报告承办单位: 数学与统计学院

报告题目: Adaptive multi-fidelity surrogate modeling for Bayesian inference in inverse problems

报告内容: The generalized polynomial chaos (gPC) are widely used as surrogate models in Bayesian inference to speed up the Markov chain Monte Carlo simulations. However, the use of gPC-surrogates introduces model errors that may severely distort the estimate of the posterior distribution. In this talk, we present an adaptive procedure to construct an adaptive gPC-surrogate. The key idea is to refine the surrogate over a sequence of samples adaptively so that the surrogate is much more accurate in the posterior region. We then introduce an adaptive surrogate modeling approach based on deep neural networks to handle problems with high dimensional parameters.

报告人姓名: 周涛

报告人所在单位: 中科院数学与系统科学研究院

报告人职称/职务及学术头衔: 副研究员

报告时间: 2021年4月17日 8:40-9:10

报告方式: 腾讯会议ID:602309725

报告人简介：周涛，中国科学院数学与系统科学研究院副研究员。曾于瑞士洛联邦理工大学从事博士后研究。主要研究方向为不确定性量化、时间并行算法以及随机最优控制等。在SIAM Review、SINUM、Math. Comput.等期刊发表论文50余篇。2016年获中国工业与应用数学学会青年科技奖，2018年获国家自然科学基金委“优秀青年科学基金”资助。2017年起担任国际不确定性量化期刊International Journal for UQ副总编,并同时担任国际科学计算权威期刊SIAM J. Sci. Comput.及Commun. Comput. Phys.等多个国际期刊编委。2018起担任国防科工局科学挑战专题领域一“复杂系统模型不确定性评定方法”首席科学家

报告承办单位: 数学与统计学院

报告题目:  Reaction coefficient inversion in nonlocal diffusion

报告内容:  Nonlocal diffusion model are widely applied in many fields, such as continuum mechanics, biology, jump process, graph theory, image analyses, machine learning, and phase transitions. In this talk, we discuss reaction coefficient inversion problem (RCIP) in three kinds of nonlocal diffusion model. The uniqueness theorems are established. Because of the ill-posedness, nonlinearity and singularity of RCIP in nonlocal diffusion. Some hybrid algorithms (such as variational regularization + Laplace approximation, variational Bayesian) are presented to recover the reaction coefficient, and capture the statistics information of the reaction coefficient. Finally, we give some numerical examples to show the effectiveness and reliability of the proposed algorithms.  

报告人姓名:  郑光辉

报告人所在单位: 湖南大学数学学院

报告人职称/职务及学术头衔:  副教授

报告时间:  2021年4月17日 9:10-9:40

报告方式: 腾讯会议ID:602309725

报告人简介:  郑光辉，湖南大学数学学院，副教授，硕士生导师。2012年博士毕业于兰州大学数学与统计学院，2015年3月--2016年3月访问巴黎高师数学系。主要从事偏微分方程反问题的理论及算法、贝叶斯统计反演与推断、等离子共振及超分辨成像等方面的研究。相关研究成果发表在《Inverse Problems》、《SIAM Journal on Numerical Analysis》、《 J. Differential Equations》、《Advances in Computational Mathematics》等多个SCI杂志上。主持国家自然科学青年基金1项和湖南省面上项目1项。

报告承办单位: 数学与统计学院

报告题目: Stein variational gradient descent with local approximations

报告内容:  Bayesian computation plays an important role in modern machine learning and statistics to reason about uncertainty. A key computational challenge in Bayesian inference is to develop efficient techniques to approximate, or draw samples from posterior distributions. Stein variational gradient decent (SVGD) has been shown to be a powerful approximate inference algorithm for this issue. However, the vanilla SVGD requires calculating the gradient of the target density and cannot be applied when the gradient is unavailable or too expensive to evaluate. In this talk we explore one way to address this challenge by the construction of a local surrogate for the target distribution which the gradient can be obtained in a much more computationally feasible manner. To this end we propose a general adaptation procedure to refine the local approximation online without destroying the convergence of the resulting SVGD. This significantly reduces the computational cost of SVGD and leads to a suite of algorithms that are straightforward to implement. The new algorithm is illustrated on a set of challenging Bayesian inverse problems, and numerical experiments demonstrate a clear improvement in performance and applicability of standard SVGD. 

