**Upcoming Talks:**

**Title: **Adaptive Gradient Methods with Energy for Optimization Problems

**Speaker: **刘海亮 (Hailiang Liu), Iowa State University

**T****ime:** 15:20-16:20 on Tuesday, July 4th, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building

**A****bstract:**

We propose AEGD, a new algorithm for gradient-based optimization of stochastic objective functions, based on adaptive updates of quadratic energy. The method is shown to be unconditionally energy stable, irrespective of the step size. In addition, AEGD enjoys tight convergence rates, yet allows a large step size. The method is straightforward to implement and requires little tuning of hyper-parameters. Experimental results demonstrate that AEGD works well for various optimization problems: it is robust with respect to initial data, capable of making rapid initial progress, shows comparable and most times better generalization performance than SGD with momentum for deep neural networks.

**Bio：**

Hailiang Liu is a Professor of Mathematics and Computer Science at the Iowa State University (ISU). He earned his Bachelor degree from Henan Normal University, Master degree from Tsinghua University, and Ph.D. degree from the Chinese Academy of Sciences, all in Mathematics. His research interests include analysis of partial differential equations, the development of high order numerical algorithms for solving these PDE problems, with diverse applications. He is the author of over 160 peer reviewed papers, and the recipient of many

awards and honors, including the Alexander von Humboldt-Research Fellow, and the inaugural Holl Chair in Applied Mathematics at Iowa State University.

Email: hliu@iastate.edu.cn

**Past Talks: **

**Title:** Multiscale Modeling of Arctic Sea Ice Floes

**Speaker: **Dr. Quanling Deng （Australian National University）

**Time: **Wed., 16:00-17:00, June 14, 2023

**Venue：**Lecture hall, 3rd floor of Jin Chun Yuan West Building (近春园西楼三层报告厅)

**Abstract: **

In this talk, I will start by presenting some quick facts about Arctic and Antarctic sea ice floes followed by a quick overview of the major sea ice continuum and particle models. I will then present our main contribution to its multiscale modelling.

The recent Lagrangian particle model based on the discrete element method (DEM) has shown improved model performance and started to gain more attention from the research groups that are working on Global Climate Models (GCMs). We adopt the DEM model for sea ice dynamical simulation. The major challenges are 1) model coupling in different frames of reference (Lagrangian for sea ice while Eulerian for the ocean and atmosphere dynamics); 2) the heavy computational cost when the number of the floes is large; and 3) inaccurate floe parameterisation when the floe distribution has multiscale features. To overcome these challenges, I will present a superfloe parameterisation to reduce the computational cost and a superparameterisation method to capture the multiscale features. In particular, the superfloe parameterisation facilitates noise inflation in data assimilation that recovers the unobserved ocean field underneath the sea ice. To capture the multiscale features, we adopt the Boltzmann equation for particles and superparameterise the sea ice floes as continuity equations governing the statistical moments. This leads to a particle-continuum coupled multiscale model. I will present several numerical experiments to demonstrate the success of the proposed method. This is joint work with Sam Stechmann (UW-Madison) and Nan Chen (UW-Madison).

**Short Bio:**

Dr. Quanling Deng is a Lecturer at the ANU School of Computing. He was born in Hunan, China and moved to the USA to study mathematics in August 2011. He graduated with a Ph.D. in computational mathematics with a topic on finite element analysis at the University of Wyoming in May 2016. He then joined Curtin University in Australia as a research associate and mainly contributed to the development of isogeometric analysis. He was a short-term visiting scholar at INRIA Paris, AGH University of Science and Technology in Poland, École des Ponts ParisTech (ENPC), USTC, and others. In March 2020, he joined the Department of Mathematics at the University of Wisconsin-Madison as a Van Vleck visiting assistant professor and worked on modelling and prediction of Arctic sea-ice dynamics. Dr. Deng has authored 35+ peer-reviewed publications. Also, he has given 15+ invited presentations and 20+ contributed talks at conferences and seminars and organised five mini-symposia at international conferences.

**Title: **Generalized Lax equivalence theory for the compressible Navier-Stokes system

**Speaker:** 佘邦伟，首都师范大学

**T****ime:** 16:00-17:00 on Thursday, June 8th, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building

**A****bstract:**

In this talk we discuss a generalized Lax equivalence theory for the compressible Navier-Stokes system: convergence = stability + consistency. First, we introduce the concept of consistent approximation representing the (energy/entropy) stability and consistency of suitable numerical solutions. Then, by passing to the limit we obtain a dissipative weak solution with the only information derived from the stability of the consistent approximation. Further, we show that the dissipative weak solution coincide with the strong solution as long as the latter exists. Consequently, any numerical solution belonging to the class of consistent approximation convergences to the strong solution. Finally, we present a numerical example.

**Bio：**

佘邦伟，毕业德国美茵茨大学，曾任捷克科学院数学所准聘、长聘研究员，现为首都师范大学研究员，主要研究方向为流体力学方程组的数值分析和模拟，在Numer. Math.、IMA J Numer. Anal.、SIAM J Numer. Anal.、Math. Comput.、J Comput. Phys.、Multi. Model Simul.等计算数学领域的知名期刊发表多篇学术论文，著有Springer专著一部。

**Title: **神经网络架构理论与应用的结合

**Speaker:** Chen Wuyang

**Time: **Wed., 10:00-11:00 am, June 7, 2023

**Online Tencent: **720-234-077

**Abstract: **

本报告将通过理论和实验分析深度神经网络的架构对其收敛速度、复杂度、泛化性能的影响，并进一步在没有任何训练成本的情况下，对网络架构的设计进行准确和高效的指导。将来，我们将进一步利用深度学习理论对训练神经网络的数据和优化过程进行指导和预测。本报告也将简单介绍Simon Fraser University和加拿大温哥华。

