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Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems

Wu, Jin-Long and Kashinath, Karthik and Albert, Adrian and Chirila, Dragos and Prabhat, Mr. and Xiao, Heng (2020) Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems. Journal of Computational Physics, 406 . Art. No. 109209. ISSN 0021-9991.

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Simulating complex physical systems often involves solving partial differential equations (PDEs) with some closures due to the presence of multi-scale physics that cannot be fully resolved. Although the advancement of high performance computing has made resolving small-scale physics possible, such simulations are still very expensive. Therefore, reliable and accurate closure models for the unresolved physics remains an important requirement for many computational physics problems, e.g., turbulence simulation. Recently, several researchers have adopted generative adversarial networks (GANs), a novel paradigm of training machine learning models, to generate solutions of PDEs-governed complex systems without having to numerically solve these PDEs. However, GANs are known to be difficult in training and likely to converge to local minima, where the generated samples do not capture the true statistics of the training data. In this work, we present a statistical constrained generative adversarial network by enforcing constraints of covariance from the training data, which results in an improved machine-learning-based emulator to capture the statistics of the training data generated by solving fully resolved PDEs. We show that such a statistical regularization leads to better performance compared to standard GANs, measured by (1) the constrained model's ability to more faithfully emulate certain physical properties of the system and (2) the significantly reduced (by up to 80%) training time to reach the solution. We exemplify this approach on the Rayleigh-Bénard convection, a turbulent flow system that is an idealized model of the Earth's atmosphere. With the growth of high-fidelity simulation databases of physical systems, this work suggests great potential for being an alternative to the explicit modeling of closures or parameterizations for unresolved physics, which are known to be a major source of uncertainty in simulating multi-scale physical systems, e.g., turbulence or Earth's climate.

Item Type:Article
Related URLs:
URLURL TypeDescription
Chirila, Dragos0000-0002-6394-4688
Xiao, Heng0000-0002-3323-4028
Additional Information:© 2019 Elsevier Inc. Received 8 May 2019, Revised 4 December 2019, Accepted 16 December 2019, Available online 27 December 2019. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC02-05CH11231
Subject Keywords:Machine learning; Generative adversarial networks; Statistical constraint; Partial differential equations; Rayleigh-Bénard convection
Record Number:CaltechAUTHORS:20200319-092437858
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Official Citation:Jin-Long Wu, Karthik Kashinath, Adrian Albert, Dragos Chirila, Prabhat, Heng Xiao, Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems, Journal of Computational Physics, Volume 406, 2020, 109209, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101991
Deposited By: Tony Diaz
Deposited On:19 Mar 2020 17:40
Last Modified:19 Mar 2020 17:40

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