Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems
Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems
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DOI：
10.1016/j.jcp.2019.109209
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发表时间：
2020-04-01
影响因子：
4.1
通讯作者：
Xiao, Heng
中科院分区：
文献类型：
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作者：
Wu, Jin-Long;Kashinath, Karthik;Xiao, Heng
模拟复杂的物理系统通常涉及求解偏微分方程（PDEs），由于存在无法完全解决的多尺度物理现象，偏微分方程具有一些闭包。尽管高性能计算的进步使得解决小规模物理问题成为可能，但这样的模拟仍然非常昂贵。因此，对于未解决的物理问题，可靠和准确的闭合模型仍然是许多计算物理问题的重要要求，例如湍流模拟。最近，一些研究人员采用生成对抗网络（GANs）来生成PDEs控制的复杂系统的解，而无需对这些PDEs进行数值求解，这是一种新的训练机器学习模型的范例。然而，已知gan在训练中是困难的，并且可能收敛到局部最小值，其中生成的样本不能捕获训练数据的真实统计。在这项工作中，我们提出了一个统计约束生成对抗网络，通过对训练数据施加协方差约束，从而改进了基于机器学习的模拟器，以捕获通过求解完全解析的偏微分方程生成的训练数据的统计信息。我们表明，与标准gan相比，这样的统计正则化导致更好的性能，通过(1)约束模型更忠实地模拟系统某些物理特性的能力和(2)显著减少（高达80%）达到解决方案的训练时间来衡量。我们在瑞利-贝纳德对流中举例说明了这种方法，瑞利-贝纳德对流是一种湍流系统，是地球大气的理想模型。随着物理系统高保真模拟数据库的增长，这项工作表明，对于未解决的物理问题，作为闭包或参数化的显式建模的替代方案具有巨大的潜力，这是模拟多尺度物理系统（例如湍流或地球气候）的主要不确定性来源。(C) 2019 Elsevier Inc.版权所有。
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-Benard 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. (C) 2019 Elsevier Inc. All rights reserved.