**Bio: **

陈武阳博士 (https://chenwydj.github.io/) 将于 2024 年秋季加入Simon Fraser University计算机系担任助理教授。2023 - 2024年，陈武阳博士将加入UC Berkeley统计系作为博士后。陈武阳本科毕业于中国科学技术大学，并于2023年获得美国德州大学奥斯汀分校电子计算机工程系的博士学位。陈武阳博士的工作发表于各大顶会期刊 (NeurIPS, ICML, ICLR, JMLR, CVPR, ICCV, ECCV), 他的研究成果在2022年被美国国家科学基金会 (National Science Foundation, NSF) 的网站新闻报道: https://www.nsf.gov/news/news_summ.jsp?cntn_id=304639&org=CISE

**Title: **Responsible Machine Learning and Machine Learning for Science

**Speaker: **Chen Tianlong

**Time:** Wed., 9:00-10:00 am, June 7, 2023

**Online Tencent:** 720-234-077

**Abstract: **

本报告分三部分：(一) 如何建立高效和可靠的机器学习系统；(二) 如何设计机器学习算法来解决科学问题，比如：药物开发和量子计算；(三) 对北卡罗来纳大学教堂山分校的简单分享。

**Bio: **

陈天龙博士 (https://tianlong-chen.github.io/) 将于 2024 年秋季加入北卡罗来纳大学教堂山分校计算机系担任助理教授。在这之前 (2023 - 2024)，他会加入麻省理工和哈佛大学担任博士后研究员。陈天龙博士分别于 2023 年和 2017 年获得了德州大学奥斯汀分校电子&计算机工程的博士学位，和中国科学技术大学 (少年班学院) 的应用数学和计算机双学士学位。他的主要研究方向是建立准确、可靠和高效的机器学习系统。他近期的研究方向主要聚焦于：(1) 重要的机器学习问题，包括稀疏神经网络、鲁棒性、可学习的优化算法、图网络和扩散模型；(2) 交叉学科的科学难题，比如生物工程、疫苗药物研发和量子计算。陈天龙博士曾先后获得了 Adobe 博士奖学金、IBM 博士奖学金、UT Austin 研究生院长奖学金和 LoG’22 最佳论文。陈天龙博士曾于各大顶会顶刊发表论文，包括 NeurIPS, ICML, ICLR, JMLR, CVPR, ICCV, ECCV, AAAI, TAPMI 等。

**Title: **From kinetic flocking model of Cucker-Smale type to self-organized hydrodynamic model

**Speaker:** 张腾飞，中国地质大学（武汉）

**T****ime:** 16:00-17:00 on Thursday, June 1st, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building

**A****bstract:**

In this talk, I will discuss our recent results on the hydrodynamic limit problem for a kinetic flocking model of Cucker-Smale type. Using the Cucker-Smale model as an example, we develop systematically a GCI-based expansion method, and micro-macro decomposition on the dual space, to justify the limits to the macroscopic system, a non-Euler type hyperbolic system. We believe our method has widely application in the collective motions and active particle systems. This is a joint work with Prof. Ning JIANG and Prof. Yi-Long LUO.

**Bio：**

张腾飞，中国地质大学（武汉）数学与物理学院副教授。主要研究领域为偏微分方程，包括复杂流体、宏微观耦合模型、分子动理学理论等方面，主要成果发表在ARMA、SIAM-JMA、CVPDE、JDE等国际学术期刊。

**Title:** Resource Constrained Revenue Management with Demand Learning and Large Action Spaces

**Speaker:** Yining Wang, University of Texas at Dallas

**T****ime:** 16:10-17:10 on Friday, May 26, 2023

**Venue: **W11, Ning Zhai

**A****bstract:**

In this talk I will present my recent works on resource constrained revenue management with demand learning and large action spaces. We study a class of well-known RM problems such as dynamic pricing and assortment optimization subject to non-replenishable inventory constraints, where demand or choice model information is unknown a priori and needs to be estimated, and the action spaces (price vectors, assortments) are large. We present a general primal-dual optimization algorithm with upper confidence bounds to achieve optimal asymptotic regret. We also extend this result to nonparametric demand modeling in network revenue management problems via a robust ellipsoid method.

Paper links:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3841273

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3948140

**Bio：**

Yining Wang is an associate professor of operations management at Naveen Jindal School of Management, University of Texas at Dallas. He graduated with a PhD in Machine Learning from Carnegie Mellon University. His research primarily focuses on machine learning and online learning methodology with applications in operations and revenue management. He is also interested in ethics questions arising from the use of machine learning and AI in personalized revenue management systems, such as data privacy protection and decision fairness issues.

**Title: **Self-supervised Deep Learning for Solving Inverse Problems in Imaging

**Speaker：**Ji Hui (纪辉)，National University of Singapore

**Time：**16:00-17:00, May 24, 2023

**Venue:** Online Tencent Meeting ID：568-971-945

**Abstract:**

Deep learning has proved to be a powerful tool in many domains, including inverse imaging problems. However, most existing successful deep learning solutions to these inverse problems are based on supervised learning, which requires many ground-truth images for training a deep neural network (DNN). This prerequisite on training datasets limits their applicability in data-limited domains, such as medicine and science. In this talk, we will introduce a series of works on self-supervised learning for solving inverse imaging problems. Our approach teaches a DNN to predict images from their noisy and partial measurements without seeing any related truth image, which is achieved by neuralization of Bayesian inference with DNN-based over-parametrization of images. Surprisingly, our proposed self-supervised method can compete well against supervised learning methods in many real-world imaging tasks.

