北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
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论坛
学院生活
住宿
交通
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周边旅游
新闻
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通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > BIMSA-清华机器学习和微分方程讨论班 Learning Nonlocal Constitutive Models with Neural Operators
Learning Nonlocal Constitutive Models with Neural Operators
组织者
熊繁升 , 杨武岳 , 雍稳安 , 朱毅
演讲者
韩劼群
时间
2022年12月22日 10:00 至 11:30
地点
1129B
线上
Zoom 537 192 5549 (BIMSA)
摘要
Constitutive models are widely used for modeling complex systems in science and engineering, when first-principle-based, well-resolved simulations are prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar-turbulent transition. However, traditional constitutive models based on PDEs often lack robustness and are too rigid to accommodate diverse calibration datasets. We propose a frame-independent, nonlocal constitutive model based on a vector-cloud neural network that represents the physics of PDEs and meanwhile can be learned with data. The proposed model can be interpreted as a neural operator, which by design, respects all the invariance properties desired by constitutive models, faithfully reflects the region of influence in physics, and is applicable to different spatial resolutions. We demonstrate its performance on modeling the Reynolds stress for Reynolds-averaged Navier--Stokes (RANS) equations in two situations: (1) emulating the Reynolds stress transport model through synthetic data and (2) calibrating the Reynolds stress through data from direct numerical simulations. Our results show that the proposed neural operator is a promising alternative to traditional nonlocal constitutive models and paves the way for developing robust and nonlocal, non-equilibrium closure models for the RANS equations.
演讲者介绍
Jiequn Han is a Research Fellow in the Center for Computational Mathematics, Flatiron Institute, Simons Foundation. His research draws inspiration from various disciplines of science and is devoted to solving high-dimensional problems arising from scientific computing. His current research interests mainly focus on solving high-dimensional partial differential equations and machine learning based-multiscale modeling. He holds a Ph.D. in Applied Mathematics from Princeton University, a B.S. in Computational Mathematics and a B.A. in Economics from Peking University.
北京雁栖湖应用数学研究院
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