ICCM 2020 Online Series of Conferences on Applied Math
The Shing-Tung Yau Center of Southeast University, Southeast University
The Nanjing Center for Applied Mathematics
The Yau Mathematical Sciences Center, Tsinghua University
The Shing-Tung Yau Center of National Chiao Tung University, National Chiao Tung University
The Institute of Mathematical Sciences, Chinese University of Hong Kong
S. Hu, University of Sciences and Technology of China
W.W. Lin, National Chiao Tung University
J.J. Liu, Southeast University
Z.Q. Shi, Tsinghua University
Z.P. Xin, Chinese Univeristy of Hong Kong
S.T. Yau, Harvard University
Section 1: June 2020
Time: June 4, 8:30-9:30 AM （Beijing time） Lecture No. 20200604-01
Lecture website (zoom):https://us02web.zoom.us/j/89536670985
Stony Brook University, USA
Title: A geometric understanding of deep learning
Abstract: This work introduces an optimal transportation (OT) view of generative adversarial networks (GANs). Natural datasets have intrinsic patterns, which can be summarized as the manifold distribution principle: the distribution of a class of data is close to a low-dimensional manifold. GANs mainly accomplish two tasks: manifold learning and probability distribution transformation. The latter can be carried out using the classical OT method. From the OT perspective, the generator computes the OT map, while the discriminator computes the Wasserstein distance between the generated data distribution and the real data distribution; both can be reduced to a convex geometric optimization process. Furthermore, OT theory discovers the intrinsic collaborative—instead of competitive—relation between the generator and the discriminator, and the fundamental reason for mode collapse. We also propose a novel generative model, which uses an autoencoder (AE) for manifold learning and OT map for probability distribution transformation. This AE–OT model improves the theoretical rigor and transparency, as well as the computational stability and efficiency; in particular, it eliminates the mode collapse. The experimental results validate our hypothesis, and demonstrate the advantages of our proposed model.
Short Bio: Dr. Xianfeng Gu got his bachelor from Tsinghua university, PhD in computer science from Harvard university, supervised by the Fields medalist, Prof. Shing-Tung Yau. Currently, Dr. Gu is a New York State Empire Innovation Professor in the Computer Science Department, Stony Brook university. Dr. Gu's research focuses on applying modern geometry in engineering and medicine fields. Together with Prof. Shing-Tung Yau, Dr. Gu and other collaborators have founded an interdisciplinary field: Computational Conformal Geometry. Dr. Gu has won NSF Career award, Morningside Gold medal in applied Mathematics.
Time: June 11, 8:30-9:30 AM （Beijing time） Lecture No. 20200611-02
Lecture website (zoom):https://us02web.zoom.us/j/84417517383
ID:84417517383 Password: 20200611
Wuhan University, China
Title: On the free boundary hard phase fluid in Minkowski space
Abstract: I will discuss a recent work on the free boundary hard phase fluid model with Minkowski background. The hard phase model is an idealized model for a relativistic fluid where the sound speed approaches the speed of light. This work consists of two results: First, we prove the well-posedness of this model in Sobolev spaces. Second, we give a rigorous justification of the non-relativistic limit for this model as the speed of light approaches infinity. This is joint work with Sohrab Shahshahani and Sijue Wu.
Short Bio: Shuang Miao is a professor at Wuhan University. His main research interests lie in the singularity formation for nonlinear wave equations and long time behavior for free boundary problems in inviscid fluids.
Time: June 18, 8:30-9:30 AM （Beijing time） Lecture No. 20200618-03
Lecture website (zoom):https://us02web.zoom.us/j/86901726807
ID: 86901726807 Password:20200618
Shenzhen Institutes of Advanced Technology,
Chinese Academy of Sciences, China
Title: Fast magnetic resonance imaging: theory, technique and application
Abstract: Magnetic resonance imaging (MRI) has become one of the most important medical revolutions and has played a significant role in modern medical imaging based diagnosis and therapy. However, the intrinsic relatively slow data acquisition has limited its applications largely. Usually, acquiring less data is an important strategy for accelerating MRI, with the proportional relationship between the number of acquired data and scanning time. However, less acquisition usually results in aliasing artifacts in reconstructions. Under this circumstance, image reconstruction problem becomes an ill-conditioned inverse problem. In this talk, we will provide an overview of the theory for fast MRI, some techniques we developed and their applications in accelerating MR imaging.