**Bio:**

Dr. Ji Hui obtained his Ph.D. in Computer Science from the University of Maryland at College Park in 2006. He currently is an Associate Professor at the Department of Mathematics and serves as the Deputy Director of the Centre for Data Science and Machine Learning at NUS. He serves on the editorial boards of several research journals, including the SIAM Journal on Imaging Sciences. His research interests lie in computational harmonic analysis, computational vision, imaging science, and machine learning.

**Title: **Development of physics-based and data-based molecular simulation methods

**Speaker: **Gao Yiqin, Peking University

**Time: **Tues., 10:00-11:00 am, May 23, 2023

**Venue:** Conference Room 1, Jin Chun Yuan West Bldg. (近春园西楼第一会议室)

**Organizer: **Bao Chenglong

**Abstract:**

Recently, molecular simulations have benefited greatly from the development and subsequent application of deep-learning methods. In this talk, we will discuss how machine-learning methods can be combined with enhanced sampling techniques to speed up molecular dynamic simulations. We will then discuss about our recent effort on learning from Alphafold2 to reproduce and improve protein structure prediction AI models. All these methods are implemented in our home-made molecular simulation package, SPONGE, an MD software rewritten using MindSpore and highly compatible with the deep-learning platform. Through these efforts, we try to generate a multi-functional package for structure prediction, molecule and sequence generation, structure evaluation, and dynamics simulation. We will also discuss the possible applications of these methods in physical, chemical and biological problems.

报告人：高毅勤

1972 年出生，1993 年本科毕业于四川大学化学系，1996 年在中科院化学所获得硕士学位，2001 年获得加州理工学院博士学位。2001 年－ 2004 年在加州理工学院和哈佛大学做博士后研究。2004 年 -2010 年在美国德克萨斯农工大学（Texas A&M University）化学系任助理教授；2010 年起任北京大学化学与分子工程学院教授，2013 年起同时担任北京大学生物医学前沿创新中心研究员。主要从事生物物理化学/ 理论化学方面的基础研究。现任北京大学理学部副主任，JCTC杂志副主编 。

**Title: **Evolving finite element approximations with artificial tangential motion for surface evolution under a prescribed velocity field

**Speaker:** 李步杨，香港理工大学应用数学系

**Time:** 16:00-17:00 on Monday, May 15, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building

**Abstract:**

A novel evolving surface finite element method is proposed to compute the evolution of a closed hypersurface $\Gamma\subset\R^d$, $d=2,3$, moving under a prescribed smooth velocity field $u$. An modified velocity $v$ with an artificial tangential motion is proposed to minimize the instantaneous rate of deformation of the evolving surface, i.e., to minimize the energy functional $\int_{\Gamma}|\nabla_\Gamma v|^2$ under the pointwise constraint $v\cdot n = u\cdot n$, in order to improve the mesh quality of the approximate evolving surface. In order to establish a complete stability and convergence theory for the parametric finite element approximations with artificial tangential motion, we reformulate the problem equivalently in terms of the transport equations of the normal vector $n$ and the second fundamental form $\nabla_\Gamma n$. A novel weak formulation and parametric finite element method are proposed for the reformulated system which couples the modified velocity equation (with artificial tangential motion) with the transport equations of $n$ and $\nabla_\Gamma n$. Optimal-order convergence of the semi-discrete parametric finite element method is proved for finite elements of polynomial degree $k\geq 3$. Numerical examples are presented to illustrate the convergence of the proposed method and the performance of the method in improving the mesh quality of the approximate surface.

**Bio：**

李步扬博士 2012 年于香港城市大学获得博士学位，先后在南京大学、（德国）图宾根大学、香港理工大学从事科研和教学，现为香港理工大学应用数学系副教授，计算数学杂志 SIAM Journal on Numerical Analysis, Mathematics of Computation, IMA Journal of Numerical Analysis等杂志编委。主要研究领域为偏微分方程的数值计算和数值分析，包括曲率流的有限元逼近和分析、非线性色散和波动方程不光滑解的计算方法、不可压 Navier–Stokes 方程的计算和分析、高频 Helmholtz 方程的有限元和 PML 方法、非线性抛物方程、相场方程、分数阶偏微分方程、Ginzburg-Landau 超导体方程、热敏电阻方程的数值分析，以及有限元法、谱方法、convolution quadrature，等等。

**Title:** Quantum speedup of Monte Carlo methods and Markov Chains

**Speaker: **Jin-Peng Liu, the Center for Theoretical Physics, MIT

**Time: **15:00-16:00 on Thursday, May 11, 2023

**Venue: **Online meeting, Tencent 394-2709-5975

**Abstract:**

Sampling from a given distribution is a fundamental computational problem and has broad applications in statistics, machine learning, physics, etc. We systematically investigate the quantum speedup of Monte Carlo methods, quantum mean estimation, and fast-forwarding of reversible Markov chains. We develop quantum algorithms for sampling log-concave distributions (with density e^{-f(x)} for convex f(x)) and for estimating their normalizing constants, achieving polynomial speedups in query complexity over the best-known classical algorithms. This is a joint work with Andrew M. Childs, Tongyang Li, Chunhao Wang, and Ruizhe Zhang.

Reference:

[1] Quantum algorithms for sampling log-concave distributions and estimating normalizing constants. https://arxiv.org/abs/2210.06539

**Bio：**

Jin-Peng Liu is a Simons Quantum Postdoctoral Fellow at Simons Institute, UC Berkeley in 2022-2023 (hosted by Umesh Vazirani and Lin Lin). He will be a Postdoctoral Associate at the Center for Theoretical Physics, MIT in 2023-2024 (hosted by Aram Harrow). He received a Ph.D. in applied mathematics at University of Maryland in 2022 spring (advised by Andrew Childs). He received a B.S. in math at Beihang University and Chinese Academy of Sciences Hua Loo Keng Class (supervised by Ya-xiang Yuan and Cong Sun).

