Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems

Area of Science:

• Computational fluid dynamics
• Scientific machine learning
• Numerical analysis

Background:

• Partial differential equations (PDEs) govern many physical systems, but solving them computationally can be resource-intensive.
• Existing deep learning models like LSTM, TCN, and CNN are adapted for time-series forecasting and spatial-feature extraction.
• Reduced-order modeling (ROM) techniques are crucial for efficient computation in large-scale and parameterized problems.

Purpose of the Study:

• To develop and evaluate deep learning models for computationally efficient forecasting of solutions to advection-dominated partial differential equations (PDEs).
• To investigate the efficacy of Convolutional Autoencoder (CAE) for data compression and CNN for time-step prediction in a non-intrusive ROM framework.
• To assess the long-term prediction accuracy and extrapolation capabilities of the proposed models on benchmark problems and a real-world scenario.

Main Methods:

• Employed deep learning techniques, specifically Convolutional Autoencoder (CAE) for compression and a CNN for future-step prediction.
• Utilized non-intrusive reduced-order modeling by compressing high-fidelity PDE solutions (snapshots) before feeding them into forecasting models.
• Tested models on 1D Burgers' equation and Stoker's dam-break problem for accuracy and extrapolation, and applied the best model to a 2D river dam-break scenario.

Main Results:

• The Convolutional Neural Network (CNN) future-step predictor significantly outperformed Long Short-Term Memory (LSTM) and Temporal Convolutional Network (TCN) in forecasting accuracy for the tested spatiotemporal problems.
• The proposed models successfully reduced computation time and power requirements for obtaining high-fidelity solutions.
• The models demonstrated effective long-term prediction accuracy, including performance outside the training domain (extrapolation).

Conclusions:

• The CNN future-step predictor, integrated with CAE-based compression, offers a highly accurate and efficient approach for solving PDEs in scientific and engineering applications.
• Deep learning-based non-intrusive reduced-order modeling provides a viable alternative to traditional computationally expensive methods.
• The proposed methodology shows promise for complex real-world simulations, such as predicting dam breaks in intricate river geometries.