GeneralInformation
Time：July 4July 7 2019
Accommodation：Jin Long International Hotel，Tianjin
天津錦龍國際酒店天津市西青區華苑高新區梅苑路16號
Meeting Room：Conference Hall inConference Center, TJNU
天津師范大學會議中心會議廳
Contact:
Wang Tongke (王同科),13752576092, wangtke@sina.com
Chang Huibin (?；圪e),17622799435, huibinchang@163.com
Hao Yonghong (郝永紅),13920255628, haoyh@sxu.edu.cn
Li Jun (李君), 18622138204, nkjunli@foxmail.com
Arrangement during the meeting（July 5, 6）
7:008:00

Breakfast, Jin Long International Hotel

8:00

Taking shuttle to Conference Hall in Conference Center

8:3012:00

Talk

12:2013:30

Lunch, Tianjin Normal University

14:0017:00

Talk

17:3018:00

Taking shuttle back to the hotel

18:0019:30

Dinner, Jin Long International Hotel

Agenda
Morning, July 5, 2019, 8:3012:00
Time

Speaker

Title

Chairman

8:309:00

校領導致辭
王奇教授講話
集體合影

The opening ceremony

Zhao Chun
(趙春)

9:009:40

Wang Qi
(王奇)
University of South Carolina

Thermodynamically consistent models, numerical approximations for multiphase flowing materials

TianChyi J. Yeh
(葉天齊)

9:4010:20

Zhan Hongbin
(詹紅兵)
Texas A&M University

Two Frontiers in StreamAquifer Interaction and Managed Artificial Recharge

10:2010:40

Tea Break

10:4011:20

Zhang Ming
(張銘)
Geological Survey of Japan, AIST

Limitations of Conventional Solutions for Laboratory Permeability Tests Improvements Based on Rigorous Solutions

Wang Qi
(王奇)

11:2012:00

TianChyi J. Yeh (葉天齊)
University of Arizona

Resolution and Ergodicity Issues of River Stage Tomography with Different Excitations

12:2013:30

Lunch, Tianjin Normal University

Afternoon, July 5, 2019, 14:0017:00
Time

Speaker

Title

Chairman

14:0014:40

Wang Hong
(王宏)
University of South Carolina

Variableorder timefractional partial differential equations: modeling and analysis

Zhang Ming
(張銘)

14:4015:20

Liu Hailiang
(劉海亮)
Iowa State University

Selection dynamics for deep neural networks

15:2015:40

Tea Break

15:4016:20

Zhang Zhiyue
(張志躍)
Nanjing Normal University

Immersed finite volume element method for elliptic PDEs with interfaces and its application

Liu Hailiang
(劉海亮)

16:2016:40

王同科
天津師范大學

天津師范大學計算數學團隊簡介及奇異問題符號數值混合算法介紹

16:4017:00

郝永紅
天津師范大學

地下水數值模擬團隊簡介
Effects of climate change and human activities on karst spring discharge in northern China

18:0019:30

Dinner, Jin Long International Hotel Tianjin

Morning, July 6, 2019, 8:3012:10
Time

Speaker

Title

Chairman

8:309:10

Tai XueCheng
(臺雪成)
Hong Kong Baptist University

Graph model for High dimensional data classification

Wang Hong
(王宏)

9:109:50

Ng Michael
(吳國寶)
Hong Kong Baptist University

Robust Tensor Completion and its Applications

9:5010:10

Tea Break

10:1010:50

ZengTieyong
（曾鐵勇）

Image Recovery: from Classical Methods to Deep Learning

Tai XueCheng
(臺雪成)

10:5011:30

LouYifei
（婁易非）
UTDallas

Phase Retrieval for Binary Signals

11:3012:10

ZhengGuoan
（鄭國安）
University of Connecticut

Phase retrieval and Fourier ptychographic imaging

12:2013:30

Lunch, Tianjin Normal University

Afternoon, July 6, 2019, 14:0017:00
Time

Speaker

Title

Chairman

14:0014:40

LiuHaiguang
（劉海廣）
北京計算科學研究中心

Xray Coherence Imaging and Data Analysis
X射線全相干成像與數據分析

Ng Michael
(吳國寶)

