Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

  • About
    • President
    • Governance
    • Partner Institutions
    • Visit
  • People
    • Management
    • Faculty
    • Postdocs
    • Visiting Scholars
    • Staff
  • Research
    • Research Groups
    • Courses
    • Seminars
  • Join Us
    • Faculty
    • Postdocs
    • Students
  • Events
    • Conferences
    • Workshops
    • Forum
  • Life @ BIMSA
    • Accommodation
    • Transportation
    • Facilities
    • Tour
  • News
    • News
    • Announcement
    • Downloads
About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations Learning Nonlocal Constitutive Models with Neural Operators
Learning Nonlocal Constitutive Models with Neural Operators
Organizers
Fan Sheng Xiong , Wu Yue Yang , Wen An Yong , Yi Zhu
Speaker
Jiequn Han
Time
Thursday, December 22, 2022 10:00 AM - 11:30 AM
Venue
1129B
Online
Zoom 537 192 5549 (BIMSA)
Abstract
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.
Speaker Intro
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.
Beijing Institute of Mathematical Sciences and Applications
CONTACT

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

Tel. 010-60661855
Email. administration@bimsa.cn

Copyright © Beijing Institute of Mathematical Sciences and Applications

京ICP备2022029550号-1

京公网安备11011602001060 京公网安备11011602001060