Jin-Peng is serving as an editor of the journal Quantum from 2023. He received the NSF QISE-NET Triplet Award in 2021. His research focuses on Quantum for Science. He attempts to develop, analyze, and optimize provably efficient quantum algorithms for computational challenges in natural and data sciences, including quantum simulations, quantum ODE/PDE solvers, q-sampling, and quantum machine learning.

**Title:** Exploring Ionic Channels and Cell Membranes Dynamics

**Speaker: **Hamidreza Mofidi, BIMSA

**Time: **10:00-11:00 on Wednesday, April 26, 2023

**Venue: **Conference Room 1, Jin Chun Yuan West Building

**Abstract:**

In my talk, I first show our study on the electrodiffusion in Ionic Channels via Poisson-Nernst-Planck Models and examine ion size effects on the flow rate of matter through a cross-section. In the second part, I focus on the effects of NMDA receptors on membrane excitation via Morris-Lecar Model. We apply bifurcation analysis and geometric singular perturbation theory to analyze the system. We also study the synchrony analysis in networks of the coupled system.

**Bio：**

I am a postdoc at the BIMSA Center, supported by the Yau Center at Tsinghua Uni. Before that, I was a VAP at the Uni. of Iowa, USA, working with Math. and Comp. Biology group in the Mathematics Department. My study lies in applied dynamical systems of DEs, math biology, and PDEs. Specifically, I am interested in using techniques such as GSP theory and Bifurcation analysis in nonlinear dynamical systems to model and analyze biological phenomena and study multiple time/spatial scale dynamics.

**Title: **新型冷冻电镜原位结构解析技术及其应用

A new cryo-electron microscopy method to solve the structure of protein complexes in situ and its applications

**Speaker:** 章新政，中国科学院生物物理研究所

**Time:** 16:00-17:00 on Thursday, April 26th, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building.

**Abstract:**

冷冻电镜电子断层以及亚单位平均方法已经在细胞样品上获得金标样核糖体优于4埃的结构解析。尽管核糖体丰度极高，其结构解析仍然需要采集数天数据，且三维分类后的构象平均分辨率在6~7埃。我们发展了新型原位结构解析方法，可以高通量、高分辨率的获得原位结构。我们在冷冻细胞切片数据上获得超级捕光复合物（3.2埃）以及核糖体（2.9埃）的结构解析，其中核糖体获得20个4埃左右的构象。此报告也将讲述该方法的基本原理和适用条件。

Combining the cryo-electron tomography and sub-tomogram averaging, the state of art method is able to directly solve ribosome, a gold standard sample to a resolution beyond 4 Å in cellular environment. Although, the abundancy of ribosome is extremely high in cell, the data collection for a tomographic dataset lasted for couple of days. During to the lack of particles, after 3D classification, an average resolution of 6~7 Å was achieved in different conformations of ribosome. We have developed a new cryo-EM method to solve protein structures in cell with high throughput and high resolution. Using this method, we have determined PBS-PSI-PSII-LHCII supercomplexes and ribosome at 3.2 Å and 2.9 Å, respectively. For ribosome, we calculated 20 conformations with an averaged resolution beyond 4 Å. This talk will be also about the fundamental theory and the application range of the new method.

**报告人简介:**

章新政，男，中国科学院生物物理研究所生物大分子国家重点实验室课题组长、研究员。2008年获得北京大学博士学位，师从俞大鹏院士，从事电子显微学相关研究，2009年赴美开展博士后研究，师从著名结构生物学家Michael Rossmann 院士，开展病毒粒子的冷冻电镜结构生物学研究。2014 年回国在生物物理所建立独立研究组。主要方向为冷冻电镜新技术、新方法的开发，提升冷冻电镜对纯化蛋白质以及细胞内蛋白质的三维结构解析能力。近年来在Nature, Science, Cell, Cell Research, Nature Communications等杂志上共发表了通讯/共通讯论文多篇。

Xinzheng Zhang, Institute of Biophysics, Chinese Academic of Science, Principal Investigator. Xinzheng got his Ph.D degree in Physics on 2008, supervised by Prof. Dapeng Yu. He went to Purdue University, United of States on 2009 as a post-doc to study the 3D structure of viruses with Prof. Michael G Rossmann. Xinzheng returned back to China on 2014 and started to lead an independent research group in Institute of Biophysics. He focused on developing of cryo-EM technologies, including single particle reconstruction method, cryo-EM sample freezing methods and cryo-EM method to solve the protein structure in vivo. In the recent years, Xinzheng published his works on journals such as Nature, Science, Cell, Cell Research and Nature Communications as a corresponding or co-corresponding author.

**Title: **地球物理油气勘探中的优化反演问题

**Speaker:** 李翔，中国石油东方地球物理公司

**T****ime:** 16:00-17:00 on Thursday, April 13th, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building.

**A****bstract:**

地震勘探是在地表激发震源，通过地下介质的传播，被布设在地表的检波器接收。通过处理地表接收的信号，我们可以得到地下结构，从而判断油气储层的位置和储量。在地震油气勘探领域中，存在大量线性和非线性的优化反演问题。本报告主要讨论了地震油气勘探中的三个主要实际问题。

