Multi-GPU implementation of a time-explicit finite volume solver using CUDA and a CUDA-Aware version of OpenMPI with application to shallow water flows

Delmas, Vincent; Soulaïmani, Azzeddine

doi:10.1016/j.cpc.2021.108190

Cited by 17 publications

(6 citation statements)

References 51 publications

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“…The data relating to the bathymetry and the roughness coefficient were provided by the Communeauté Métropolitaine de Montréal (CMM) from measurements and observations. The sub-domain of study is composed of an unstructured triangular mesh with elements and nodes, over which high-fidelity solutions of the quantities of interest are collected from an in-house multi-GPU finite volume solver for shallow water equations [ 45 ]. A detailed description of the physical domain of this test case was addressed in [ 13 ].…”

Section: Resultsmentioning

confidence: 99%

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.

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

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Section: Resultsmentioning

confidence: 99%

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.

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“…The data relating to the bathymetry and the roughness coefficient were provided by the Communeauté Métropolitaine de Montréal (CMM) from measurements and observations. The sub-domain of study is composed of an unstructured triangular mesh with 16 763 elements and N e = 10 200 nodes, over which highfidelity solutions of the quantities of interest are collected from an in-house multi-GPU finite volume solver for shallow water equations [43]. A detailed description of the physical domain of this test case was addressed in [13].…”

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

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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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.

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“…The study area consists of an unstructured triangular mesh comprising 16,763 elements and 10,200 nodes, where accurate solutions of the quantities of interest are obtained using an in-house multi-GPU finite volume solver specifically designed for shallow water equations [35]. For a comprehensive understanding of the physical domain of this test case, a detailed description was provided in [36]. An imaginary breach scenario was initiated in a hypothetical dam, as indicated by the line in Fig.…”

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

confidence: 99%

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

Bhatt,

Kumar,

Soulaïmani

2023

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

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Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep learning techniques developed especially for time-series forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN, are employed to model the system dynamics for advection-dominated problems. This paper proposes a Convolutional Autoencoder(CAE) model for compression and a CNN future-step predictor for forecasting. These models take as input a sequence of high-fidelity vector solutions for consecutive time steps obtained from the PDEs and forecast the solutions for the subsequent time steps using auto-regression; thereby reducing the computation time and power needed to obtain such high-fidelity solutions. Non-intrusive reduced-order modeling techniques such as deep auto-encoder networks are utilized to compress the high-fidelity snapshots before feeding them as input to the forecasting models in order to reduce the complexity and the required computations in the online and offline stages. The models are tested on numerical benchmarks (1D Burgers’ equation and Stoker’s dam-break problem) to assess the long-term prediction accuracy, even outside the training domain (i.e. extrapolation). The most accurate model is then used to model a hypothetical dam break in a river with complex 2D bathymetry. The proposed CNN future-step predictor revealed much more accurate forecasting than LSTM and TCN in the considered spatiotemporal problems.

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Multi-GPU implementation of a time-explicit finite volume solver using CUDA and a CUDA-Aware version of OpenMPI with application to shallow water flows

Cited by 17 publications

References 51 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

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

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

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