Close Search Advanced
Journals
Resources
About Us
Open Access

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

Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability
Preview
Add to basket

Year:    2021

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

Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0064

Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 97–123

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

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

Author Details

Zhen Gao

Qi Liu

Jan S. Hesthaven

Bao-Shan Wang

Wai Sun Don

Xiao Wen

  1. Fourier neural operator for large eddy simulation of compressible Rayleigh–Taylor turbulence

    Luo, Tengfei | Li, Zhijie | Yuan, Zelong | Peng, Wenhui | Liu, Tianyuan | Wang, Liangzhu (Leon) | Wang, Jianchun

    Physics of Fluids, Vol. 36 (2024), Iss. 7

    https://doi.org/10.1063/5.0213412 [Citations: 0]

  2. A physics-based reduced order model for urban air pollution prediction

    Khamlich, Moaad | Stabile, Giovanni | Rozza, Gianluigi | Környei, László | Horváth, Zoltán

    Computer Methods in Applied Mechanics and Engineering, Vol. 417 (2023), Iss. P.116416

    https://doi.org/10.1016/j.cma.2023.116416 [Citations: 4]

  3. Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy

    Vitullo, Piermario | Franco, Nicola Rares | Zunino, Paolo

    Foundations of Data Science, Vol. 0 (2024), Iss. 0 P.0

    https://doi.org/10.3934/fods.2024022 [Citations: 0]

  4. Reduced basis methods for time-dependent problems

    Hesthaven, Jan S. | Pagliantini, Cecilia | Rozza, Gianluigi

    Acta Numerica, Vol. 31 (2022), Iss. P.265

    https://doi.org/10.1017/S0962492922000058 [Citations: 41]

  5. Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression

    Cicci, Ludovica | Fresca, Stefania | Guo, Mengwu | Manzoni, Andrea | Zunino, Paolo

    Computers & Mathematics with Applications, Vol. 149 (2023), Iss. P.1

    https://doi.org/10.1016/j.camwa.2023.08.016 [Citations: 9]

  6. Adaptive Data-Driven Model Order Reduction for Unsteady Aerodynamics

    Nagy, Peter | Fossati, Marco

    Fluids, Vol. 7 (2022), Iss. 4 P.130

    https://doi.org/10.3390/fluids7040130 [Citations: 3]

  7. Nonlinear model order reduction for problems with microstructure using mesh informed neural networks

    Vitullo, Piermario | Colombo, Alessio | Franco, Nicola Rares | Manzoni, Andrea | Zunino, Paolo

    Finite Elements in Analysis and Design, Vol. 229 (2024), Iss. P.104068

    https://doi.org/10.1016/j.finel.2023.104068 [Citations: 5]
  8. High Performance Computing

    Reservoir Computing in Reduced Order Modeling for Chaotic Dynamical Systems

    Nogueira, Alberto C. | Carvalho, Felipe C. T. | Almeida, João Lucas S. | Codas, Andres | Bentivegna, Eloisa | Watson, Campbell D.

    2021

    https://doi.org/10.1007/978-3-030-90539-2_4 [Citations: 1]
  9. Error Control, Adaptive Discretizations, and Applications, Part 1

    Model reduction techniques for parametrized nonlinear partial differential equations

    Nguyen, Ngoc Cuong

    2024

    https://doi.org/10.1016/bs.aams.2024.03.005 [Citations: 2]