A deep learning enabler for nonintrusive reduced order modeling of fluid flows
Abstract
Here in this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various DNN architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equation, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a nonintrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly nonintrusive since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate and can be used as a robust predictive tool for nonintrusive model order reduction of complex fluid flows.
- Authors:
-
[1];
[1];
[1];
- Oklahoma State Univ., Stillwater, OK (United States). School of Mechanical and Aerospace Engineering
- Norwegian Univ. of Science and Technology, Trondheim (Norway)
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, Oklahoma 73019, USA
- Publication Date:
- Research Org.:
- Oklahoma State Univ., Stillwater, OK (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); NVIDIA Corporation
- OSTI Identifier:
- 1593560
- Alternate Identifier(s):
- OSTI ID: 1545970
- Grant/Contract Number:
- SC0019290
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Fluids
- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 8; Journal ID: ISSN 1070-6631
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Dynamical systems; Deep learning; Neural networks; Reduced order modeling; Proper orthogonal decomposition
Citation Formats
Pawar, S., Rahman, S. M., Vaddireddy, H., San, O., Rasheed, A., and Vedula, P. A deep learning enabler for nonintrusive reduced order modeling of fluid flows. United States: N. p., 2019.
Web. doi:10.1063/1.5113494.
Pawar, S., Rahman, S. M., Vaddireddy, H., San, O., Rasheed, A., & Vedula, P. A deep learning enabler for nonintrusive reduced order modeling of fluid flows. United States. https://doi.org/10.1063/1.5113494
Pawar, S., Rahman, S. M., Vaddireddy, H., San, O., Rasheed, A., and Vedula, P. Thu .
"A deep learning enabler for nonintrusive reduced order modeling of fluid flows". United States. https://doi.org/10.1063/1.5113494. https://www.osti.gov/servlets/purl/1593560.
@article{osti_1593560,
title = {A deep learning enabler for nonintrusive reduced order modeling of fluid flows},
author = {Pawar, S. and Rahman, S. M. and Vaddireddy, H. and San, O. and Rasheed, A. and Vedula, P.},
abstractNote = {Here in this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various DNN architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equation, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a nonintrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly nonintrusive since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate and can be used as a robust predictive tool for nonintrusive model order reduction of complex fluid flows.},
doi = {10.1063/1.5113494},
journal = {Physics of Fluids},
number = 8,
volume = 31,
place = {United States},
year = {2019},
month = {8}
}
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FIG. 1: Iterative prediction using the trained DNN model for different frameworks proposed in this study. The input to the neural network consists of state history for p time steps. For the DNN-R framework, r is the residual predicted by the neural network. For the DNN-B framework, r is themore »
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