近日，中国科学院力学研究所流固耦合系统力学重点实验室的王一伟及其研究小组取得一项新进展。经过不懈努力，他们提出基于匹配渐近展开求解高雷诺数边界层流动的多尺度物理信息神经网络方案。相关研究成果已于2023年1月19日在国际知名学术期刊《理论与应用力学快报》上发表。

多尺度系统是流体力学、生物学等领域的经典科学问题。本文提出了一种多尺度内嵌物理知识神经网络（msPINNs）方案，可以在不需要任何数据的情况下求解高雷诺数边界层流动问题。该方案基于普朗特边界理论，将流动划分为若干不同尺度的区域，并采用不同尺度的控制方程进行求解。同时，采用匹配渐近展开法使流场连续。高雷诺数半无限大平板上的流动被认为是一个多尺度问题，因为边界层尺度远小于外部流动尺度。

通过对该问题进行研究，并将结果与参考数值解进行了比较，表明多尺度内嵌物理知识神经网络可以解决高雷诺数流动中边界层的多尺度问题。该方案可以用于解决未来FC碰碰胡老虎机法典-提高赢钱机率的下注技巧的多尺度问题。

附：英文原文

Title: Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Author: Jianlin Huang, Rundi Qiu, Jingzhu Wang, Yiwei Wang

Issue&Volume: 2023-01-19

Abstract: Multi-scale system remains a classical scientific problem in fluid dynamics, biology, etc. In the present study, a scheme of multi-scale Physics-informed neural networks (msPINNs) is proposed to solve the boundary layer flow at high Reynolds numbers without any data. The flow is divided into several regions with different scales based on Prandtl’s boundary theory. Different regions are solved with governing equations in different scales. The method of matched asymptotic expansions is used to make the flow field continuously. A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale. The results are compared with the reference numerical solutions, which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows. This scheme can be developed for more multi-scale problems in the future.

DOI: 10.1016/j.taml.2024.100496

Source: http://taml.cstam.org.cn/article/doi/10.1016/j.taml.2024.100496