Short Bio: Dr. Dong Liang is a Full Professor of Biomedical Engineering at Shenzhen Institutes of Advanced Technology (SIAT), Chinese Academy of Sciences (CAS). He is the Director of Research center for Artificial Intelligence in Medicine and Deputy Director of Research center for Biomedical Imaging, SIAT. Dr. Liang’s research has focused on high-speed magnetic resonance imaging. He has published over 100 peer-reviewed papers and holds 3 U.S. patents and 30 China patents. His research has been well funded by state agencies, including NSF of China and The Ministry of Science and Technology of China, province agencies, and CAS. He received First prize in the BME award from the Chinese Society of Biomedical Engineering in 2019. He currently serves on the Editorial Board of Magnetic Resonance in Medicine and is an Associate Editor of the IEEE Transactions on Medical Imaging. He is a senior member of IEEE and is an elected member of IEEE Computational Imaging Technical Committee.
Time: June 25, 15:30-16:30（Beijing time） Lecture No. 20200625-04
Lecture website (zoom):https://us02web.zoom.us/j/84580522524
RICAM Austrian Academy of Sciences, Austria
Title: Mathematical analysis of the photo-acoustic imaging modality using dielectric nanoparticles as contrast agents
Abstract: We will discuss our recent results on the mathematical analysis of the imaging modalities using injected highly contrasting small agents as the acoustic imaging, optical imaging and photo-acoustic imaging. It is known that without using such contrast agents, these imaging modalities are highly instable. However, using them shows improvement of the stability of the reconstruction, at least for benign anomalies, see for instance  and . Our goal is to understand and mathematically quantify these findings by providing reconstruction formulas linking the corresponding measured data, of each modality, to the desired parameters of the model. To show this, we will mainly focus on the photo-acoustic imaging modality using dielectric nanoparticles as contrast agents. The main argument in our analysis here is that these dielectric nanoparticles resonate at certain, computable, frequencies. Exciting the medium with propagating incident waves at frequencies close to such resonances creates local spots, around the injected nanoparticles, and enhance the measured fields. This feature is used to extract the unknown parameters of the model from the remotely measured data. We will also discuss the acoustic or /and the optical imaging modalities using the corresponding contrasting agents (i.e. bubbles and nanoparticles respectively). Parts of the results presented in this talk can be found in the preprints  and .
 S. Qin, C. F. Caskey and K. W. Ferrara. Ultrasound contrast microbubbles in imaging and therapy: physical principles and engineering. Phys Med Biol. (2009).
. W. Li and X. Chen, Gold nanoparticles for photoacoustic imaging, Nanomedicine (Lond.) 10(2), 2015.
. A. Ghandriche and M. Sini. Mathematical Analysis of the Photo-acoustic imaging modality using resonating dielectric nanoparticles: The 2D TM-model. arXiv:2003.03162
. A. Dabrowski, A. Ghandriche and M. Sini, Mathematical analysis of the acoustic imaging modality using bubbles as contrast agents at nearly resonating frequencies. arXiv:2004.07808
This work is supported by the Austrian Science Fund (FWF): P 30756-NBL.
Short Bio: Mourad Sini received his PhD degree from University of Provence, France, in 2002. Then he moved to Hokkaido University, Japan, where he worked during the two years 2003-2005 as a postdoc fellow of the Japanese Society for the Promotion of Sciences (JSPS). He spent the academic year 2005-2006 as a visiting professor at Yonsei University in Seoul, Korea. Since 2006, he joined the Radon Institute, RICAM, of the Austrian Academy of Sciences where he is affiliated as a senior fellow. Mourad Sini is an applied mathematician working in inverse problems, mathematical imaging and material sciences.
