一周活动预告（8.24-8.30）
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目录：
Unconditional convergence of mass- and energy- preserving Fourier pseudo-spectral methods for solving the nonlinear Schrodinger equation（王延春 教授）
一个基于位势理论的直角网格方法（应文俊 教授）
正交约束优化的新方法 (刘歆 研究员)
Nonconforming finite element Stokes complexes in three dimensions（黄学海 教授）
Discontinuous Galerkin Methods for Fourth Order Variational Inequality（崔金涛 助理教授）
Finite element diagram chasing（胡凯博 博士）
Nonlocal electromagnetic dispersion model coupling with Schrodinger equations and its finite element approximation (姚昌辉 教授)
Analysis of Gradient Descent on Wide Two-Layer ReLU Neural Networks (Lénaïc Chizat)
Multiscale Model Reduction for Heterogeneous Problems（Prof. Li Guanglian）
Direct sampling methods for general nonlinear inverse problems（Prof. Jun Zou）
Unsupervised deep learning of forward and inverse solutions for PDE-based imaging (Nir Sochen)
基于深度学习的分子动力学模拟（王涵 研究员）
Space-Time Discontinuous Galerkin Finite element methods for Partial Differential Equations (详情见第二条推送)
Mathematical Challenges and Opportunities for Autonomous Vehicles Tutorials
一个基于位势理论的直角网格方法
报 告 人： 应文俊 教授（上海交通大学）
报告时间：2020-08-24 10:00:00
报告链接：腾讯会议 ID：277 324 614
https://meeting.tencent.com/s/bDEHCoSoTd5i
摘要：本报告将介绍一个求解椭圆型、抛物型和反应扩散型偏微分方程在不规则区域上边值问题、界面问题的基于位势理论的笛卡尔直角网格方法。在我们过去的研究工作中，该方法主要是结合直角网格上的有限差分法来使用的，给人的印象是该方法属于有限差分方法。其实，该方法也能结合有限元方法用于椭圆型偏微分方程的数值求解。这个报告打算在讲解该算法的基本思想后，重点介绍该算法跟有限元方法的结合：求解不规则区域上问题基于位势理论及直角网格的有限元方法。
正交约束优化的新方法
报告人：刘歆 研究员 （中国科学院数学与系统科学研究院）
报告时间：2020-8-24 10:00
报告链接：腾讯会议ID：439 583 112
https://meeting.tencent.com/s/Q75vDq2hzMQX
摘要：正交约束优化在统计大数据分析、材料计算、机器学习等领域有着重要的应用。本报告给大家介绍求解正交约束优化问题的罚函数算法框架。在该框架下我们可以设计相应的一阶方法、二阶方法，算法具有高可扩展性。当目标函数具有非光滑项时，还可以设计相应的邻近点梯度方法。我们可以建立新方法完整的收敛性，并且通过数值实验展示新方法的高效性和稳定性。
信息来源：
Nonconforming finite element Stokes complexes in three dimensions
报 告 人： 黄学海 教授 （上海财经大学）
报告时间：2020-08-24 15:00:00
报告地点：腾讯会议 ID：829 618 411
https://meeting.tencent.com/s/Gv3yDJIks4WV
摘要：Two nonconforming finite element Stokes complexes ended with the nonconforming P1-P0 element for the Stokes equation in three dimensions are constructed. And commutative diagrams are also shown by combining nonconforming finite element Stokes complexes and interpolation operators. The lower order H(gradcurl)-nonconforming finite element only has 14 degrees of freedom, whose basis functions are explicitly given in terms of the barycentric coordinates. The H(gradcurl)-nonconforming elements are applied to solve the quad-curl problem, and optimal convergence is derived. By the nonconforming finite element Stokes complexes, the mixed finite element methods of the quad-curl problem is decoupled into two mixed methods of the Maxwell equation and the nonconforming P1-P0 element method for the Stokes equation, based on which a fast solver is developed.
信息来源：天元东北中心有限元主题系列报告 | Nonconforming finite element Stokes...
Discontinuous Galerkin Methods for Fourth Order Variational Inequality
报 告 人： 崔金涛 助理教授 (香港理工大学)
报告时间： 2020-08-25 10:00:00
报告地点：腾讯会议ID：286 832 435
https://meeting.tencent.com/s/v0FB6yb8BqE6
摘要：In this work we study a family of discontinuous Galerkin methods for the displacement obstacle problem of Kirchhoff plates on convex polyhedral domains, which are characterized as fourth order elliptic variational inequalities of the first kind. We develop a unified approach for DG methods where the weak complementarity form of the variational inequality is used. We derive the optimal error estimate in energy norm for the quadratic method, where the convergence rate is determined by the geometry of the domain. Under additional regularity assumptions on the solution and contact set, we derive an improved error estimate for the cubic method. Numerical experiments demonstrate the performance of the methods and confirm the theoretical results.
信息来源：天元东北中心有限元主题系列报告 | Discontinuous Galerkin Methods for Fourth...
Finite element diagram chasing
报 告 人： 胡凯博 博士（University of Minnesota）
报告时间：2020-08-26 10:00:00
报告地点： 腾讯会议ID：418 227 590
https://meeting.tencent.com/s/4M7QFoY5DCgN
摘要：There is a close relation between Maxwell’s equations and the de Rham complex. The perspective of continuous and discrete differential forms has inspired key progress in computational electromagnetism. This complex point of view also plays an important role in, e.g., continuum theory of defects, intrinsic elasticity and relativity. In this talk, we briefly review the de Rham complexes and their smoother versions, known as the Stokes complexes with applications in fluid mechanics. Then we generate new complexes from them and study their algebraic and analytic properties. As an example, we construct Sobolev and finite element elasticity complexes by diagram chasing. Special cases of this cohomological approach generalize results in classical elasticity, e.g., the Korn inequality and the Cesàro-Volterra path integral.
信息来源：天元东北中心有限元主题系列报告 | Finite element diagram chasing
Analysis of Gradient Descent on Wide Two-Layer ReLU
Neural Networks
Speaker: Lénaïc Chizat
Time: August 26th 12:00 noon ET
Abstract: In this talk, we propose an analysis of gradient descent on wide two-layer ReLU neural networks that leads to sharp characterizations of the learned predictor. The main idea is to study the dynamics when the width of the hidden layer goes to infinity, which is a Wasserstein gradient flow. While this dynamics evolves on a non-convex landscape, we show that its limit is a global minimizer if initialized properly. We also study the "implicit bias" of this algorithm when the objective is the unregularized logistic loss. We finally discuss what these results tell us about the generalization performance. This is based on joint work with Francis Bach.
Info Source and Registration Link:
https://www.oneworldml.org/
Multiscale Model Reduction for Heterogeneous Problems
Speaker：Prof. Li Guanglian（The University of Hong Kong）
Time : 15:00-16:00, 27 August, 2020 (Thursday)
Venue : Online Talk via Zoom(Meeting ID: 931 9239 2419)
https://polyu.zoom.us/j/93192392419?pwd=TkFoT0J0elpzeUJoUmMwajFNTU5Rdz09
Info Source：
https://www.polyu.edu.hk/ama/files/_web_AMA_Online_Seminar_20200827-Multiscale_Model_Reduction_for_Heterogeneous_Problems.pdf
Abstract：
Heterogeneous problems with high contrast, multiscale and possibly also random coefficients arise frequently in practice, e.g., reservoir simulation and material sciences. However, due to the disparity of scales, their efficient and accurate simulation is notorious challenging. First, I will describe some important applications, and review several state-of- the-art multiscale model reduction algorithms, especially the Generalized Multiscale Finite Element Method (GMsFEM). Then I will describe recent efforts on developing a mathematical theory for GMsFEM, and ongoing works on algorithmic developments and novel applications.
（灰色区域内上下滑动阅读全部内容）
Direct sampling methods for
general nonlinear inverse problems
Speaker: Prof. Jun Zou (The Chinese University of Hong Kong)
Time: 2020-8-27 15:00-16:00
Zoom ID: 69287082106 Password:20200827
(ICCM2020 Online Series Of Conf On Applied Math)
Info Source:
http://www.ims.cuhk.edu.hk/cgi-bin/SeminarAdmin/bin/Web
Unsupervised deep learning of forward and inverse solutions for PDE-based imaging
Speaker: Nir Sochen (University of Tel Aviv)
Time: August 27 2:30 PM EDT
Venue:
https://www.google.com/url?q=https%3A%2F%2Fmsu.zoom.us%2Fj%2F97753106540&sa=D&sntz=1&usg=AFQjCNGX-umTTumz60sfB4llP5b0Jrc3Pg
Info Source:
https://sites.google.com/view/minds-seminar/home
Abstract:
Many imaging modalities are based on inverse problems of physical processes that are given as PDEs. Traditional methods for solving these PDE-based forward and inverse problems are based on discretizations of the domain. Deep learning methods are based on an excessive amount of input-output pairs. Both approaches encounter problems either by numerical instabilities and by being limited to low dimensions or by the lack of sufficient data. We suggest an alternative method of unsupervised deep learning method were the network parametrizes the solution and the loss function minimizes the deviation from the PDE. The input set are points sampled randomly in the domain and the output is the deviation from the PDE, namely zero. One key issue in the loss function is the introduction of the L_infty term that guaranty the uniform convergence of the network to the solution. We demonstrate our method on the Electrical Impedance Tomography (EIT).
（灰色区域内上下滑动阅读全部内容）
基于深度学习的分子动力学模拟
授课导师：王涵 研究员 （北京应用物理与计算数学研究所）
举办日期：14:00-17:30, 2020年08月24日 ~ 08月25日
课程链接：腾讯会议，会议ID：942 6039 8798 会议密码：082425
Space-Time Discontinuous Galerkin Finite element methods for Partial Differential Equations
报告人：J.J.W. van der Vegt (University of Twente)
报告链接：腾讯会议 会议号 339 6612 3504
报告时间：15:00-17:00，2020年8月31日— 9月4日（每天下午）
详情见本次推送第二个推文
信息来源：
https://math.ustc.edu.cn/2020/0821/c18822a444515/page.htm
Mathematical Challenges and Opportunities for Autonomous Vehicles Tutorials
Time: Sep 15th-25th, 2020
Key mathematical themes:
• Robustness of machine learning
• Connecting micro and the macro scales
• Reinventing traffic flow theory in a non-local world
• Multi-agents systems, sparse controls, distributed leaders
• Fleet optimization and routing in a fully connected world
• Mathematics of societal impact of AVs
Info Source and Registration Link:
https://www.ipam.ucla.edu/programs/long-programs/mathematical-challenges-and-opportunities-for-autonomous-vehicles/?tab=application
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