第一个问题是缺失的地震数据重构。在实际数据的采集中，由于各种地表复杂构造的原因，我们经常缺失很多震源激发的位置。因此，可以通过构建线性反演问题来重构缺失数据。

第二个问题是井中地震的多次波成像问题。由于井中地震震源位置不易确定，多次波成像技术可以成功地避免对震源信息的需求。

最后，我们讨论了全波形反演技术。该技术通过求解非线性优化问题反演地震波在地下传播介质的性质。本文讨论的该方法在陆地复杂地区中的应用。

**报告人简介：**

李翔，2007年及2009年于吉林大学地球探测科学域技术学院分别获得应用地球物理学士及硕士学位，2015于加拿大英属哥伦比亚大学地震正演成像实验室（Seismic Laboratory for Imaging and Modeling）获得地球物理博士学位，师从Felix Herrmann教授。毕业之后在PGS公司工作，担任地球物理研究员。2017年加入中国石油东方地球物理公司，担任休斯顿高级技术专家。

**Title: **Proximal linearization methods for Schatten p-quasi-norm minimization

**Speaker:** Chao Zeng, Nankai University

**T****ime:**10:00-11:00 on Monday, April 10th, 2023

**Venue: **Conference Room 1, Floor 1, Jin Chun Yuan West Building

**A****bstract:**

Schatten p-quasi-norm minimization has advantages over nuclear norm minimization in recovering low-rank matrices. However, Schatten p-quasi-norm minimization is much more difficult, especially for generic linear matrix equations. We first extend the lower bound theory of l_p minimization to Schatten p-quasi-norm minimization. Motivated by this property, we propose a proximal linearization method, whose subproblems can be solved efficiently by the (linearized) alternating direction method of multipliers. The convergence analysis of the proposed method involves the nonsmooth analysis of singular value functions. We give a necessary and sufficient condition for a singular value function to be a Kurdyka–Lojasiewicz function. The subdifferentials of related singular value functions are computed. The global convergence of the proposed method is established under some assumptions. Experiments on matrix completion, Sylvester equation and image deblurring show the effectiveness of the algorithm.

**报告人简介：**

曾超，南开大学副教授。本科和博士毕业于中科大，之后在南开大学、香港浸会大学、香港大学等学校做博士后研究。研究方向为数值代数、数值优化、图像处理。在Numer. Math.，SIAM J. Numer. Anal., SIAM J. Matrix Anal. Appl. , SIAM J. Imaging Sci.等期刊发表论文十余篇。

**Title: **A class of efficient Hamiltonian conservative spectral methods for Korteweg-de Vries equations

**Speaker:** Waixiang Cao, Beijing Normal University

**T****ime:** 16:00-17:00 on Thursday, April 6th, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building

**A****bstract:**

In this talk, we present and introduce two efficient Hamiltonian conservative fully discrete numerical schemes for Korteweg-de Vries equations. The new numerical schemes are constructed by using time-stepping spectral Petrov-Galerkin (SPG) or Gauss collocation (SGC) methods for the temporal discretization coupled with the $p$-version/spectral local discontinuous Galerkin (LDG) methods for the space discretization. We prove that the fully discrete SPG-LDG scheme preserves both the momentum and the Hamilton energy exactly for generalized KdV equations. While the fully discrete SGC-LDG formulation preserves the momentum and the Hamilton energy exactly for linearized KdV equations. As for nonlinear KdV equations, the SGC-LDG scheme preserves the momentum exactly and is Hamiltonian conserving up to some spectral accuracy. Furthermore, we show that the semi-discrete $p$-version LDG methods converge exponentially with respect to the polynomial degree. The numerical experiments are provided to demonstrate that the proposed numerical methods preserve the momentum, $L^2$ energy and Hamilton energy and maintain the shape of the solution phase efficiently over long time period.

**报告人简介：**

曹外香，北京师范大学数学科学学院副教授，研究方向为偏微分方程数值解法和数值分析，主要研究有限元方法、有限体积方法，间断有限元方法高效高精度数值计算。主要结果发表在SIAM J. Numer. Anal., Math. Comp., J. Sci. Comput., J. Comput. Phys. 等期刊上。曾获中国博士后基金一等资助和特别资助，广东省自然科学二等奖，主持国家自然科学基金青年基金一项，面上项目两项。

**Title: **An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation

**Speaker:** Yong Liu, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.

**T****ime:** 10:00-11:00 on Tuesday, March 28, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building.

**A****bstract:**

In this talk, we consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. We propose new basis functions for the interface elements to control the growth of the condition number of the stiffness matrix in terms of the finite element approximation order, the number of elements of the mesh, and the interface deviation which quantifies the mesh resolution of the geometry of the interface. Numerical examples are presented to illustrate the competitive performance of the method.

**Bio：**

刘勇，中科院数学与系统科学研究院，计算数学所，优秀青年副研究员。分别于2015年，2020年获中国科学技术大学学士和博士学位。2018年至2020年在美国布朗大学应用数学系联合培养。2020年至2022年在中科院数学与系统科学研究院，华罗庚数学科学中心做博士后。主要研究领域为高精度数值计算方法，包括间断有限元方法的算法设计及其数值分析、磁流体力学方程的数值模拟、非拟合网格有限元方法等。曾获2020年中科院院长奖特别奖，2021年中科院优博。2023年，获国家自然科学基金青年项目，入选中科院青年创新促进会，入选中科院数学与系统科学研究院“陈景润未来之星”人才计划。在SINUM, SISC, JCP等SCI期刊发表论文10余篇。

**Title: **Conservative, Positivity Preserving and Energy Dissipative Numerical Methods for the Poisson-Nernst-Planck Equations

**Speaker:** Zhongming Wang, Florida International University

**T****ime:** 10:00-11:00 on Thursday, March 23, 2023

**Venue: **Tencent Meeting: 394-2709-5975

**A****bstract:**

We design and analyze some numerical methods for solving the Poisson-Nernst-Planck (PNP) equations. The numerical schemes, including finite difference method and discontinuous Galerkin method, respect three desired properties that are possessed by analytical solutions: I) conservation, II) positivity of solution, and III) free-energy dissipation. Advantages of different types of methods are discussed. Numerical experiments are performed to validate the numerical analysis. Modified PNP system that incorporating size and solvation effect is also studied to demonstrate the effectiveness of our schemes in solving realistic problems.

