Deep Convolutional Architectures for Extrapolative Forecasts in Time-Dependent Flow Problems

Bhatt, Pratyush; Kumar, Y V Ravi; Soulaïmani, Azzeddine

doi:10.2139/ssrn.4229792

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…12b. The downstream part of the dam is considered as dry whereas the free surface of the upstream part is considered as a random input parameter whose values are uniformly generated within its plausible variability range η up ∈ U [29,32] m. The snapshot matrix is obtained by running the numerical solver for each value of the upstream free surface, selected randomly from the generated sample set, for the whole N t = 100 simulation time steps that constitute the temporal domain (t ∈ [0, 50] s). For each parameter-time combination, a so-called high-fidelity solution is stored in a vector of dimension N x = 10 200, representing the free surface values at each node of the computational domain.…”

Section: Application To a Hypothetical Dam-break In A Rivermentioning

confidence: 99%

“…The key idea behind the popular recurrent network, long-short term memory, (LSTM) [29] is the so-called cell state, which helps to overcome the problems associated with the vanishing/exploding phenomena that are caused by the long-term dependencies within the network. Some configurations combine CAEs with LSTMs or TCNs [19,[30][31][32][33] to provide a tool for time predictions over the latent space. This paper proposes a non-intrusive reduced order modeling (NIROM) framework for parametrized and time-dependent flow problems.…”

Section: Introductionmentioning

confidence: 99%

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

Abdedou

Soulaïmani

2023

Preprint

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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 timedependent problems governed by partial differential equations, which are commonly encountered in many engineering and science problems.

show abstract

Section: Application To a Hypothetical Dam-break In A Rivermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Abdedou

Soulaïmani

2023

Preprint

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Inverse Airfoil Design for Hydrokinetic Turbine Blades Using Non-intrusive Reduced Order Modeling

Bhatt,

Mittal,

Taneja

et al. 2024

Lecture Notes in Mechanical Engineering

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

Abdedou

Soulaïmani

2023

Adv. Model. and Simul. in Eng. Sci.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Deep Convolutional Architectures for Extrapolative Forecasts in Time-Dependent Flow Problems

Cited by 3 publications

References 27 publications

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

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

Inverse Airfoil Design for Hydrokinetic Turbine Blades Using Non-intrusive Reduced Order Modeling

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

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