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
会议
学术会议
工作坊
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 operators using deep neural networks for multiphysics, multiscale & multifidelity problems
Learning operators using deep neural networks for multiphysics, multiscale & multifidelity problems
组织者
熊繁升 , 杨武岳 , 雍稳安 , 朱毅
演讲者
Lu Lu
时间
2022年10月27日 10:00 至 11:00
地点
1129B
线上
Zoom 537 192 5549 (BIMSA)
摘要
It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. In this talk, I will present the deep operator network (DeepONet) to learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. I will also present several extensions of DeepONet, such as DeepM&Mnet for multiphysics problems, DeepONet with proper orthogonal decomposition (POD-DeepONet), MIONet for multiple-input operators, and multifidelity DeepONet. More generally, DeepONet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously. I will demonstrate the effectiveness of DeepONet and its extensions to diverse multiphysics and multiscale problems, such as nanoscale heat transport, bubble growth dynamics, high-speed boundary layers, electroconvection, and hypersonics.
演讲者介绍
Lu Lu is an Assistant Professor in the Department of Chemical and Biomolecular Engineering at University of Pennsylvania. He is also a faculty of Graduate Group in Applied Mathematics and Computational Science of Penn Institute for Computational Science. Prior to joining Penn, he was an Applied Mathematics Instructor in the Department of Mathematics at Massachusetts Institute of Technology from 2020 to 2021. He obtained his Ph.D. degree in Applied Mathematics at Brown University in 2020, master's degrees in Engineering, Applied Mathematics, and Computer Science at Brown University, and bachelor's degrees in Mechanical Engineering, Economics, and Computer Science at Tsinghua University in 2013. Lu has a multidisciplinary research background with research experience at the interface of applied mathematics, physics, computational biology, and computer science. His current research interest lies in scientific machine learning, including theory, algorithms, software, and its applications to engineering, physical, and biological problems. His broad research interests focus on multiscale modeling and high performance computing for physical and biological systems. Lu has received the 2022 U.S. Department of Energy Early Career Award, and 2020 Joukowsky Family Foundation Outstanding Dissertation Award of Brown University.
北京雁栖湖应用数学研究院
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No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

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