连续对称随机动力系统的模型降阶
Model order reduction for stochastic dynamical systems with continuous symmetries
摘要：
具有连续对称性的随机动力系统在自然界中普遍存在，并且经常产生相干的时空模式。然而，由于它们的随机位置，这些模式不能很好地捕获当前的降阶技术和大量的模式通常是必要的一个准确的解决方案。在这项工作中，我们介绍了一种新的方法，有效地降低了这种系统的方法相结合（i）切片的方法，对称性降低工具，与（ii）任何标准的降阶技术，从而在有效的混合的混合维数降低计划。特别地，在第二步中，利用动态正交（DO）方程，我们得到了一个新的非线性对称约化动态正交（SDO）格式。我们证明了SDO计划的性能上的随机解的一维Korteweg-de Vries和二维纳维-斯托克斯方程。
英文摘要：
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order reduction techniques and a large number of modes is typically necessary for an accurate solution. In this work, we introduce a new methodology for efficient order reduction of such systems by combining (i) the method of slices, a symmetry reduction tool, with (ii) any standard order reduction technique, resulting in efficient mixed symmetry-dimensionality reduction schemes. In particular, using the Dynamically Orthogonal (DO) equations in the second step, we obtain a novel nonlinear Symmetry-reduced Dynamically Orthogonal (SDO) scheme. We demonstrate the performance of the SDO scheme on stochastic solutions of the 1D Korteweg-de Vries and 2D Navier-Stokes equations.
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