Section 2: July 2020
Time: July 2, 8:00-9:00 AM (Beijing time) Lecture No. 20200702-05
Lecture website (zoom): https://us02web.zoom.us/j/82212867797
Hong Kong Baptist University, China
Title: Deep neural networks for convex shape representations
Abstract: Convex Shapes (CS) are common priors for optic disc and cup segmentation in eye fundus images. It is important to design proper techniques to represent convex shapes. So far, it is still a problem to guarantee that the output objects from a Deep Neural Convolution Networks (DCNN) are convex shapes. In this work, we propose a technique which can be easily integrated into the commonly used DCNNs for image segmentation and guarantee that outputs are convex shapes. This method is flexible and it can handle multiple objects and allow some of the objects to be convex. Our method is based on the dual representation of the sigmoid activation function in DCNNs. In the dual space, the convex shape prior can be guaranteed by a simple quadratic constraint on a binary representation of the shapes. Moreover, our method can also integrate spatial regularization and some other shape prior using a soft thresholding dynamics (STD) method. The regularization can make the boundary curves of the segmentation objects to be simultaneously smooth and convex. We design a very stable active set projection algorithm to numerically solve our model. This algorithm can form a new plug-and-play DCNN layer called CS-STD whose outputs must be a nearly binary segmentation of convex objects. In the CS-STD block, the convexity information can be propagated to guide the DCNN in both forward and backward propagation during training and prediction process. As an application example, we apply the convexity prior layer to the retinal fundus images segmentation by taking the popular DeepLabV3+ as a backbone network. Experimental results on several public datasets show that our method is efficient and outperforms the classical DCNN segmentation methods. This talk is based on joint works with Jun Liu and S.Luo.
Short Bio: Prof Tai Xue-Cheng is currently a full professor at the Department of Mathematics, Hong Kong Baptist University. He received his Bachelor degree in Mathematical Science from Zhengzhou University, Licenciate and Ph.D. degrees from the University of Jyvaskyla. His research interests include Numerical PDEs, optimization techniques, inverse problems, and image processing. He has done significant research work in his research areas and published many research papers in top quality international conferences and journals. He served as organizing and program committee members for a number of international conferences and has been often invited speakers for international conferences. He has served as referee and reviewers for many premier conferences and journals. Dr. Tai is members of the editor boards for several international journals.
Time: July 9, 8:00-9:00 AM (Beijing time) Lecture No. 20200709-06
Lecture website (zoom): https://us02web.zoom.us/j/87853763335ID:87853763335 Password:20200709
Columbia University, USA
Title: Inverse problems with the quadratic Wasserstein distance
Abstract: The quadratic Wasserstein distance has recently been proposed as an alternative to the classical $L^2$ distance for measuring data mismatch in computational inverse problems. Extensive computational evidences showing the advantages of using the Wasserstein distance has been reported. The objective of this talk is to provide some simple observations that might help us explain the numerically-observed differences between results based on the quadratic Wasserstein distance and those based on the $L^2$ distance for general linear and nonlinear inverse problems.
Short Bio: Kui Ren received his PhD in applied mathematics from Columbia University. He then spent a year at the University of Chicago as a L. E. Dickson instructor before moving to University of Texas at Austin to become an assistant professor in the Department of Mathematics and the Institute for Computational Engineering and Sciences (the Oden Institute). He returned to Columbia University in 2018 as a professor in applied mathematics. Kui Ren's recent research interests include inverse problems, mathematical imaging, random graphs, fast algorithms, kinetic modeling, and computational learning.
Time: July 16, 8:00-9:00 AM (Beijing time) Lecture No. 20200716-07
Lecture website (zoom): https://us02web.zoom.us/j/83355453878ID:83355453878 Password:20200716
University of Kentucky, USA
Title: Numerical Linear Algebra Methods in Recurrent Neural Networks
Abstract: Deep neural networks have emerged as one of the most powerful machine learning methods. Recurrent neural networks (RNNs) are special architectures designed to efficiently model sequential data by exploiting temporal connections within a sequence and handling variable sequence lengths in a dataset. However, they suffer from so-called vanishing or exploding gradient problems. Recent works address this issue by using a unitary/orthogonal recurrent matrix. In this talk. we will present some numerical linear algebra based methods to improve RNNs. We first introduce a simpler and novel RNN that maintains orthogonal recurrent matrix using a scaled Cayley transform. We then develop a complex version with a unitary recurrent matrix that allows direct training of the scaling matrix in the Cayley transform. We further extend our architecture to use a block recurrent matrix with a spectral radius bounded by one to effectively model both long-term and short-term memory in RNNs. Our methods achieve superior results with fewer trainable parameters than other variants of RNNs in a variety experiments.
Short Bio: Prof. Qiang Ye is currently a full professor at the Department of Mathematics, University of Kentucky. He received his Bachelor degree from University of Science and Technology of China and Ph.D. degree from University of Calgary. His research interests include numerical analysis, numerical linear algebra, and machine learning algorithm.