14:4015:20

?；圪e、李君、
盧越、趙志學、
廉歡、曹清潔、
朱曉建、劉志方

The team members ofcomputationalmathematics report to the Expert Committee (each person 5 minutes)
計算數學創新團隊成員向專家組匯報工作，專家組指導（每人介紹自己的工作5分鐘）

15:2015:40

Tea Break

15:4017:00

Expert Committee Meeting

Zhao Chun
(趙春)

17:3019:00

Dinner, Jin Long International Hotel Tianjin

Thermodynamically consistent models, numerical approximations for multiphase flowing materials
Qi Wang (王奇)
University of South Carolina
Abstract: I will discuss a thermodynamical paradigm consisting of the generalized Onsager principle which can be used to derive thermodynamic and hydrodynamic models for various materials systems. This formulation provides a clear physical and mathematical structure allows one to develop consistent numerical approximations to arrive at efficient and accurate numerical algorithms. Applications to liquidliquid phase separation in animal cells will be discussed as well.
Two Frontiers in StreamAquifer Interaction and
Managed Artificial Recharge
Hongbin Zhan (詹紅兵), Ph.D., P.G.
Department of Geology and Geophysics, Texas A&M University
Limitations of Conventional Solutions for Laboratory Permeability Tests Improvements Based on Rigorous Solutions
Ming Zhang (張銘)
Geological Survey of Japan, AIST
Abstract: Conventional laboratory permeability tests have been performed based on Darcy’s law, and can only obtain the value of hydraulic conductivity of test specimen under steady or quasisteady state of flow. The techniques cannot be effectively used to test specimens having hydraulic conductivities less than 10^{7} cm/s. This presentation introduces a set of rigorous theoretical solutions to different kinds of laboratory permeability tests under different boundary conditions. By using the rigorous solutions together with early unsteady state records of a permeability test, both the hydraulic conductivity and specific storage, another important parameter related to transient flow in porous media can be obtained through numerical inversion. In addition, errors that may be induced due to compliance of tubing system can also be eliminated. With the improved technologies, the time required for testing low permeability can be greatly reduced while the accuracy of hydraulic parameters being characterized can be increased.
Resolution and Ergodicity Issues of River Stage Tomography
with Different Excitations
TianChyi J. Yeh (葉天齊)
University of Arizona, USA
Abstract: This study investigates spatiotemporal crosscorrelation between the observed head and the hydraulic diffusivity parameters in heterogeneous aquifers under static and migrating periodic excitations with different frequencies and other factors, and a moving single excitation along a river boundary. Results of the crosscorrelation analysis are verified by estimating the parameters in a synthetic heterogeneous aquifer under these excitations. For assuring the statistical significance of the results based on a single realization, Monte Carlo experiments of estimating the parameters with these excitations are conducted. The experiments also explore the relationship between the resolution of the estimated parameters and the distance from the excitation to the observation wells, the frequency, and amplitude of the excitation, and the mean diffusivity of the aquifer. In addition, the relationship between the resolution of the estimates and monitoring network spatial density is investigated. Finally, the usefulness of moving single excitations, effects of frequencies of the periodic excitations under different situations, the density of monitoring network in term of correlation scale, and the ergodicity issue corresponding to the number of observation and size of simulation domain are discussed.
Variableorder timefractional partial differential equations: modeling and analysis
Hong Wang (王宏)
University of South Carolina, USA
Abstract: Fractional partial differential equations (FPDEs) provide more accurate descriptions of anomalously diffusive transport than integerorder PDEs do. However, solutions to timefractional PDEs (tFPDEs) have nonphysical singularity at the initial time t=0, which does not seem physically relevant to anomalously diffusive transport they model. But there is no consensus on how to correct the nonphysical behavior of tFPDEs.
We argue that the order of a physically correct tFPDE model should vary smoothly near the initial time to account for the impact of the locality of the initial condition. Moreover, variableorder tFPDEs themselves also occur in a variety of applications. However, rigorous analysis on variableorder tFPDEs is meager.
We outline the proof of the wellposedness and smoothing properties of tFPDEs. More precisely, we prove that their solutions have the similar regularities to their integerorder analogues if the order has an integer limit at the initial time or have the same singularity near the initial time as their constantorder analogues otherwise.
Selection dynamics for deep neural networks
Hailiang Liu (劉海亮)
Iowa State University
Abstract: Deep learning is machine learning using neural networks with many hidden layers, and it has become a primary tool in a wide variety of practical learning tasks, such as image classification, speech recognition, driverless cars, or game intelligence.
This work introduces the mathematical formulation of deep residual neural networks as a PDE optimal control problem. We study the wellposedness, the large time solution behavior, and the characterization of the steady states for the forward problem. We state and prove optimality conditions for the inverse deep learning problem, using the HamiltonJacobiBellmann equation and the Pontryagin maximum principle. This serves to establish a mathematical foundation for investigating the algorithmic and theoretical connections between optimal control and deep learning.
Immersed finite volume element method for elliptic PDEs with interfaces and its application
張志躍
南京師范大學
Abstract: An immersed finite volume element method is developed to solve 2D elliptic interface problems with a variable coefficient that has a finite jump across an interface. The numerical method consists of an immersed finite element method in the physical space and a sparse grid collocation method based on the Smolyak construction in the probability space is proposed for solving elliptic PDEs with both random input and interfaces. At last, a immersed finite element method based on the variational discretization concept is applied to the optimal control problems with interfaces. Numerical experiments demonstrate the convergence rates of the proposed method and confirm the theoretical results.
Graph model for High dimensional data classification
XueCheng Tai (臺雪成)
Department of Mathematics, Hong Kong Baptist University
Abstract: This talk contains 3 parts.
1. In the 1st part, we present our work to use graph models for high dimensional data classification. Especially, we show how to get fast algorithms using mincut and maxflow algorithms. Moreover, we add a regional force to our model which has demonstrated to give superior accuracy for many applications.
2. In the second part, show that the wellknown modularity maximization algorithm is in fact is volume balancing model. Using total variation on graphs, we show that we can turn the modularity maximization into a minimization problem with volume balancing property with a convex energy functional. This is a new observation and also gives some new ways to solve the modularity minimization problems.
3. In the 3rd part, we will use similar ideas to add spatial regularization effect to popular deep neural networks. We use numerical experiments to show that the regularized DNN always has smooth boundary when used for image segmentation and similar classification problems.
Robust Tensor Completion and its Applications
Michael K.P. Ng (吳國寶)
Department of Mathematics, Hong Kong Baptist University
Abstract: In this talk, we report the results of robust tensor completion using tubal singular value decomposition, and its applications. Several applications and theoretical results are discussed. Numerical examples are also presented for demonstration.
Image Recovery: from Classical Methods to Deep Learning
TieyongZeng (曾鐵勇)
Department of Mathematics,The Chinese University of Hong Kong
Abstract: We will report some works in image recovery, first by the classical variational methods, then by Deep Learning.
Phase Retrieval for Binary Signals
Yifei Lou (婁易非)
Mathematical Sciences, UT Dallas (美國德克薩斯大學達拉斯分校)
Abstract: Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly useful is the analysis revealing that the common gradientbased regularization does not contain more information other than the magnitude measurements for phase retrieval. Focusing on binary signals, we show that a box relaxation to the binary constraint is equivalent to the original problem. We further prove that binary signals can be recovered uniquely up to trivial ambiguities under certain conditions. Finally, we use the characterization theorem to develop an efficient denoising algorithm.
X射線全相干成像與數據分析
劉海廣
北京計算科學研究中心
摘要：X射線自由電子激光（簡稱XFEL，或者X射線激光）是最新涌現出來的新型光源。圍繞這種新型光源的特性，大量的成像與結構探測的應用研究迅速發展起來。我將簡單介紹X射線激光在全球范圍內的發展情況，以及利用其進行全相干成像的一些進展，以及重要的數學、計算問題。
參考文獻：
[1] XFEL data analysis for structural biology. Liu H. & J.C.H. Spence, Quantitative Biology 4: 159. doi:10.1007/s404840160076z (2016);
[2] The principle of Xray free electron lasers and their applications in biological molecular structure determination, Shi Y. & H. Liu. ，Wuli《物理》, 47, 426436 (2018) ;
[3] Evaluation of the performance of classification algorithms for XFEL singleparticle imaging data. Shi. Y et al., IUCrJ 6, 331340 (2019).
Phase retrieval and Fourier ptychographic imaging
Guoan Zheng (鄭國安)
University of Connecticut (美國康涅狄格大學)
Abstract: Fourier ptychography (FP) is a recently developed phase retrieval technique for widefield, highresolution imaging. This technique stitches together many variably illuminated, lowresolution measurements in the Fourier space to expand the frequency passband and recover the highresolution complex sample image. Without involving any mechanical scanning, it facilitates gigapixel imaging in a simple and robust manner. In this talk, I will discuss the principle of the FP approach and its applications in microscopy, quantitative phase imaging, 3D holographic imaging, and macroscopic imaging. I will discuss how to extend the FP approach for other imaging settings. The FP innovation may provide new insights for the development of highresolution, highthroughput imaging platforms using photon, Xray, and electron.
天津師范大學數學科學學院簡介
天津師范大學數學科學學院前身數學系于1958年創建，是學校最早成立的院系之一。學院秉承教育為根，育人為本；數學為基，創新為主的辦學理念，經過六十年的發展，形成了優良的辦學傳統，贏得了較高的社會聲譽。
學院師資隊伍實力雄厚，結構合理，業務扎實?，F有教職工60人，其中專任教師47人，教授及研究員9人，副教授及副研究員16人，博士學位教師32人，具有博士學位教師占專任教師的68％。學院教師學科背景深厚，現有雙聘院士一名，海外高層次講座專家2人，天津市特聘教授青年學者1名，天津市“131”創新型人選第二層次人選1名、第三層次人選7名，享受國務院特殊津貼教師1名，同時還聘請了多名國內外數學專家為兼職教授。
學院擁有數學和科學技術史兩個一級學科碩士點，其中數學學科為天津市重點學科。學院下設數學系和信息與計算科學系，開設數學與應用數學和信息與計算數學兩個本科專業，其中數學與應用數學專業為天津師范大學優勢特色專業，信息與計算科學專業為天津市“十二五”戰略性新興產業相關建設專業。學院建有高性能計算中心，科學史研究所，數學教育與數學奧林匹克研究所三個研究所。
學院將一如既往地堅持以學科建設為龍頭，以教學、科研為中心，以全面提高辦學質量和科研水平為目標，以博學、創新、進取的精神，建設和發展具有教師教育特色的數學科學學院。
計算數學是學院重點發展的二級學科，研究領域涵蓋了數學問題的基礎算法設計和一些應用問題的建模、理論研究和數值模擬等，目前已形成了三個研究團隊，分別為天津市創新團隊“交叉學科中一些應用問題的建模和計算方法研究”，天津師范大學融合創新研究團隊“地下水運動建模及高性能數值算法”，天津師范大學杰出青年創新團隊“高性能數值計算及在材料科學中的應用”。研究方向主要有
1．微分和積分方程的高精度數值解法
2．圖像處理與優化算法
3．地下水運動建模及數值算法研究
4．多相物質的建模和計算
期待各位專家對于計算數學學科的發展給予指導！