報告承辦單位: 數學與統(tǒng)計學院
報告題目: Adaptive multi-fidelity surrogate modeling for Bayesian inference in inverse problems
報告內容: 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.
報告人姓名: 周濤
報告人所在單位: 中科院數學與系統(tǒng)科學研究院
報告人職稱/職務及學術頭銜: 副研究員
報告時間: 2021年4月17日 8:40-9:10
報告方式: 騰訊會議ID:602309725
報告人簡介：周濤，中國科學院數學與系統(tǒng)科學研究院副研究員。曾于瑞士洛聯(lián)邦理工大學從事博士后研究。主要研究方向為不確定性量化、時間并行算法以及隨機最優(yōu)控制等。在SIAM Review、SINUM、Math. Comput.等期刊發(fā)表論文50余篇。2016年獲中國工業(yè)與應用數學學會青年科技獎，2018年獲國家自然科學基金委“優(yōu)秀青年科學基金”資助。2017年起擔任國際不確定性量化期刊International Journal for UQ副總編,并同時擔任國際科學計算權威期刊SIAM J. Sci. Comput.及Commun. Comput. Phys.等多個國際期刊編委。2018起擔任國防科工局科學挑戰(zhàn)專題領域一“復雜系統(tǒng)模型不確定性評定方法”首席科學家
報告承辦單位: 數學與統(tǒng)計學院
報告題目: Reaction coefficient inversion in nonlocal diffusion
報告內容: 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.
報告人姓名: 鄭光輝
報告人所在單位: 湖南大學數學學院
報告人職稱/職務及學術頭銜: 副教授
報告時間: 2021年4月17日 9:10-9:40
報告方式: 騰訊會議ID:602309725
報告人簡介: 鄭光輝，湖南大學數學學院，副教授，碩士生導師。2012年博士畢業(yè)于蘭州大學數學與統(tǒng)計學院，2015年3月--2016年3月訪問巴黎高師數學系。主要從事偏微分方程反問題的理論及算法、貝葉斯統(tǒng)計反演與推斷、等離子共振及超分辨成像等方面的研究。相關研究成果發(fā)表在《Inverse Problems》、《SIAM Journal on Numerical Analysis》、《 J. Differential Equations》、《Advances in Computational Mathematics》等多個SCI雜志上。主持國家自然科學青年基金1項和湖南省面上項目1項。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: Stein variational gradient descent with local approximations
報告內容: 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.
報告人姓名: 閆亮
報告人所在單位: 東南大學數學學院
報告人職稱/職務及學術頭銜: 副教授
報告時間: 2021年4月17日 9:40-10:10
報告方式: 騰訊會議ID:602309725
報告人簡介: 閆亮，副教授、博士生導師。主要從事不確定性量化、貝葉斯反問題理論與算法的研究。2018年入選東南大學“至善青年學者”（A層次）支持計劃，2017年入選江蘇省高校“青藍工程”優(yōu)秀青年骨干教師培養(yǎng)對象。目前主持國家自然科學基金面上項目一項，主持完成國家自然科學基金青年項目和江蘇省自然科學基金青年項目各一項。已經在《SIAM J. Sci. Comput.》、《Inverse Problems》、《J. Comput. Phys.》等國內外刊物上發(fā)表20多篇學術論文.
報告承辦單位: 數學與統(tǒng)計學院
報告題目: Physical-Insight Assisted Machine Learning for Solving Inverse Scattering Problem
報告內容: 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.
報告人姓名: 陳旭東
報告人所在單位: National University of Singapore
報告人職稱/職務及學術頭銜: 教授
報告時間: 2021年4月17日 10:30-11:00
報告方式: 騰訊會議ID:602309725
報告人簡介: 陳旭東教授主要從事電磁逆散射和計算成像技術研究。在浙江大學取得本科和碩士學位，并在麻省理工學院取得博士學位，現(xiàn)任新加坡國立大學教授。陳教授是IEEE Fellow和國際電磁學會Fellow。共發(fā)表SCI期刊論文160余篇，其通過Wiley出版的專著《Computational Methods for Electromagnetic Inverse Scattering》已經被多個國家的課程選為教材或參考書。擔任過IEEE Transactions on Microwave Theory and Techniques 和IEEE Transactions on Geoscience and Remote Sensing等雜志的副主編。先后擔任10多次電磁和反問題相關的大會主席、副主席、技術委員會主席等職務。陳教授是2010年國際無線電科學聯(lián)盟 (URSI) 青年科學家獎和2019年IEEE ICCEM會議最佳論文獎的獲得者。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: The decay estimates of higher order elliptic operators
報告內容: 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.