Time: July 23, 08:00-09:00 AM (Beijing time) Lecture No. 20200723-08
Lecture website (zoom): https://us02web.zoom.us/j/89288847777ID:89288847777 Password:20200723
The University of Tokyo, Japan
Title: Theory of the direct problem and inverse problems for time-fractional partial differential equations
Short Bio: Prof. Masahiro Yamamoto is currently a full professor at the Graduate School of Mathematical Sciences, The University of Tokyo. He received his Bachelor degree, Master degree and Ph.D. degree from The University of Tokyo. His research interests include inverse problems and optimal control problems for partial differential equations, industrial mathematics, and fractional PDEs. He has done significant research works and published many research papers in top quality international journals. Prof. Yamamoto is members of the editor boards for several journals.
Time: July 30, 08:00-09:00 AM (Beijing time) Lecture No. 20200730-09
Lecture website (zoom):https://us02web.zoom.us/j/89953618967ID:89953618967 Password:20200730
Fudan University, China
Title: A Linear Time Delay Model for Outbreak of COVID-19 and Parameter Identification
Abstract: The novel corona virus pneumonia (COVID-19) is a major serious event in the world. Whether we can establish the mathematical models to describe the characteristics of epidemic spread and evaluate the effectiveness of the control measures we have taken is a question of concern. From January 26, 2020, our team began to conduct research on the modeling of new crown epidemic. A kind of linear nonlocal dynamical system model with time delay is proposed to describe the development of covid-19 epidemic. Based on the public data published by the government, the transmission rate and isolation rate, which may not be directly observed in the process of epidemic development are obtained by inversion method On the basis of that, a reasonable prediction of the development of the epidemic is made. These provide the reasonable data support for government decision-making and various needs of the public.
Short Bio: Dr. Cheng Jin, Professor of Fudan University and director of Shanghai Key Laboratory of Contemporary Applied Mathematics. He is also the president of Shanghai Society of Industry and Applied Mathematics, Fellow of Institute of Physics (UK) and the member of the Steering Committee of International Association of Inverse Problems. Prof. Cheng’s main research field is inverse problems and ill posed problems of mathematical physics. He has published more than 100 papers in scientific journals and was invited to give the invited talks in Applied Inverse Problems and other important conferences. Prof. Cheng has cooperated with industry to work on the mathematical modelling and inverse problems in industry.
Section 3: August 2020
Time: August 6, 8:00-9:00 AM (Beijing time) Lecture No. 20200806-10
Lecture website (zoom):https://zoom.com.cn/j/63698277532ID:63698277532 Password:20200806
Brown University, USA
Title: Inverse Lax-Wendroff Procedure for Numerical Boundary Conditions
Abstract: When solving partial differential equations, finite difference methods have the advantage of simplicity, however they are usually only designed on Cartesian meshes.In this talk, we will discuss a class of high order finite difference numerical boundary condition for solving hyperbolic Hamilton-Jacobi equations, hyperbolic conservation laws, and convection-diffusion equations on complex geometry using a Cartesian mesh.The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary may not be aligned with the mesh. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions coupled with traditional extrapolation or weighted essentially non-oscillatory (WENO) extrapolation for outflow boundary conditions.The schemes are shown to be high order and stable, under the standard CFL condition for the inner schemes, regardless of the distance of the first grid point to the physical boundary, that is, the ``cut-cell'' difficulty is overcome by this procedure.Recent progress in nonlinear conservation laws with sonic points, and a conservative version of the method, will be discussed.Numerical examples are provided to illustrate the good performance of our method.
Short Bio: Professor Chi-Wang Shu received his B.S. degree in Mathematics from the University of Science and Technology of China in 1982 and his Ph.D. degree in Mathematics from University of California at Los Angeles in 1986.Since 1987 he has been at the Division of Applied Mathematics of Brown University, as Professor since 1996, as Chair of the Division of Applied Mathematics between 1999 and 2005, and as the Theodore B. Stowell University Professor since 2008. In 1995 he received the first Feng Kang Prize of Scientific Computing from the Chinese Academy of Sciences.In 2007 he received the SIAM/ACM Prize in Computational Science and Engineering for the development of numerical methods that have had a great impact on scientific computing, including TVD temporal discretization, ENO and WENO finite difference schemes, discontinuous Galerkin methods, and spectral methods (from the prize citation).Professor Shu was selected in 2009 as an inaugural Fellow of the Society for Industrial and Applied Mathematics (SIAM), and in 2012 as an inaugural Fellow of the American Mathematical Society (AMS).In 2014 he was an Invited Speaker of the International Congress of Mathematicians (ICM) held in Seoul.Currently Professor Shu is the Chief Editor of the Journal of Scientific Computing, the Chief Editor of Communications on Applied Mathematics and Computation, and a Co-Chief Editor, Editor or Associate Editor of several other research journals including Mathematics of Computation and Journal of Computational Physics.
