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Reduced-order modeling for stochastic large-scale and time-dependent flow problems using deep spatial and temporal
Azzedine Abdedou1, Azzeddine Soulaimani1
11100 Notre-Dame W., Montreal, H3C 1K3 QC Canada Department of Mechanical Engineering, Ecole de technologie superieure.
Advanced Modeling and Simulation in Engineering Sciences
|May 22, 2023
Summary
This study introduces a novel convolutional autoencoder model for efficient uncertainty analysis in complex fluid flow problems. The data-driven approach enables rapid, accurate predictions of flow outputs, even for unseen parameters, avoiding oscillations common in traditional methods.
Area of Science:
- Computational Fluid Dynamics
- Machine Learning for Scientific Computing
- Stochastic Modeling
Background:
- Stochastic spatiotemporal large-scale flow problems require efficient methods for uncertainty quantification.
- Traditional reduced-order models can be computationally expensive and may produce oscillating results.
Purpose of the Study:
- To develop a non-intrusive, data-driven reduced-order model for accurate and rapid uncertainty analysis of fluid flow outputs.
- To enable efficient computation of statistical moments for flow outputs with uncertain input parameters.
Main Methods:
- Utilized convolutional autoencoders for spatial and temporal data compression.
- Employed a regression-based multilayer perceptron to map latent vectors to input parameters.
- Generated training data from a high-fidelity flow solver.
Main Results:
- The proposed model demonstrated strong predictive capabilities for approximating output statistical moments.
- Achieved oscillation-free statistical moments, outperforming traditional proper orthogonal decomposition.
- Validated on benchmark problems (1D Burgers, Stoker's solutions) and a dam break flow simulation.
Conclusions:
- The convolutional autoencoder-based reduced-order model offers an efficient and accurate tool for uncertainty analysis in fluid dynamics.
- The framework is simple to implement and applicable to various parametric, time-dependent partial differential equation problems.
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