This is joint work with D. Jie, H. Liu, P. Yin, H. Yu and S. Zhou.

**Bio：**

Zhongming Wang, Ph.D., received his bachelor's degree in Computing Mathematics from City University of Hong Kong in 2003 and doctorate degree in Applied Mathematics from Iowa State University in 2008. He was a Postdoctoral Fellow at the University of California, San Diego from 2008 to 2011. He joined the Department of Mathematics and Statistics, Florida International University in 2011 and was promoted to associate professor in 2016.

Dr. Wang's research interests are in computational and applied mathematics. In particular, he has been working on

1. level set methods for high frequency wave propagations, two-phase flows and the Euler-Poisson equations;

2. direct Discontinuous Galerkin method for nonlinear Fokker-Planck equations

3. conservative, positivity preserving and energy dissipative numerical methods for the Poisson-Nernst-Planck equations.

**Title: **Quadrature-based moment methods for kinetic equations: Stability analysis and multidimensional models

**Speaker:** Qian Huang, Tsinghua University

**T****ime:** 16:00-17:00 on Thursday, March 16^{th}, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building

**A****bstract:**

Numerical solution of the kinetics equation is crucial to engineering applications, but remains an extremely challenging task. In recent years, the quadrature-based moment methods (QBMM) are shown as effective numerical methods which preserve positivity of the distributions, have the conservation form and are numerically efficient. However, the mathematical theory of QBMM largely incomplete, and it is difficult to extend the existing approaches to tackle multidimensional problems. In this talk, I will present our recent efforts to clarify the well-posedness of QBMM. The hyperbolicity, realizability and dissipative properties of the moment closure systems are investigated. Then, we develop a discrete-velocity-direction model (DVDM) with minimum entropy principle as a novel and convenient multidimensional extension of the QBMM. In the DVDM, the molecular motion is confined to some prescribed directions but the speed is still a continuous variable in each orientation. Numerical tests with a series of 1-D and 2-D flow problems show the efficiency of the DVDM.

**简介**

黄骞，清华大学能动系助研，于2017年毕业于清华大学获博士学位。主要从事动理学矩方法、清洁低碳燃烧技术等领域研究，承担自然基金等十余项课题，曾获教育部自然科学一等奖（2022）。https://www.researchgate.net/profile/Qian-Huang-6

**Title: **Parametric polynomial preserving recovery on manifolds

**Speaker: **Hailong Guo, The University of Melbourne, Australia.

**Time: **16:00-17:00, Thursday, March 9th, 2023

**Venue: **Lecture Hall, Floor 3, Jin Chun Yuan West Building

**Abstract: **

In this talk, we will introduce gradient recovery schemes for data defined on discretized manifolds. The proposed method, parametric polynomial preserving recovery (PPPR), does not require the tangent spaces of the exact manifolds which have been assumed for some significant gradient recovery methods in the literature. Another advantage of PPPR is that superconvergence is guaranteed without the symmetric condition which is required in the existing techniques. We also will talk about several applications.

**Bio: **

郭海龙，2015年博士毕业于美国韦恩州立大学，于2015年到2018年在美国加州大学圣塔芭芭拉分校任访问助理教授，2018年加入澳大利亚墨尔本大学，先后历任讲师和高级讲师。主要研究兴趣包括有限元超收敛后处理、界面问题的数值方法、机器学习算法等，在Comput. Methods Appl. Mech. Engrg., J. Comput. Phys., Math. Models Methods Appl. Sci., Math. Comp., Numer. Math., SIAM J. Numer. Anal., SIAM J. Sci. Comput. 等主流期刊发表论文20多篇。

**Title: **Efficient natural gradient method for large-scale optimization problems

**Speaker: **Yunan Yang, ETH Zürich, Switzerland.

**Time: **10:00-11:00 am, Wednesday, March 8th, 2023

**Venue:** Conference Room 1, Floor 1, Jin Chun Yuan West Building

**Abstract: **

First-order methods are workhorses for large-scale optimization problems, but they are often agnostic to the structural properties of the problem under consideration and suffer from slow convergence, being trapped in bad local minima, etc. Natural gradient descent is an acceleration technique in optimization that takes advantage of the problem's geometric structure and preconditions the objective function's gradient by a suitable "natural" metric. Despite its success in machine learning, the natural gradient descent method is far from a mainstream computational technique due to the computational complexity of calculating and inverting the preconditioning matrix. This work aims at a unified computational framework and streamlining the computation of a general natural gradient flow via efficient tools from numerical linear algebra. We obtain robust numerical methods for natural gradient flows without directly calculating, storing, or inverting the dense preconditioning matrix. We treat various natural gradients in a unified framework for any loss function.

**Bio: **

Yunan Yang is an applied mathematician working in inverse problems, optimization, and applied optimal transport. Currently, Yunan is an Advanced Fellow at the Institute for Theoretical Studies at ETH Zurich. She will be a Tenure-Track Assistant Professor in the Department of Mathematics at Cornell University starting in July 2023. Yunan Yang earned a Ph.D. degree in mathematics from the University of Texas at Austin in 2018, supervised by Prof. Bjorn Engquist. From September 2018 to August 2021, Yunan was a Courant Instructor at the Courant Institute of Mathematical Sciences, New York University.