Time: August 13, 15:00-16:00 PM (Beijing time) Lecture No. 20200813-11
Lecture website (zoom):https://zoom.com.cn/j/67665194189ID:67665194189 Password:20200813
ETH Zürich, Switzerland
Title: Wave Interaction with Subwavelength Resonators
Abstract: In this lecture, the speaker reviews recent results on subwavelength resonances. His main focus is on developing a mathematical and computational framework for their analysis. By characterizing and exploiting subwavelength resonances in a variety of situations, he proposes a mathematical explanation for super-focusing of waves, double-negative metamaterials, Dirac singularities in honeycomb subwavelength structures, and topologically protected defect modes at the subwavelength scale. He also describes a new resonance approach for modelling the cochlea which predicts the existence of a travelling wave in the acoustic pressure in the cochlea fluid and offers a basis for the tonotopic map.
Short Bio: Habib Ammari is a Professor of Applied Mathematics at ETH Zürich. Before moving to ETH, he was a Director of Research at the Department of Mathematics and Applications at Ecole Normale Supérieure in Paris. He received a Bachelor's degree in 1992, a Master's degree in 1993, and a Ph.D. in applied mathematics in 1995, all from the Ecole Polytechnique, France. Following this, he received a Habilitation degree in Mathematics from the University of Pierre & Marie Curie in Paris three years later. Habib Ammari is a world leading expert in wave propagation phenomena in complex media, mathematical modelling in photonics and phononics, and mathematical biomedical imaging. He has published more than two hundred research papers, eight high profile research-oriented books and edited eight books on contemporary issues in applied mathematics. He has advised thirty four PhD students and twenty three postdoctoral researchers. Habib Ammari was awarded a European Research Council Advanced Grant in 2010 in recognition of the excellence of his achievements and his outstanding research program in mathematical imaging. He was named the 2013 winner of the Kuwait Prize in Basic Sciences and received this prestigious prize from His Highness the Emir of Kuwait. In 2015, he was the recipient of the Khwarizmi International Award in Basic Sciences, which is the highest honor accorded by His Excellency the President of the Islamic Republic of Iran for intellectual achievement. Habib Ammari has been a fellow of the Tunisian Academy of Sciences, Letters and Arts since 2015 and of the European Academy of Sciences since 2018. He is also listed as an ISI highly cited researcher.
Time: August 20, 08:00-09:00 AM (Beijing time) Lecture No. 20200820-12
Lecture website (zoom):https://zoom.com.cn/j/63159023950ID:63159023950 Password:20200820
University of Texas at Arlington, USA
Title: Large-Scale Semi-supervised Learning via Graph Structure Learning over High-dense Points
Abstract: We focus on developing a novel scalable graph-based semi-supervised learning (SSL) method for a small number of labeled data and a large amount of unlabeled data. Due to the lack of labeled data and the availability of large-scale unlabeled data, existing SSL methods usually encounter either suboptimal performance because of an improper graph or the high computational complexity of the large-scale optimization problem. In this paper, we propose to address both challenging problems by constructing a proper graph for graph-based SSL methods. Different from existing approaches, we simultaneously learn a small set of vertexes to characterize the high-dense regions of the input data and a graph to depict the relationships among these vertexes. A novel approach is then proposed to construct the graph of the input data from the learned graph of a small number of vertexes with some preferred properties. Without explicitly calculating the constructed graph of inputs, two transductive graph-based SSL approaches are presented with the computational complexity in linear with the number of input data. Extensive experiments on synthetic data and real datasets of varied sizes demonstrate that the proposed method is not only scalable for large-scale data, but also achieve good classification performance, especially for extremely small number of labels.
Short Bio: Dr. Li Wang is currently an assistant professor with Department of Mathematics and Department of Computer Science Engineering, University of Texas at Arlington, Texas, USA. She worked as a research assistant professor with Department of Mathematics, Statistics, and Computer Science at University of Illinois at Chicago, Chicago, USA from 2015 to 2017. She worked as the Postdoctoral Fellow at University of Victoria, BC, Canada in 2015 and Brown University, USA, in 2014. She received her Ph.D. degree in Department of Mathematics at University of California, San Diego, USA, in 2014. Her research interests include data science, large-scale optimization and machine learning.
