Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
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发表时间：
2021-04
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通讯作者：
S. Dutta;Peter Rivera-Casillas;M. Farthing
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作者：
S. Dutta;Peter Rivera-Casillas;M. Farthing
流体流动模拟的模型简化一直是许多科学和工程领域的研究热点。在这里，我们探索使用神经常微分方程组，这是最近引入的一族连续深度可微网络(Chen等人，2018)，作为在降阶模型中传播潜在空间动力学的一种方式。我们将它们的行为与基于本征正交分解、径向基函数内插和动态模式分解的两种经典非侵入式方法进行了比较。我们考虑的测试问题包括圆柱体周围的不可压缩流动，以及浅水流体动力学在河流和河口系统中的真实应用。我们的发现表明，神经微分学为潜在空间动力学的稳定和准确演化提供了一个优雅的框架，具有很好的外推预测潜力。然而，为了促进它们在大规模系统中的广泛采用，需要做出重大努力来加快它们的培训时间。这将使我们能够更全面地探索超参数空间，以便在广泛的系统动力学范围内建立可推广的神经微分方程组近似。
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of continuous-depth, differentiable networks (Chen et al 2018), as a way to propagate latent-space dynamics in reduced order models. We compare their behavior with two classical non-intrusive methods based on proper orthogonal decomposition and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible flow around a cylinder as well as real-world applications of shallow water hydrodynamics in riverine and estuarine systems. Our findings indicate that Neural ODEs provide an elegant framework for stable and accurate evolution of latent-space dynamics with a promising potential of extrapolatory predictions. However, in order to facilitate their widespread adoption for large-scale systems, significant effort needs to be directed at accelerating their training times. This will enable a more comprehensive exploration of the hyperparameter space for building generalizable Neural ODE approximations over a wide range of system dynamics.