**题目：**基于冷冻电镜技术的病毒非对称重构研究

**报告人：**刘红荣 湖南师范大学

**时间：**2023年3月3日 周五上午 10:00-11:00

**地点：**近春园西楼 三楼报告厅

**组织者：**包承龙

**摘要: **

病毒颗粒是一种精准的纳米机器。结构决定功能，病毒结构研究有助于理解其入侵、复制、组装等生命周期，同时也有助于相关的疾病防控、药物设计、疫苗开发等。多数病毒颗粒由一个二十面体对称的衣壳和衣壳内部无对称性的基因组及相关蛋白组成，现有的结构研究大多数仅限于其二十面体对称的衣壳，非对称结构解析是该领域的一大瓶颈。本报告将介绍：1）我们发展的系列冷冻电镜病毒非对称三维重构方法；2）利用新方法解析的系列病毒非对称三维结构，及其揭示病毒生命周期的相关分子机制。本报告将涉及数理科学、计算科学、生命科学等多学科交叉的内容。

**报告人：**刘红荣 湖南师范大学

刘红荣，湘潭大学凝聚态物理博士、美国加州大学洛杉矶分校博士后。现任湖南师范大学教授，交叉科学研究院院长，长江学者特聘教授、国家“万人计划”科技创新领军人才。主要从事冷冻电镜生物大分子三维重构研究，在病毒原子结构解析、病毒对称失配与非对称重构领域做出了系列创新成果，相关工作发表在Science, PNAS等期刊，成果被同行评价为“当代电子显微学的代表作”、“开创性的发现”等。作为项目负责人先后承担了国家自然科学基金重大研究计划项目、重点、面上项目，国家重点研发计划课题等科研项目。

**Title:** Modeling and Solving Compressible Flow with Irregular, Moving, and Colliding Geometries

**Speaker:** Huangrui Mo（莫晃锐）, Assistant Professor, Institute of Mechanics, Chinese Academy of Sciences

**Time: **16:00-17:00, Thursday, February 23rd, 2023

**Venue:** Lecture Hall, Floor 3, Jin Chun Yuan West Bldg.

**Organizer:** Hui Yu

**Abstract:**

Compressible flow involving irregular, moving, and colliding geometries is an essential description of a wide range of natural and industrial flow phenomena. However, the solution of this type of flow systems is confronted with many modeling and numerical challenges. This talk introduces a numerical framework aimed at tackling related challenges. By developing a descriptive field function, an immersed boundary method treating arbitrarily irregular and moving boundaries, and a multibody contact and collision model, as well as integrating high-order temporal-spatial discretization schemes, this numerical framework is able to solve dynamic gas-solid systems ranging from subsonic to hypersonic speeds with high fidelity. This talk also shares a 3D solver established on that framework, along with its application to a set of flow cases and the automated construction of numerical wind tunnels.

**Bio:**

Dr. Huangrui Mo is currently an Assistant Professor in the Institute of Mechanics, CAS. He received a Bachelor, Master, and PhD from Huazhong University of Science and Technology, Institute of Mechanics, CAS, and the University of Waterloo, Canada, respectively. From 2019 to 2021, he did his postdoc at Tsinghua University. He has developed novel models and methods in the field of computational fluid dynamics and physical chemistry, with first-authored works published on journals like Int. J. Numer. Methods Fluids, J. Appl. Phys., Shock Waves, and Phys. Chem. Chem. Phys. He also developed several influential open-source projects on Github. His current research interests include numerical methods for hypersonic flows and first-principle prediction of molecular transport coefficients.

**Title: **High-order bound-preserving numerical methods for chemically reacting flows

**Speaker：**Prof. Yang Yang (Michigan Technological University)

**Time：**10:00-11:00am, Dec.15th (Thur.) 2022

**Venue：**Zoom Meeting ID: 271 534 5558 Passcode: YMSC

https://zoom.us/j/2715345558?pwd=eXRTTExpOVg4ODFYellsNXZVVlZvQT09

**Abstract: **

Chemically reacting flows have many applications in combustion. There are several difficulties in constructing high-order numerical methods: (1) Due to the rapid reaction rate, the system may contain stiff source terms. (2) The transition points near the shocks may trigger the stiff source leading to spurious shock speed. (3) Physically, the density, internal energy are positive, and the mass fractions are between 0 and 1. In this talk, we discuss recent advances of high-order discontinuous Galerkin and finite difference methods for chemically reacting flows. We introduce the bound-preserving techniques for spatial derivatives. Several effective time integrations are developed. Finally, to suppress oscillations, we discuss the oscillation-free algorithm.

**Bio：**

In 2005, Professor Yang Yang joined the Department of Modern Mechanics at University of Science and Technology of China. One year later, he transferred to the Math Department and studied pure math, especially analysis. After receiving his Bachelor's degree of Mathematics in 2009, he started his graduate studies at Brown University and worked with Professor Chi-Wang Shu on Numerical Analysis. His work mainly focused on high order numerical methods for time-dependent problems. It includes three parts: Approximations to delta-functions, Superconvergence of discontinuous Galerkin methods and Numerical cosmology. After obtaining his Ph.D. degree in 2013, he joined the Department of Mathematical Sciences at Michigan Technological University. In 2017, he was promoted to associate professor with tenure. In 2021, he was promoted to professor with tenure.

**Title:** A Type of Robust Bound-preserving MUSCL-Hancock Schemes

**Speaker:** Chen Guoxian (Wuhan University)

**Time：**16:00-17:00, Dec.15th (Thur.) 2022

**Venue：**Tencent Meeting ID: 431642438

Join the meeting：https://meeting.tencent.com/dm/PyxmpJWoWQDb

**Abstract:**

The MUSCL-Hancock upwind scheme, as a variation of the MUSCL scheme, only do the initial data reconstruction once in every cell and solve the Riemann problem once at every cell interface in one time step and is widely used to solve hyperbolic conservation laws. The MMP property of the scheme with CFL number 1/2 for scalar equation is proved in [A. Suresh. SIAM Journal on Scientific Computing, 22(4):1184-1198, 2000.]. For general problems the most often cited sufficient stability conditions are obtained in [C. Berthon. Numerische Mathematik, 104(1):27-46, 2006.]: the CFL number is 1/4 of the first order scheme; the initial data reconstruction admits only the basic most dissipative minmod limiter. These contradict the faster speed and higher resolution claims of the scheme. In practice people often use robust but risk settings such as the UNO/super-bee etc. slope limiters and the CFL number up to 1/2.

