基于数据驱动的流场控制方程的稀疏识别

江昊; 王伯福; 卢志明

doi:10.6052/0459-1879-21-052

基于数据驱动的流场控制方程的稀疏识别

doi: 10.6052/0459-1879-21-052

上海大学, 力学与工程科学学院, 上海市应用数学和力学研究所, 上海 200072

基金项目: 1)国家自然科学基金资助项目(12072185);国家自然科学基金资助项目(11732010);国家自然科学基金资助项目(11972220)

详细信息

作者简介:
2)卢志明, 教授, 主要研究方向: 湍流, 环境流体力学, 计算流体力学. E-mail: zmlu@shu.edu.cn

通讯作者:
卢志明

中图分类号: O357
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- 被引次数: 0
出版历程
- 收稿日期: 2021-01-29
- 刊出日期: 2021-06-01

DATA-DRIVEN SPARSE IDENTIFICATION OF GOVERNING EQUATIONS FOR FLUID DYNAMICS

Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China

摘要

摘要: 利用有限数据建立系统的非线性动力学模型是具有挑战性的重要课题. 数据驱动的稀疏识别方法是近年来发展的从数据识别动力系统控制方程的有效方法. 本文基于数据驱动稀疏识别方法对不同流场的控制方程进行了识别. 采用非线性动力学偏微分方程函数识别(partial differential equations functional identification of nonlinear dynamics, PDE-FIND)方法和最小绝对收缩和选择算子(least absolute shrinkage and selection operator, LASSO)方法对二维圆柱绕流、顶盖驱动方腔流、Rayleigh-Bénard (RB)对流和三维槽道湍流的控制方程进行了识别. 在稀疏识别过程中, 采用直接数值模拟得到的流场数据来计算过完备候选库中的每一项, 候选库中变量最高保留到二次, 变量导数最高保留到二阶, 非线性项最高保留到四阶. 结果发现PDE-FIND方法和LASSO方法对于不含有非线性项的控制方程, 如涡量输运方程、热输运方程和连续性方程, 都能准确识别. 对于含有强非线性项的控制方程, 如Navier-Stokes方程的识别, PDE-FIND方法正确地识别出了控制方程及流场的Rayleigh数和Reynolds数, 而LASSO方法识别结果不正确, 这是因为候选库中的项之间存在分组效应, LASSO方法通常只取分组中的一项. 本文还发现选择流动结构丰富的区域的数据进行控制方程的稀疏识别可以提高识别的准确性.
- 数据驱动 /
- 纳维斯托克斯方程 /
- 稀疏识别 /
- 偏微分方程识别方法 /
- 套索方法
Abstract: It is a challenging and important issue to establish a nonlinear dynamic model of system by use of limited data. The data-driven sparse identification method is an effective method developed recently to identify the governing equations of the dynamic system from data developed in recent years. In this paper, governing equations for different flows are identified by data-driven sparse identification methods. Partial differential equation functional identification of nonlinear dynamics (PDE-FIND) scheme and least absolute shrinkage and selection operator (LASSO) scheme are used to identify the governing equations of two-dimensional flow past a circular cylinder, liddriven cavity flow, Rayleigh-Bénard convection and three-dimensional turbulent channel flow. An over-complete candidate library is constructed by direct numerical simulation flow field data in the process of identification. Variables in the library are retained up to second order, variable derivatives are retained up to second order, and nonlinear terms are retained up to fourth order. By comparing the results from the two methods, we find both methods show good performance in identifying governing equation with no nonlinear terms, i.e., vorticity transport equation, heat transport equation and continuity equation. PDE-FIND scheme correctly identified the governing equations and Rayleigh number and Reynolds number for the flow field. But LASSO scheme failed to identify the governing equations which contain strong nonlinear terms, i.e., Navier-Stokes equations. This is because grouping effect may occur among the items in the candidate library and only one item in the group is chosen in such case in LASSO scheme. So PDE-FIND scheme is more effective than LASSO scheme in sparse identification of strongly nonlinear partial differential equation. It is also found that selecting data from regions with abundant flow structures can improve the accuracy of data-driven sparse identification results.
- data-driven /
- Navier-Stokes equation /
- sparse identification /
- PDE-FIND /
- LASSO

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