Reduced-order modeling for stochastic large-scale and time-dependent flow problems using deep spatial and temporal convolutional autoencoders

A non-intrusive reduced-order model based on convolutional autoencoders is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatiotemporal large-scale flow problems. The objective is to perform accurate and rapid uncertainty analyses of the flow outpu...

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Vydané v:Advanced modeling and simulation in engineering sciences Ročník 10; číslo 1; s. 7 - 27
Hlavní autori: Abdedou, Azzedine, Soulaimani, Azzeddine
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 19.05.2023
Springer Nature B.V
Springer
SpringerOpen
Predmet:
Accuracy
Artificial neural networks
Classical and Continuum Physics
Computational Science and Engineering
Convolutional autoencoders
Deep learning
Engineering
Engineering Sciences
Finite element method
Mathematical models
Multilayer perceptrons
Parameter uncertainty
Partial differential equations
Proper Orthogonal Decomposition
Reduced order models
Reduced-order modeling
Research Article
Solvers
Statistical analysis
Theoretical and Applied Mechanics
Time compression
Time dependence
Uncertainty analysis
Uncertainty propagation
Deep learning
Uncertainty propagation
Convolutional autoencoders
Reduced-order modeling
ISSN:2213-7467, 2213-7467
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Popis
Shrnutí:A non-intrusive reduced-order model based on convolutional autoencoders is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatiotemporal large-scale flow problems. The objective is to perform accurate and rapid uncertainty analyses of the flow outputs of interest for which the input parameters are deemed uncertain. The data are constituted from a set of high-fidelity snapshots, collected using an inhouse high-fidelity flow solver, which correspond to a sample of the uncertain input parameters. The method uses a 1D-convolutional autoencoder to reduce the spatial dimension of the unstructured meshes used by the flow solver. Another convolutional autoencoder is used for the time compression. The encoded latent vectors, generated from the two compression levels, are then mapped to the input parameters using a regression-based multilayer perceptron. The proposed model allows for rapid predictions for unseen parameter values, allowing the output statistical moments to be computed efficiently. The accuracy of the proposed approach is compared to that of the linear reduced-order technique based on an artificial neural network through two benchmark tests (the one-dimensional Burgers and Stoker’s solutions) and a hypothetical dam break flow problem, with an unstructured mesh and over a complex bathymetry river. The numerical results show that the proposed methods present strong predictive capabilities to accurately approximate the statistical moments of the outputs. In particular, the predicted statistical moments are oscillations-free, unlike those obtained with the traditional proper orthogonal decomposition method. The proposed reduction framework is simple to implement and can be applied to other parametric and time-dependent problems governed by partial differential equations, which are commonly encountered in many engineering and science problems.
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ISSN:2213-7467
2213-7467
DOI:10.1186/s40323-023-00244-0