Time: August 27, 15:00-16:00 PM (Beijing time) Lecture No. 20200827-13
Lecture website (zoom):https://zoom.com.cn/j/69287082106ID:69287082106 Password:20200827
The Chinese University of Hong Kong, China
Title: Direct sampling methods for general nonlinear inverse problems
Abstract: In this talk we will address the up-to-date developments of direct sampling methods (DSMs) for solving general nonlinear inverse problems of PDEs. DSMs were initially proposed for inverse acoustic scattering problems, using far-field or near-field data, then extended for inverse Maxwell scattering problems, and further developed for non-wave type inverse problems, including EIT, DOT, Radon transform problems as well as recovering moving inhomogeneous inclusions. The DSMs are computationally cheap, highly parallel, and robust against noise, particularly applicable to the cases when very limited data is available. General motivations, principles and justifications of DSMs are presented in this talk. Numerical experiments are demonstrated for various inverse problems.
Short Bio: Prof. Jun Zou is Choh-Ming Li Chair Professor of Mathematics of The Chinese University of Hong Kong , and Chairman of Department of Mathematics. Before taking up his current position in Hong Kong, he had worked two years (93-95) in University of California at Los Angeles as a post-doctoral fellow and a CAM Assistant Professor , worked two and a half years (91-93) in Technical University of Munich as a Visiting Assistant Professor and an Alexander von Humboldt Research Fellow (Germany), and worked two years (89-91) in Chinese Academy of Sciences (Beijing) as an Assistant Professor. Jun Zou was elected as a Fellow of Society for Industrial and Applied Mathematics (SIAM) in 2019.
Section 4: September 2020
Time: September 10, 15:00-16:00 PM (Beijing time) Lecture No. 20200910-14
Lecture website (zoom):https://zoom.com.cn/j/64691294982ID:64691294982 Password:20200910
DWD/BMVI, Germany,University of Reading, UK
Title: Nonlinear methods for data assimilation and reconstruction
Abstract: We discuss the development of non-linear filtering methods for very high-dimensional systems. In this talk, non-linear filtering is developed in the framework of the ensemble data assimilation system of the German Weather Service DWD, both for the global forecasting model and convective scale atmospheric forecasting. We will discuss the role of covariance information for reconstruction of states or parameter functions, and the need and importance of using non-Gaussian distributions within the reconstruction algorithms. In a broader framework, we discuss ongoing research and results on the localized adaptive particle filter (LAPF) and a Localized Mixture Coefficient Particle Filter (LMCPF). We discuss how to overcome filter collapse or divergence by adaptive rejuvenation by mapping into ensemble space and by using adaptive spread estimators. Recent progress is shown on the LMCPF particle filters for Lorenz 63 and 96 models, where now with Gaussian mixture particles and proper covariance inflation the particle filter usually shows comparable or better o-b statistics than the LETKF.
Short Bio: Prof. Roland Potthast is currently the director and professor for data assimilation at DWD/BMVI, Germany, and full professor for applied mathematics, University of Reading, UK. Prof. Potthast received his PhD from University of Gottingen, Germany in 1994. Then he worked two years (1995-1996) in University of Delaware as s post-doctoral fellow. He got his Habilitation in Mathematics from University of Gottingen in 1999. His research interests include inverse problems and data assimilation. He has done significant research works and published many research papers in top quality international journals, plus three books. Prof. Potthast is heading the data assimilation division of DWD with 38 researchers, working on data assimilation for the atmosphere and the earth system on both regional and global scale.
