長沙理工大學(xué)學(xué)術(shù)活動(dòng)預(yù)告
報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: On the time-domain acoustic waves reflected by a cluster of small sound-soft obstacles
報(bào)告內(nèi)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.
報(bào)告人姓名: 王海兵
報(bào)告人所在單位: 東南大學(xué)數(shù)學(xué)學(xué)院
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 教授
報(bào)告時(shí)間: 2020年10月31日11:40-12:20
報(bào)告方式: 理科樓A-419
報(bào)告人簡介: 王海兵，男，教授，博士研究生導(dǎo)師，主要從事數(shù)學(xué)物理反問題的研究。2012年獲得北海道大學(xué)和東南大學(xué)的理學(xué)博士學(xué)位，2014年獲得江蘇省優(yōu)秀博士學(xué)位論文，2016年入選江蘇高校“青藍(lán)工程”中青年學(xué)術(shù)帶頭人培養(yǎng)對(duì)象，2017年作為第二完成人獲得教育部自然科學(xué)二等獎(jiǎng)，2018年獲得江蘇省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)第二屆“工業(yè)與應(yīng)用數(shù)學(xué)獎(jiǎng)青年獎(jiǎng)”?，F(xiàn)任中國數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)常務(wù)委員。主持三項(xiàng)國家自然科學(xué)基金和一項(xiàng)江蘇省自然科學(xué)基金，在SIAP, SIAM-MMS, IP, JCP等國內(nèi)外刊物上發(fā)表三十余篇學(xué)術(shù)論文，多次訪問東京大學(xué)、北海道大學(xué)、仁荷大學(xué)和奧地利科學(xué)院RICAM，受邀在國際學(xué)術(shù)會(huì)議上作報(bào)告十余次。
報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: Inverse source problems with a single far-field data
報(bào)告內(nèi)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.
報(bào)告人姓名: 胡廣輝
報(bào)告人所在單位: 南開大學(xué)數(shù)學(xué)科學(xué)學(xué)院
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 特聘研究員
報(bào)告時(shí)間: 2020年10月31日14:00－14:40
報(bào)告方式: 理科樓 A-419
報(bào)告人簡介: 胡廣輝，現(xiàn)任南開大學(xué)數(shù)學(xué)科學(xué)學(xué)院科學(xué)工程與計(jì)算系特聘研究員。2009年獲中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院博士學(xué)位。2009至2016年在德國萊布尼茨協(xié)會(huì)維爾斯特拉斯研究所做博士后工作，在2012至2015年獨(dú)立主持德國研究協(xié)會(huì)科研項(xiàng)目一項(xiàng)。2016年3月份入選國家海外高層次青年人才計(jì)劃，2016.09-2020.05就職于北京計(jì)算科學(xué)研究中心.胡廣輝博士主要從事波動(dòng)方程的數(shù)學(xué)理論研究和偏微分方程反問題及計(jì)算方法的研究，目前已發(fā)表論文60余篇。
報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: Inversion analysis for magnetic resonance elastography
報(bào)告內(nèi)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.
報(bào)告人姓名: 江渝
報(bào)告人所在單位: 上海財(cái)經(jīng)大學(xué)數(shù)學(xué)學(xué)院
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 副教授、院長助理。日本北海道大學(xué)博士畢業(yè)、中國數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)第十屆委員
報(bào)告時(shí)間: 2020年10月31日14:40－15:20
報(bào)告方式: 理科樓A-419
報(bào)告人簡介: 江渝博士2009年獲日本北海道大學(xué)理學(xué)博士。長期從事醫(yī)學(xué)成像相關(guān)反問題方面的研究。特別是對(duì)超聲波彈性成像法、核磁共振彈性成像法和光 CT 成像軟硬件方面的各種問題點(diǎn)和數(shù)值反演解法有比較全面的了解。在日本北海道大學(xué)攻讀博士期間就獲日本學(xué)術(shù)振興會(huì) 2 年關(guān)于 MRE 反問題研究的基金資助，并在獲得博士畢業(yè)后順利結(jié)題。之后參加了日本科學(xué)技術(shù)振興機(jī)構(gòu)資助的 3 年重大項(xiàng)目，主要就是對(duì)Micro-MRE 系統(tǒng)的開發(fā)，承擔(dān)了反演軟件和 MRE 成像序列的開發(fā)，相關(guān)成果獲得日本專利一項(xiàng)（日本專利號(hào)：P5773171，國際專利號(hào)：W02012/026543.）。通過對(duì)實(shí)測(cè)數(shù)據(jù)的分析來反演建模，利用有限元的方法實(shí)現(xiàn)了數(shù)值模擬，同時(shí)也驗(yàn)證了設(shè)定模型的正確性。在反演技術(shù)上，提出了多種數(shù)值反演算法。其數(shù)值結(jié)果和通過和其他基準(zhǔn)測(cè)試方法得到的數(shù)據(jù)對(duì)比，達(dá)到了很高的精度，在日本和國際上得到公認(rèn)。現(xiàn)作為主要參與者參與國家自然科學(xué)基金面上項(xiàng)目1項(xiàng)，曾主持完成青年科學(xué)基金項(xiàng)目1項(xiàng)，參與青年項(xiàng)目1項(xiàng)，天元項(xiàng)目1項(xiàng)。目前已在《Inverse Problems》等期刊發(fā)表論文29篇，出版專（譯）著2部，多次受邀訪問東京大學(xué)、北海道大學(xué)進(jìn)行學(xué)術(shù)交流，參加本專業(yè)大型國際會(huì)議并作報(bào)告。
報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目:Adaptive Surrogate Modeling Based on Deep Neural Networks for Bayesian Inverse Problems
報(bào)告內(nèi)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.
報(bào)告人姓名: 閆亮
報(bào)告人所在單位: 東南大學(xué)數(shù)學(xué)學(xué)院
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 副教授
報(bào)告時(shí)間: 2020年10月31日11:00－11:40
報(bào)告方式: 理科樓A-419
報(bào)告人簡介: 閆亮，副教授、博士生導(dǎo)師，2011年畢業(yè)于蘭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院。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(xué)“至善青年學(xué)者”（A層次）支持計(jì)劃，2017年入選江蘇省高校“青藍(lán)工程”優(yōu)秀青年骨干教師培養(yǎng)對(duì)象。目前主持國家自然科學(xué)基金面上項(xiàng)目一項(xiàng)，主持完成國家自然科學(xué)基金青年項(xiàng)目和江蘇省自然科學(xué)基金青年項(xiàng)目各一項(xiàng)。已經(jīng)在《SIAM J. Sci. Comput.》、《Inverse Problems》、《J. Comput. Phys.》等國內(nèi)外刊物上發(fā)表20多篇學(xué)術(shù)論文.