Year: 2021
Author: Yang Zeng, Jin-Long Wu, Heng Xiao
Communications in Computational Physics, Vol. 30 (2021), Iss. 3 : pp. 635–665
Abstract
Generative adversarial networks (GANs) were initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical question must be answered before GANs can be considered trusted emulators for physical systems: do GANs-generated samples conform to the various physical constraints? These include both deterministic constraints (e.g., conservation laws) and statistical constraints (e.g., energy spectrum of turbulent flows). The latter have been studied in a companion paper (Wu et al., Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems. Journal of Computational Physics. 406, 109209, 2020). In the present work, we enforce deterministic yet imprecise constraints on GANs by incorporating them into the loss function of the generator. We evaluate the performance of physics-constrained GANs on two representative tasks with geometrical constraints (generating points on circles) and differential constraints (generating divergence-free flow velocity fields), respectively. In both cases, the constrained GANs produced samples that conform to the underlying constraints rather accurately, even though the constraints are only enforced up to a specified interval. More importantly, the imposed constraints significantly accelerate the convergence and improve the robustness in the training, indicating that they serve as a physics-based regularization. These improvements are noteworthy, as the convergence and robustness are two well-known obstacles in the training of GANs.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0106
Communications in Computational Physics, Vol. 30 (2021), Iss. 3 : pp. 635–665
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Generative adversarial networks physics constraints physics-informed machine learning.