Time: September 17, 8:00-9:00 AM (Beijing time) Lecture No. 20200917-15
Lecture website (zoom):https://zoom.com.cn/j/68053997286ID:68053997286 Password:20200917
University of Texas at Arlington, USA
Title: SCF Iteration for Orthogonal Canonical Correlation Analysis
Abstract: Canonical Correlation analysis (CCA) is a standard statistical technique and widely-used feature extraction paradigm for two sets of multidimensional variables. It finds basis vectors for the two sets of variables such that the correlations between the projections of the variables onto these basis vectors are mutually maximized. Mathematically, CCA is an optimization problem that can be turned into a singular value problem. Orthogonal CCA (OCCA) is a term that was coined broadly as a collection of variants of CCA imposing orthogonality among basis vectors. The most simple variant is the plain CCA followed by performing the Gram-Schmidt orthgonalization process on the two sets of basis vectors. A more straightforward way is to impose orthogonality while optimizing the same objective function as CCA. It has been observed that orthonormal bases by the latter are more effective than the most simple way in data science applications. However, directly optimizing the objective function with orthogonality constraints on the basis vectors is nontrivial. In the data science community, today it is solved most by generic optimization methods. In this talk, we will present an alternating numerical scheme whose core is a customizedself-consistent-field (SCF) iteration for a maximization problem on the Stiefel manifold. Along the line, an orthogonal multiset CCA (OMCCA) will be discussed. Extensive experiments are conducted to evaluate the proposed algorithms against existing methods including two real world data science applications: multi-label classification and multi-view feature extraction.This talk is based a recent joint work with Lei-hong Zhang (Soochow University), Li Wang (UT Arlington), and Zhaojun Bai (UC Davis).
Short Bio: Ren-Cang Li is a professor with the Department of Mathematics, University of Texas at Arlington, Texas. He received his BS from Xiamen University in 1985, his MS from the Chinese Academy of Science in 1988, and his PhD from University of California at Berkeley in 1995. He was awarded the 1995 Householder Fellowship in Scientific Computing by Oak Ridge National Laboratory, a Friedman memorial prize in Applied Mathematics from the University of California at Berkeley in 1996, and CAREER award from NSF in 1999. His research interest includes floating-point support for scientific computing, large and sparse linear systems, eigenvalue problems, and model reduction, machine learning, and unconventional schemes for differential equations.
Time: September 24, 8:00-9:00 AM (Beijing time) Lecture No. 20200924-16
Lecture website (zoom):https://zoom.com.cn/j/64609873723ID:64609873723 Password:20200924
Duke University, USA
Title: Data-driven solvers and optimal control for conformational transitions based on high dimensional point clouds with manifold structure
Abstract: Consider Langevin dynamics with collected dataset that distributed on a manifold M in a high dimensional Euclidean space. Through the diffusion map, we learn the reaction coordinates for N which is a manifold isometrically embedded into a low dimensional Euclidean space. This enables us to efficiently approximate the dynamics described by a Fokker-Planck equation on the manifold N. Based on this, we propose an implementable, unconditionally stable, data-driven upwind scheme which automatically incorporates the manifold structure of N and enjoys the weighted l^2 convergence to the Fokker-Planck equation. The proposed upwind scheme leads to a Markov chain with transition probability between the nearest neighbor points, which enables us to directly conduct manifold-related computations such as finding the minimal energy path via optimal control that represents chemical reactions or conformational changes. This is a joint work with Yuan GAO and Nan WU.
Short Bio: Jian-Guo Liu is a Professor of Mathematics and Physics at Duke University. He received a BS and MS from Fudan University in 1982 and 1985 respectively, and a PhD from UCLA in 1990. His research focuses on analysis of numerical methods for fluid dynamics, kinetic theory, and nonlinear partial differential equations, and applied mathematics in general. He is an AMS Fellow 2017.
Section 5: October 2020
Time: October 08, 15:00-16:00 PM (Beijing time) Lecture No. 20201008-17
Lecture website (zoom):https://zoom.com.cn/j/69148274109ID:69148274109 Password:20201008
Sergey Igorevich Kabanikhin
the Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences
Title: Mathematical Problems Driven by Covid-19
Abstract: We discuss and analyse several mathematical problems which occur to be very actual during the epidemy of Covid-19, including inverse problems, optimization, big data analyses, neural networks and mean field games. We will describe SEIR-type models and agent models. The propagation of COVID-19 has significant spatial characteristic. Actions such as travel restrictions, physical distancing and self-quarantine are taken to slow down the spread of the epidemic. It seems to be very important to have a spatial-type SIR model to study the spread of the infectious disease and movement of individuals. Since the epidemic has affected the society and individuals significantly, mean-field games provide a perspective to study and understand the underlying population dynamics. We describe a mean-field game model for controlling the virus spreading within a spatial domain. The goal is to minimize the number of infectious agents and the amount of movement of the population.