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:  2021年4月17日 9:40-10:10

报告方式: 腾讯会议ID:602309725

报告人简介:  闫亮，副教授、博士生导师。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. 

报告承办单位: 数学与统计学院

报告题目:  Physical-Insight Assisted Machine Learning for Solving Inverse Scattering Problem

报告内容:  This talk addresses inverse scattering problem using physical-insight-assisted machine learning (ML).  Solving wave imaging problems using ML has attracted researchers’ interests in recent years. However, most existing works in this direction directly adopt ML as a black box. ML approaches have not yet had the profound impact on scientific computation problems as they have had for object classification. In fact, researchers have gained, over several decades, much insightful domain knowledge on wave physics and in addition some of these physical laws present well-known mathematical properties (even analytical formulas), which do not need to be learnt by training with a lot of data. This talk demonstrates that it is of paramount importance to address the problem of how profitably combining ML with the available knowledge on underlying wave physics.  

报告人姓名:  陈旭东

报告人所在单位: National University of Singapore

报告人职称/职务及学术头衔:    教授

报告时间:  2021年4月17日 10:30-11:00

报告方式: 腾讯会议ID:602309725

报告人简介:  陈旭东教授主要从事电磁逆散射和计算成像技术研究。在浙江大学取得本科和硕士学位，并在麻省理工学院取得博士学位，现任新加坡国立大学教授。陈教授是IEEE Fellow和国际电磁学会Fellow。共发表SCI期刊论文160余篇，其通过Wiley出版的专著《Computational Methods for Electromagnetic Inverse Scattering》已经被多个国家的课程选为教材或参考书。担任过IEEE Transactions on Microwave Theory and Techniques 和IEEE Transactions on Geoscience and Remote Sensing等杂志的副主编。先后担任10多次电磁和反问题相关的大会主席、副主席、技术委员会主席等职务。陈教授是2010年国际无线电科学联盟 (URSI) 青年科学家奖和2019年IEEE ICCEM会议最佳论文奖的获得者。

报告承办单位: 数学与统计学院

报告题目: The decay estimates of higher order elliptic operators

报告内容:  It was well-known that the L^p decay estimates of Schrodinger operators, is a widely studied topic, which specially plays an important role in the well-posedness of nonlinear dispersive equations and the long time (asymptotic) stability of solitary waves. In this talk, we will address some recent works on the time decay estimates of the higher order elliptic operators (poly-harmonic type) with bounded decay potentials. Our methods depend on the detailed analysis of free resolvent and spectral perturbation techniques, where the classifications of zero resonances and zero asymptotic expansions of resolvent are the basic parts, which are indispensable to establish all kinds of results with general potentials.

报告人姓名:  尧小华

报告人所在单位: 华中师范大学数学与统计学学院

报告人职称/职务及学术头衔:    教授

报告时间:  2021年4月17日 11:00-11:30

报告方式: 腾讯会议ID:602309725

报告人简介:  华中师范大学数学与统计学院教授、博士生导师，2010年入选教育部新世纪人才计划；主要从事调和分析与微分算子的研究；在色散方程、微分算子及函数空间等方向上开展研究工作；完成和发表论文40余篇，主要学术成果发表在“Comm. Math. Phys.”、 “Trans. AMS”、 “Inter. Math. Res. Notices”、“J. Functional Analysis”、“Comm. Partial Differential equation”、Siam J. Math. Appl.等国际重要数学期刊上；连续主持过多项国家自然科学基金面上项目，也曾主持过教育部科学技术研究重点项目及新世纪优秀人才计划等多个科研项目；作为核心成员参与了华中师范大学教育部创新团队（偏微分方程）建设。

报告承办单位: 数学与统计学院

报告题目:  Inverse random potential scattering for elastic waves

报告内容:  In this talk, an inverse scattering problem for the time-harmonic elastic wave equation with a rough potential will be introduced. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian random field with the covariance operator being described by a classical pseudo-differential operator. The goal is to determine the principal symbol of the covariance operator from the scattered wave measured in a bounded domain which has a positive distance from the domain of the potential. For such a rough potential, the well-posedness of the direct scattering problem in the distribution sense is established by studying an equivalent Lippmann– Schwinger integral equation. For the inverse scattering problem, it is shown with probability one that the principal symbol of the covariance operator can be uniquely determined by the amplitude of the scattered waves averaged over the frequency band from a single realization of the random potential. 

报告人姓名:  王旭

报告人所在单位: 普渡大学

报告人职称/职务及学术头衔: 博士后

报告时间:  2021年4月17日 11:30-12:00

报告方式: 腾讯会议ID:602309725

报告人简介:  王旭博士2013至2018年期间在中国科学院数学与系统科学研究院洪佳林研究员指导下攻读博士学位，从事随机偏微分方程保结构算法研究。2018至2021年，赴普渡大学开展博士后研究，合作导师为李培军教授，主要从事随机波方程反源问题、反势函数问题的研究。

报告承办单位: 数学与统计学院

报告题目:  Explicit Estimation of Derivatives from Data and Differential Equations by Gaussian Process Regression

报告内容:  In this work, we employ the Bayesian inference framework to robustly estimate the derivatives of a function from noisy observations of only the function values at given location points, under the assumption of a physical model in the form of differential equation governing the function and its derivatives. To overcome the instability of numerical differentiation of the fitted function solely from the data or the prohibitive costs of solving the differential equation on the whole domain, we use the Gaussian processes to jointly model the solution, the derivatives, and the differential equation, by utilising the fact that differentiation is a linear operator. By regarding the linear differential equation as a linear constraint, we develop the Gaussian process regression with constraint method (GPRC) at Bayesian perspective to improve the prediction accuracy of derivatives. For nonlinear equations, we propose a Picard-iteration approximation of linearization around the Gaussian process obtained only from data to iteratively apply our GPRC. Besides, a product of experts method is applied if the initial or boundary condition is also available. We present several numerical results to illustrate the advantages of our new method and show the new estimation of the derivatives from GPRC improves the parameter identification with less data samples.

报告人姓名:  王洪桥

报告人所在单位: 中南大学数学与统计学院

报告人职称/职务及学术头衔:    讲师

报告时间:  2021年4月17日 14:00-14:30

报告方式: 腾讯会议ID:602309725

报告人简介:  王洪桥博士2018年于上海交通大学数学科学学院获得博士学位。2018-2019在香港城市大学数据科学学院从事博士后研究工作。2019年入职中南大学数学与统计学院。主要研究兴趣包括：贝叶斯反问题，高斯过程，实验设计，不确定性量化等。曾在Journal of Computational Physics和Neural Computation等期刊发表学术论文。

报告承办单位: 数学与统计学院

报告题目: Variational Bayesian inversion for the reaction coefficient in space-time nonlocal diffusion equations

报告内容: In this talk, a variational Bayesian method is used to identify the reaction coefficient for space-time nonlocal diffusion equations using nonlocal averaged flux data. To show the posterior measure to be well-defined, we rigorously prove that the forward operator is continuous with respect to the unknown reaction field. Then gradient-based prior information is proposed to explore oscillation features in the reaction coefficient. Moreover, the Bayesian inverse problem is shown to be well-posed in Hellinger distance. To accurately characterize the posterior density using uncorrelated samples, an efficient variational Bayesian method is used to estimate the reaction coefficient in the nonlocal models. A few numerical results are presented to illustrate the efficacy of the proposed approach and confirm some theoretic discoveries.

