结束语(心理学)
伽辽金法
应用数学
计算机科学
还原(数学)
简单(哲学)
参数统计
动力系统理论
人工神经网络
数学
数学优化
算法
人工智能
非线性系统
物理
哲学
统计
几何学
认识论
量子力学
经济
市场经济
作者
Emmanuel Menier,Michele Alessandro Bucci,Mouadh Yagoubi,Lionel Mathelin,Marc Schoenauer
标识
DOI:10.1016/j.cma.2023.115985
摘要
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.
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