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Volume 30, Issue 1
Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

Zhen Gao, Qi Liu, Jan S. Hesthaven, Bao-Shan Wang, Wai Sun Don & Xiao Wen

DOI: 10.4208/cicp.OA-2020-0064

Commun. Comput. Phys., 30 (2021), pp. 97-123.

Published online: 2021-04

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  • Abstract

A non-intrusive reduced order model (ROM) that combines a proper orthogonal decomposition (POD) and an artificial neural network (ANN) is primarily studied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and strong gradients accurately and resolving fine-scale structures efficiently for hyperbolic conservation laws. Its accuracy is demonstrated by solving a high-dimensional parametrized ODE and the one-dimensional viscous Burgers' equation with a parameterized diffusion coefficient. The two-dimensional single-mode Rayleigh-Taylor instability (RTI), where the amplitude of the small perturbation and time are considered as free parameters, is also simulated. An adaptive sampling method in time during the linear regime of the RTI is designed to reduce the number of snapshots required for POD and the training of ANN. The extensive numerical results show that the ROM can achieve an acceptable accuracy with improved efficiency in comparison with the standard full order method.

  • Keywords

Rayleigh-Taylor instability, non-intrusive reduced basis method, proper orthogonal decomposition, artificial neural network, adaptive sampling method.

  • AMS Subject Headings

35L65, 35Q35, 76N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-97, author = {Gao , ZhenLiu , QiHesthaven , Jan S.Wang , Bao-ShanDon , Wai Sun and Wen , Xiao}, title = {Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {1}, pages = {97--123}, abstract = {

A non-intrusive reduced order model (ROM) that combines a proper orthogonal decomposition (POD) and an artificial neural network (ANN) is primarily studied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and strong gradients accurately and resolving fine-scale structures efficiently for hyperbolic conservation laws. Its accuracy is demonstrated by solving a high-dimensional parametrized ODE and the one-dimensional viscous Burgers' equation with a parameterized diffusion coefficient. The two-dimensional single-mode Rayleigh-Taylor instability (RTI), where the amplitude of the small perturbation and time are considered as free parameters, is also simulated. An adaptive sampling method in time during the linear regime of the RTI is designed to reduce the number of snapshots required for POD and the training of ANN. The extensive numerical results show that the ROM can achieve an acceptable accuracy with improved efficiency in comparison with the standard full order method.

}, issn = {1991-7120}, doi = {https://doi.org/ 10.4208/cicp.OA-2020-0064}, url = {http://global-sci.org/intro/article_detail/cicp/18875.html} }
TY - JOUR T1 - Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability AU - Gao , Zhen AU - Liu , Qi AU - Hesthaven , Jan S. AU - Wang , Bao-Shan AU - Don , Wai Sun AU - Wen , Xiao JO - Communications in Computational Physics VL - 1 SP - 97 EP - 123 PY - 2021 DA - 2021/04 SN - 30 DO - http://doi.org/ 10.4208/cicp.OA-2020-0064 UR - https://global-sci.org/intro/article_detail/cicp/18875.html KW - Rayleigh-Taylor instability, non-intrusive reduced basis method, proper orthogonal decomposition, artificial neural network, adaptive sampling method. AB -

A non-intrusive reduced order model (ROM) that combines a proper orthogonal decomposition (POD) and an artificial neural network (ANN) is primarily studied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and strong gradients accurately and resolving fine-scale structures efficiently for hyperbolic conservation laws. Its accuracy is demonstrated by solving a high-dimensional parametrized ODE and the one-dimensional viscous Burgers' equation with a parameterized diffusion coefficient. The two-dimensional single-mode Rayleigh-Taylor instability (RTI), where the amplitude of the small perturbation and time are considered as free parameters, is also simulated. An adaptive sampling method in time during the linear regime of the RTI is designed to reduce the number of snapshots required for POD and the training of ANN. The extensive numerical results show that the ROM can achieve an acceptable accuracy with improved efficiency in comparison with the standard full order method.

Gao , ZhenLiu , QiHesthaven , Jan S.Wang , Bao-ShanDon , Wai Sun and Wen , Xiao. (2021). Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability. Communications in Computational Physics. 30 (1). 97-123. doi: 10.4208/cicp.OA-2020-0064
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