Short Bio: Sergey Igorevich Kabanikhin is a corresponding member of Russian Academy of Sciences. He is currently the chief research scientist of the Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, the chief research scientist of Laboratory of Wave Processes of Sobolev Institute of Mathematics SB RAS, and a full professor of Novosibirsk State University and the head of the chair of Mathematical Methods of Geophysics. Prof. Kabanikhin received his B.S. and M.S. from Novosibirsk State University, and Ph.D. from Siberian Branch of Russian Academy of Science in 1978. His research interests include inverse and ill-posed problems, integral and differential equations, inverse problems of mathematical physics, inverse problems in geophysics, etc. Prof. Kabanikhin has done significant research works and published more than 110 papers and 12 books. Now Prof. Kabanikhin is the Editor-in-Chief of <Journal of Inverse and Ill-posed Problems> and <Numerical Analysis and Applications>.
Time: October 15, 8:00-9:00 AM (Beijing time) Lecture No. 20201015-18
Lecture website (zoom):https://zoom.com.cn/j/67071127703ID:67071127703 Password:20201015
Chinese University of Hong Kong
Title: Free Interface Problems for The Incompressible Inviscid Resistive MHD
Abstract: In this talk I will discuss the global well-posedness of free interface problems for the incompressible inviscid resistive MHD. Both plasma-vacuum and plasma-plasma interface problems in a horizontally periodic slab impressed by a uniform transversal magnetic field will be studied. The global well-posedness of both problems with suitable boundary conditions around the equilibrium is established, and the solutions are shown to decay almost exponentially to the equilibrium. The results reveal the strong stabilizing effects of the transversal magnetic field. One of the key observations here is an induced damping structure for the fluid vorticity due to the resistivity and tranversallity of the magnetic field. This is a joint work with Yanjin Wang.
Short Bio: Dr. Zhouping Xin is currently the executive director of The Institute of Mathematical Sciences and William M. W. Mong Professor of Mathematics of The Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong. He received his B.S. and M.S. in mathematics from Northwestern University, and his Ph.D. in Mathematics from University of Michigan. Prof. Xin joined Courant Institute at New York University in 1988, where he became full Professor of Mathematics in 1995, and left for The Chinese University of Hong Kong in 2001. Prof. Xin’s main research interests include partial differential equations, fluid dynamics, mathematical physics, theoretical and numerical analysis of nonlinear conservation laws. etc. He has done significant research works and published many research papers in top quality international journals. Prof. Xin is the Co-Editor-in-Chief of the journal <Methods and Applications of Analysis> since 1998, and editorial board members or associate editors for more than 10 journals. Prof. Xin has got many honours, including the Morningside Gold Medal Award in Mathematics, ICCM, 2004, invited speaker for ICM 2002, Presidential Fellow (USA 1993), Sloan Research Follow (USA, 1991) , etc.
Time: October 22, 8:00-9:00 AM (Beijing time) Lecture No. 20201022-19
Lecture website (zoom):https://zoom.com.cn/j/66839430615ID:66839430615 Password:20201022
New York University, USA
Title: Linear and nonlinear inverse problems in imaging
Abstract: Inverse problems arise routinely in imaging and structure determination using a variety of experimental modalities. After an overview of numerical aspects of medical imaging, we will consider inverse acoustic scattering and protein structure determination from cryo-electron microscopy data (cryo-EM). These are computationally intensive tasks that are typically formulated as non-convex optimization problems. In cryo-EM, the raw data is extremely noisy and existing methods are generally based on some version of maximum likelihood estimation, with a low resolution starting guess. In inverse acoustic scattering, the underlying physical problem is ill-posed and requires both regularization and high-order methods to solve a sequence of forward scattering problems. We will present some algorithms for accelerating image reconstruction in all these settings, illustrate their performance with several examples, and discuss open problems in the field.
Short Bio: Leslie Greengard received his B.A. degree in Mathematics from Wesleyan University in 1979, and his Ph.D. degree in Computer Science and M.D. degree from Yale University in 1987. He has been a member of the faculty at the Courant Institute of Mathematical Sciences, NYU since 1989, and was Director of the Institute from 2006-2011. He is also Professor of Electrical and Computer Engineering at NYU’s Tandon School of Engineering, and presently serves as Director of the Center for Computational Mathematics at the Flatiron Institute, a division of the Simons Foundation. Greengard, together with V. Rokhlin, developed the Fast Multipole Method (FMM) for problems in gravitation, electrostatics and electromagnetics. For their work, in 2001 they received the Steele Prize from the American Mathematical Society. Much of Greengard’s research has been aimed at the development of high-order accurate integral equation based methods for partial differential equations in complex geometry. He is a member of the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences.