论文标题
CD-ROM：补充的深度降级模型
CD-ROM: Complemented Deep-Reduced Order Model
论文作者
论文摘要
通过POD-Galerkin方法减少模型订单可以在解决物理问题方面的计算效率方面带来巨大的提高。但是，该方法对非线性高维动力系统（例如Navier-Stokes方程）的适用性已被证明是有限的，产生了不准确的模型，有时会产生不稳定的模型。本文提出了一种基于深度学习的闭合建模方法，用于经典的Pod-galerkin减少订单模型（ROM）。所提出的方法是从理论上扎根的，使用神经网络近似研究良好的操作员。与大多数以前的作品相反，当前的CD-ROM方法基于可解释的连续记忆公式，该记忆公式来自对部分观察到的动态系统的行为的简单假设。因此，可以使用大多数经典的时间步进方案来模拟最终校正的模型。 CD-ROM方法的功能在来自计算流体动力学的两个经典示例中得到了证明，以及一个参数情况，即库拉莫托 - sivashinsky方程。
Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems such as the Navier-Stokes equations has been shown to be limited, producing inaccurate and sometimes unstable models. This paper proposes a deep learning based closure modeling approach for classical POD-Galerkin reduced order models (ROM). The proposed approach is theoretically grounded, using neural networks to approximate well studied operators. In contrast with most previous works, the present CD-ROM approach is based on an interpretable continuous memory formulation, derived from simple hypotheses on the behavior of partially observed dynamical systems. The final corrected models can hence be simulated using most classical time stepping schemes. The capabilities of the CD-ROM approach are demonstrated on two classical examples from Computational Fluid Dynamics, as well as a parametric case, the Kuramoto-Sivashinsky equation.
