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A deep learning enabler for nonintrusive reduced order modeling of fluid flows

机译：一种深度学习推动器，用于流体流动的非流体减少秩序建模

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摘要

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. Published under license by AIP Publishing.
机译：在本文中，我们介绍了一种模块化的深神经网络（DNN）框架，用于数据驱动的减少阶数建模与流体流动。我们提出了各种DNN架构，其通过使用系统的离散状态或斜率信息来实现数量地预测动态系统的演化。我们的方法已经使用剩余公式和后向差分方案公式进行了证明。但是，它也可以容易地推广到许多不同的数值方案中。我们展示了我们三个例子的框架：（i）kraichnan-orszag系统，一个说明性耦合非线性常微分方程，（ii）Lorenz系统表现出混沌行为，（iii）两者的非流体模型顺序减少框架尺寸Boussinesq方程，在各种瑞利码中具有差动加热的腔流量设置。在离散时间实例中仅使用状态变量的快照，我们的数据驱动方法可以被认为真正不可消息，因为不需要有关基础管理方程式的任何先前信息来生成减少的订单模型。我们的后验分析表明，所提出的数据驱动方法非常准确，可用作复杂流体流量的非流体模型顺序减少的强大预测工具。通过AIP发布在许可证下发布。

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  • 来源
    《Physics of fluids》 |2019年第8期|共28页
  • 作者

    Pawar S.; Rahman S. M.; Vaddireddy H.; San O.; Rasheed A.; Vedula P.;

  • 作者单位

    Oklahoma State Univ Sch Mech &

    Aerosp Engn Stillwater OK 74078 USA;

    Oklahoma State Univ Sch Mech &

    Aerosp Engn Stillwater OK 74078 USA;

    Oklahoma State Univ Sch Mech &

    Aerosp Engn Stillwater OK 74078 USA;

    Oklahoma State Univ Sch Mech &

    Aerosp Engn Stillwater OK 74078 USA;

    Norwegian Univ Sci &

    Technol Dept Engn Cybernet N-7465 Trondheim Norway;

    Univ Oklahoma Sch Aerosp &

    Mech Engn Norman OK 73019 USA;

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  • 正文语种 eng
  • 中图分类 流体力学;
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