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报告承办单位: 数学与统计学院

报告题目:  On the time-domain acoustic waves reflected by a cluster of small sound-soft obstacles

报告内容:  

Consider the time-domain acoustic scattering problem by a cluster of small sound-soft obstacles. Based on the retarded boundary integral equation method, we derive the asymptotic expansion of the scattered field as the size of the holes goes to zero. Under certain geometrical constraints on the size and the minimum distance of the holes, we show that the scattered field is approximated by a linear combination of point-sources where the weights are given by the capacitance of each hole and the causal signals (of these point-sources) can be computed by solving a, retarded in time, linear algebraic system. A rigorous justification of the asymptotic expansion and the unique solvability of the linear algebraic system are shown under natural conditions on the cluster of holes. As an application of the asymptotic expansion, we derive, in the limit case when the holes are densely distributed and occupy a bounded domain, the equivalent effective acoustic medium (an equivalent mass density characterized by the capacitance of the holes) that generates, approximately, the same scattered field as the cluster of holes. Finally, we numerically verify the asymptotic expansions by comparing the asymptotic approximations with the numerical solutions of the scattered fields via the finite element method. 

报告人姓名:  王海兵

报告人所在单位: 东南大学数学学院

报告人职称/职务及学术头衔:  教授

报告时间:  2020年10月31日11:40-12:20

报告方式: 理科楼A-419 

报告人简介:  王海兵，男，教授，博士研究生导师，主要从事数学物理反问题的研究。2012年获得北海道大学和东南大学的理学博士学位，2014年获得江苏省优秀博士学位论文，2016年入选江苏高校“青蓝工程”中青年学术带头人培养对象，2017年作为第二完成人获得教育部自然科学二等奖，2018年获得江苏省工业与应用数学学会第二届“工业与应用数学奖青年奖”。现任中国数学会计算数学分会常务委员。主持三项国家自然科学基金和一项江苏省自然科学基金，在SIAP, SIAM-MMS, IP, JCP等国内外刊物上发表三十余篇学术论文，多次访问东京大学、北海道大学、仁荷大学和奥地利科学院RICAM，受邀在国际学术会议上作报告十余次。

报告承办单位: 数学与统计学院

报告题目:  Inverse source problems with a single far-field data

报告内容:  

We show that a polygonal source term can be uniquely determined by the far-field pattern at a fixed frequency, provided the source function belongs to an admissible set of analytic functions. Moreover, a class of radiating sources embedded in an inhomogeneous medium will be characterized. Finally, source terms whose support contains an arbitrarily weakly singular point will be discussed.    

报告人姓名:  胡广辉

报告人所在单位: 南开大学数学科学学院

报告人职称/职务及学术头衔:    特聘研究员

报告时间:  2020年10月31日14:00－14:40

报告方式: 理科楼 A-419

报告人简介: 胡广辉，现任南开大学数学科学学院科学工程与计算系特聘研究员。2009年获中国科学院数学与系统科学研究院博士学位。2009至2016年在德国莱布尼茨协会维尔斯特拉斯研究所做博士后工作，在2012至2015年独立主持德国研究协会科研项目一项。2016年3月份入选国家海外高层次青年人才计划，2016.09-2020.05就职于北京计算科学研究中心.胡广辉博士主要从事波动方程的数学理论研究和偏微分方程反问题及计算方法的研究，目前已发表论文60余篇。 

报告承办单位: 数学与统计学院

报告题目:  Inversion analysis for magnetic resonance elastography

报告内容:  

A diagnosing modality called MRE (Magnetic Resonance Elastography) whose hardware consists of a MRI and vibration system can measure the displacement vector of a shear wave inside a human tissue. The so called elastogram of MRE is to recover viscoelasticity of human tissue from the {\it MRE measured data}. This is an inverse problem with single interior measurement. The importance of MRE is that it can realize doctors' palpation inside a human body which had been dreamed by doctors for a long time. Although the hardware of MRE is developing very quickly, the elastogram has not yet developed enough and there are so many challenging questions for elastogram. I will introduce the fundamental principal and mathematical model of MRE in the talk. Some inversion sheme to recover the unknown viscoelastic coefficients will also be present. This is a joint work with Prof. Gen Nakamura in Hokkaido University, Japan.

报告人姓名:  江渝

报告人所在单位: 上海财经大学数学学院

报告人职称/职务及学术头衔:    副教授、院长助理。日本北海道大学博士毕业、中国数学会计算数学分会第十届委员

报告时间:  2020年10月31日14:40－15:20

报告方式: 理科楼A-419 

报告人简介:  江渝博士2009年获日本北海道大学理学博士。长期从事医学成像相关反问题方面的研究。特别是对超声波弹性成像法、核磁共振弹性成像法和光 CT 成像软硬件方面的各种问题点和数值反演解法有比较全面的了解。在日本北海道大学攻读博士期间就获日本学术振兴会 2 年关于 MRE 反问题研究的基金资助，并在获得博士毕业后顺利结题。之后参加了日本科学技术振兴机构资助的 3 年重大项目，主要就是对Micro-MRE 系统的开发，承担了反演软件和 MRE 成像序列的开发，相关成果获得日本专利一项（日本专利号：P5773171，国际专利号：W02012/026543.）。通过对实测数据的分析来反演建模，利用有限元的方法实现了数值模拟，同时也验证了设定模型的正确性。在反演技术上，提出了多种数值反演算法。其数值结果和通过和其他基准测试方法得到的数据对比，达到了很高的精度，在日本和国际上得到公认。现作为主要参与者参与国家自然科学基金面上项目1项，曾主持完成青年科学基金项目1项，参与青年项目1项，天元项目1项。目前已在《Inverse Problems》等期刊发表论文29篇，出版专（译）著2部，多次受邀访问东京大学、北海道大学进行学术交流，参加本专业大型国际会议并作报告。

报告承办单位: 数学与统计学院

报告题目:Adaptive Surrogate Modeling Based on Deep Neural Networks for Bayesian Inverse Problems

报告内容:  

In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear concentration of the posterior, traditional surrogate approaches are still not feasible for large scale problems. In this talk, we present an adaptive multi-fidelity surrogate modeling framework based on deep neural networks (DNN). More precisely, we first construct offline a DNN-based surrogate according to the prior distribution, and then, this prior-based surrogate will be adaptively refined online using only a few high-fidelity simulations. In particular, in the refine procedure, we construct a new shallow neural network that view the previous constructed surrogate as an input variable – yielding a composite multi-fidelity neural network approach. This makes the online computational procedure rather efficient. Numerical examples are presented to confirm that the proposed approach can obtain accurate posterior information with a limited number of forward simulations.

报告人姓名:  闫亮

报告人所在单位: 东南大学数学学院

报告人职称/职务及学术头衔:    副教授

报告时间:  2020年10月31日11:00－11:40

报告方式: 理科楼A-419 

报告人简介:  闫亮，副教授、博士生导师，2011年毕业于兰州大学数学与统计学院。主要从事不确定性量化、贝叶斯反问题理论与算法的研究。2018年入选东南大学“至善青年学者”（A层次）支持计划，2017年入选江苏省高校“青蓝工程”优秀青年骨干教师培养对象。目前主持国家自然科学基金面上项目一项，主持完成国家自然科学基金青年项目和江苏省自然科学基金青年项目各一项。已经在《SIAM J. Sci. Comput.》、《Inverse Problems》、《J. Comput. Phys.》等国内外刊物上发表20多篇学术论文.