報告人姓名: 堯小華
報告人所在單位: 華中師范大學數學與統(tǒng)計學學院
報告人職稱/職務及學術頭銜: 教授
報告時間: 2021年4月17日 11:00-11:30
報告方式: 騰訊會議ID:602309725
報告人簡介: 華中師范大學數學與統(tǒng)計學院教授、博士生導師，2010年入選教育部新世紀人才計劃；主要從事調和分析與微分算子的研究；在色散方程、微分算子及函數空間等方向上開展研究工作；完成和發(fā)表論文40余篇，主要學術成果發(fā)表在“Comm. Math. Phys.”、 “Trans. AMS”、 “Inter. Math. Res. Notices”、“J. Functional Analysis”、“Comm. Partial Differential equation”、Siam J. Math. Appl.等國際重要數學期刊上；連續(xù)主持過多項國家自然科學基金面上項目，也曾主持過教育部科學技術研究重點項目及新世紀優(yōu)秀人才計劃等多個科研項目；作為核心成員參與了華中師范大學教育部創(chuàng)新團隊（偏微分方程）建設。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: Inverse random potential scattering for elastic waves
報告內容: 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.
報告人姓名: 王旭
報告人所在單位: 普渡大學
報告人職稱/職務及學術頭銜: 博士后
報告時間: 2021年4月17日 11:30-12:00
報告方式: 騰訊會議ID:602309725
報告人簡介: 王旭博士2013至2018年期間在中國科學院數學與系統(tǒng)科學研究院洪佳林研究員指導下攻讀博士學位，從事隨機偏微分方程保結構算法研究。2018至2021年，赴普渡大學開展博士后研究，合作導師為李培軍教授，主要從事隨機波方程反源問題、反勢函數問題的研究。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: Explicit Estimation of Derivatives from Data and Differential Equations by Gaussian Process Regression
報告內容: 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.
報告人姓名: 王洪橋
報告人所在單位: 中南大學數學與統(tǒng)計學院
報告人職稱/職務及學術頭銜: 講師
報告時間: 2021年4月17日 14:00-14:30
報告方式: 騰訊會議ID:602309725
報告人簡介: 王洪橋博士2018年于上海交通大學數學科學學院獲得博士學位。2018-2019在香港城市大學數據科學學院從事博士后研究工作。2019年入職中南大學數學與統(tǒng)計學院。主要研究興趣包括：貝葉斯反問題，高斯過程，實驗設計，不確定性量化等。曾在Journal of Computational Physics和Neural Computation等期刊發(fā)表學術論文。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: Variational Bayesian inversion for the reaction coefficient in space-time nonlocal diffusion equations
報告內容: 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.
報告人姓名: 宋曉燕
報告人所在單位: 湖南工商大學數學與統(tǒng)計學院
報告人職稱/職務及學術頭銜: 講師
報告時間: 2021年4月17日 14:30-15:00
報告方式: 騰訊會議ID:602309725
報告人簡介: 宋曉燕博士于2020年12月獲湖南大學理學博士學位。2019年9月至2020年8月，赴新西蘭奧克蘭大學聯(lián)合培養(yǎng)。主要從事貝葉斯反問題的研究，目前的研究興趣為非局部方程反問題，發(fā)表SCI論文3篇。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: Inverse Scattering By Random Periodic Structures
報告內容: 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.
報告人姓名: 徐翔
報告人所在單位: 浙江大學數學科學學院
報告人職稱/職務及學術頭銜: 長聘副教授
報告時間: 2021年4月17日 15:20-15:50
報告方式: 騰訊會議ID:602309725
報告人簡介: 徐翔，浙江大學數學科學學院長聘副教授。徐翔的研究主要集中在反問題的理論與計算，共發(fā)表SCI論文30余篇，部分論文被列為ESI高引論文和Inverse Problems亮點收錄。2013年獲得曙光青年學術獎，2014年入選“海外高層次人才計劃青年項目”、浙江省特聘專家，2016年入選浙江省151人才工程。主持國家自然科學基金委面上項目，參與國家自然科學基金委創(chuàng)新群體項目、重大研究計劃重點項目、國際（地區(qū)）交流合作等多項項目。現(xiàn)擔任中國計算數學會第九屆理事，浙江省數學會第十二屆理事和浙江省數理醫(yī)學會首屆理事。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: An inverse boundary value problem for a nonlinear elastic wave equation
報告內容: 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.
報告人姓名: 翟劍
報告人所在單位: 香港科技大學
報告人職稱/職務及學術頭銜: 博士
報告時間: 2021年4月17日 15:50-16:20
報告方式: 騰訊會議ID:602309725
報告人簡介: 翟劍博士2018年獲美國萊斯大學博士學位。2018年至今，先后在美國華盛頓大學、香港科技大學開展博士后研究。翟劍博士的研究興趣為數學物理反問題，主要研究與地震波成像相關的反問題。
報告承辦單位: 數學與統(tǒng)計學院
報告題目: On recovery of the interface between the fluid and piezoelectric material
報告內容: 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.
報告人姓名: 楊家青
報告人所在單位: 西安交通大學數學與統(tǒng)計學院
報告人職稱/職務及學術頭銜: 教授
報告時間: 2021年4月17日 16:20-16:50
報告方式: 騰訊會議ID:602309725
報告人簡介: 楊家青教授2012年獲中國科學院數學與系統(tǒng)科學研究院博士學位，2012-2014年在中國科學院數學與系統(tǒng)科學研究院做博士后，2014-2015年在香港中文大學做Research Fellow，2015年入職于西安交通大學。研究興趣為反問題的數學理論與計算方法。先后主持國家自然科學基金項目2項，在SIAM系列、IP等發(fā)表論文20余篇。
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