies to reduce drag and noise in aerospace and marine engineering applications. While traditional full-order models based on the Navier-Stokes equations are not feasible, advanced model reduction techniques can be inefficient for active control tasks, especially with strong non-linearity and convection-dominated phenomena. Using convolutional recurrent autoencoder network architectures, deep learning-based reduced-order models have been recently shown to be effective while performing several orders of magnitude faster than full-order simulations. However, these models encounter significant challenges outside the training data, limiting their effectiveness for active control and optimization tasks. In this study, we aim to improve the extrapolation capability by modifying network architecture and integrating coupled space-time physics as an implicit bias. Reduced-order models via deep learning generally employ decoupling in spatial and temporal dimensions, which can introduce modeling and approximation errors. To alleviate these errors, we propose a novel technique for learning coupled spatial-temporal correlation using a 3D convolution network. We assess the proposed technique against a standard encoder-propagator-decoder model and demonstrate a superior extrapolation performance. To demonstrate the effectiveness of 3D convolution network, we consider a benchmark problem of the flow past a circular cylinder at laminar flow conditions and use the spatio-temporal snapshots from the full-order simulations. Our proposed 3D convolution architecture accurately captures the velocity and pressure fields for varying Reynolds numbers. Compared to the standard encoder-propagator-decoder network, the spatio-temporal-based 3D convolution network improves the prediction range of Reynolds numbers outside of the training data.

Indu Kant Deo, Rajeev Jaiman

Accurate prediction over long time horizons is crucial for modeling complex physical processes such as wave propagation. Although deep neural networks show promise for real-time forecasting, they often struggle with accumulating phase and amplitude errors as predictions extend over a long period. To address this issue, we propose a novel loss decomposition strategy that breaks down the loss into separate phase and amplitude components. This technique improves the long-term prediction accuracy of neural networks in wave propagation tasks by explicitly accounting for numerical errors, improving stability, and reducing error accumulation over extended forecasts.

Indu Kant Deo, Rajeev Jaiman

In this paper, we present a deep learning technique for data-driven predictions of wave propagation in a fluid medium. The technique relies on an attention-based convolutional recurrent autoencoder network (AB-CRAN). To construct a low-dimensional representation of wave propagation data, we employ a denoising-based convolutional autoencoder. The AB-CRAN architecture with attention-based long short-term memory cells forms our deep neural network model for the time marching of the low-dimensional features. We assess the proposed AB-CRAN framework against the standard recurrent neural network for the low-dimensional learning of wave propagation. To demonstrate the effectiveness of the AB-CRAN model, we consider three benchmark problems, namely, one-dimensional linear convection, the nonlinear viscous Burgers equation, and the two-dimensional Saint-Venant shallow water system. Using the spatial-temporal datasets from the benchmark problems, our novel AB-CRAN architecture accurately captures the wave amplitude and preserves the wave characteristics of the solution for long time horizons. The attention-based sequence-to-sequence network increases the time-horizon of prediction compared to the standard recurrent neural network with long short-term memory cells. The denoising autoencoder further reduces the mean squared error of prediction and improves the generalization capability in the parameter space.