报告人姓名: 宋晓燕

报告人所在单位: 湖南工商大学数学与统计学院

报告人职称/职务及学术头衔: 讲师

报告时间: 2021年4月17日 14:30-15:00

报告方式: 腾讯会议ID:602309725

报告人简介: 宋晓燕博士于2020年12月获湖南大学理学博士学位。2019年9月至2020年8月，赴新西兰奥克兰大学联合培养。主要从事贝叶斯反问题的研究，目前的研究兴趣为非局部方程反问题，发表SCI论文3篇。

报告承办单位: 数学与统计学院

报告题目:  Inverse Scattering By Random Periodic Structures

报告内容:  In this talk, we discuss an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo technique for sampling the probability space, a continuation method with respect to the wavenumber, and the KL expansion of the random structure, which reconstructs key statistical properties of the profile for the unknown random periodic structure from boundary measurements of the scattered fields away from the structure. Numerical results are presented to demonstrate the reliability and efficiency of the proposed method.

报告人姓名:  徐翔

报告人所在单位: 浙江大学数学科学学院

报告人职称/职务及学术头衔: 长聘副教授

报告时间:  2021年4月17日 15:20-15:50

报告方式: 腾讯会议ID:602309725

报告人简介:  徐翔，浙江大学数学科学学院长聘副教授。徐翔的研究主要集中在反问题的理论与计算，共发表SCI论文30余篇，部分论文被列为ESI高引论文和Inverse Problems亮点收录。2013年获得曙光青年学术奖，2014年入选“海外高层次人才计划青年项目”、浙江省特聘专家，2016年入选浙江省151人才工程。主持国家自然科学基金委面上项目，参与国家自然科学基金委创新群体项目、重大研究计划重点项目、国际（地区）交流合作等多项项目。现担任中国计算数学会第九届理事，浙江省数学会第十二届理事和浙江省数理医学会首届理事。

报告承办单位: 数学与统计学院

报告题目:  An inverse boundary value problem for a nonlinear elastic wave equation

报告内容: We consider an inverse boundary value problem for a nonlinear model of elastic waves. We show that all the material parameters appearing in the equation can be uniquely determined from boundary measurements under certain geometric conditions. The proof is based on the construction of Gaussian beam solutions.

报告人姓名:  翟剑

报告人所在单位: 香港科技大学

报告人职称/职务及学术头衔:    博士

报告时间:  2021年4月17日 15:50-16:20

报告方式: 腾讯会议ID:602309725

报告人简介:  翟剑博士2018年获美国莱斯大学博士学位。2018年至今，先后在美国华盛顿大学、香港科技大学开展博士后研究。翟剑博士的研究兴趣为数学物理反问题，主要研究与地震波成像相关的反问题。

报告承办单位: 数学与统计学院

报告题目:  On recovery of the interface between the fluid and  piezoelectric material

报告内容:  This talk is concerned with an inverse scattering problem for the interaction between the fluid and piezoelectric material. We show that the piezo-ceramic elastic body can be uniquely determined by the acoustic far-field pattern at a fixed frequency. The factorization method is then justified for the corresponding iinverse interaction problem. Finally, we investigate the associated interior transmission eigenvalue problem. It is shown that there exist at most countable eigenvalues under some assumption on the parameters.

报告人姓名:  杨家青

报告人所在单位: 西安交通大学数学与统计学院

报告人职称/职务及学术头衔:    教授

报告时间:  2021年4月17日 16:20-16:50

报告方式: 腾讯会议ID:602309725 

报告人简介:  杨家青教授2012年获中国科学院数学与系统科学研究院博士学位，2012-2014年在中国科学院数学与系统科学研究院做博士后，2014-2015年在香港中文大学做Research Fellow，2015年入职于西安交通大学。研究兴趣为反问题的数学理论与计算方法。先后主持国家自然科学基金项目2项，在SIAM系列、IP等发表论文20余篇。