In this talk we introduce new stability conditions in the sense of bound-preserving for the scheme: a) The CFL number is $(\sqrt{3}-1)/2$ which admits almost 0.73 times the time step of MUSCL scheme and then gives faster simulation; b) The preliminary reconstruction is corrected by a bound-preserving slope limiter. The slope corrector gives the bound-preserving approximation if global bound is considered, and provides a non-oscillation simulation if local bound is considered. The corrector is omitted if the well-konwn generalized minmod limiter is used for the preliminary reconstruction on scalar problem. Numerical examples verify the sharpness of these two settings and demonstrate the robustness of the schemes for advection problem with spacial variable and general nonlinear problem, we also apply the method on general nonlinear system.

**Bio:**

陈国贤，武汉大学数学与统计学院副教授，博士生导师。主要研究自适应移动网格方法、计算水动力学和双曲守恒律的计算方法等。

**Title:** Efficient spectral methods and error analysis for nonlinear Hamiltonian systems

**Speaker：**Prof. Zhang Zhimin (张智民，Wayne State University )

**Time：**Thur.,9:00-10:00am, Dec.8,2022

**Venue：**Tencent Meeting ID: 431642438

Join the meeting：https://meeting.tencent.com/dm/PyxmpJWoWQDb

**Abstract: **

We investigate efficient numerical methods for nonlinear Hamiltonian systems. Three polynomial spectral methods (including spectral Galerkin, Petrov-Galerkin, and collocation methods). Our main results include the energy and symplectic structure preserving properties and error estimates. We prove that the spectral Petrov-Galerkin method preserves the energy exactly and both the spectral Gauss collocation and spectral Galerkin methods are energy conserving up to spectral accuracy. While it is well known that collocation at Gauss points preserves symplectic structure, we prove that the Petrov-Galerkin method preserves the symplectic structure up to a Gauss quadrature error and the spectral Galerkin method preserves the symplectic structure to spectral accuracy. Furthermore, we prove that all three methods converge exponentially (with respect to the polynomial degree) under sufficient regularity assumption. All these aforementioned properties make our methods possible to simulate the long time behavior of the Hamiltonian system. Numerical experiments indicate that our algorithms are efficient.

**Bio：**

张智民：中国科技大学学士（1982）硕士（1985，导师石钟慈），马里兰大学（University of Maryland at College Park）博士 (1991，导师Ivo Babuska)； 德州理工大学（Texas Tech University ）客座助理教授（Visiting Assistant Professor，1991）助理教授（ Assistant Professor Tenure-track，1993）副教授（Associate Professor with tenure，1997），韦恩州立大学（Wayne State University ）副教授 （1999）教授（full Professor，2002） Charles H. Gershenson Distinguished Faculty Fellow (2014)； 教育部长江学者讲座教授（中山大学，2010-2012）；担任或曾任“Mathematics of Computation“、“Journal of Scientific Computing”等9个国际计算数学杂志编委，研究方向是偏微分方程数值解，包括有限元，有限体积，谱方法等，发表学术论文200余篇；提出的多项式保持重构Polynomial Preserving Recovery PPR）格式于2008年被国际上广为流行的大型商业软件 COMSOL Multiphysics 采用，并使用至今。

**Title:** Moving Boundary Problems and Scientific Computing

**Speaker: **Dr. Shuang Liu（刘爽，University of California at San Diego）

**Time：**Thur.,10:00-11:00am, Dec.8,2022

**Venue：**Zoom Meeting ID: 271 534 5558 Passcode: YMSC

https://zoom.us/j/2715345558?pwd=eXRTTExpOVg4ODFYellsNXZVVlZvQT09

**Abstract: **

The moving boundary (or often called ”the free boundary”) problems arise in various mathematical models, encompassing applications that range from financial to physical and biological phenomena. However, there are challenges in the numerical study of moving boundary problems. Examples include difficulties in solving PDEs in irregular domains, handling moving boundaries efficiently and accurately, as well as computing efficiency difficulties. In this talk, I will describe our efforts in three types of moving boundary problems, with specific applications to ecology (population dynamics), plasma physics (ITER tokamak machine design), and cell biology (cell movement). In addition, some techniques of scientific computing will be discussed.

**Bio: **

Shuang Liu received a PhD in Applied and Computational Mathematics from the University of South Carolina in 2019. Previously, she was a Postdoc Research Associate in applied mathematics and plasma physics group at TDS center, Los Alamos National Laboratory, (2020-2021). Currently she is a Stefan E. Warschawski Assistant Professor in the Department of Mathematics at the University of California, San Diego. Her research interests lie in numerical partial differential equations and scientific computing, with applications in mathematical and computational biology, ecology, plasma physics, and biomolecular simulations. Especially, her research focuses on moving boundary (interface) problems using the level set method and other fast and scalable computational methods.

**Title: **Towards fault-tolerant quantum computation: near term and the future

**Speaker: **Zheng Yicong (TQL)

**Time：**Thur.,14:00-15:00, Dec.1st,2022

**Venue：**Tencent Meeting ID: 431642438

Join the meeting：https://meeting.tencent.com/dm/PyxmpJWoWQDb

**Abstract: **

Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms on large-scale quantum computers. However, realizing practical quantum error correction (QEC) and fault-tolerant quantum computation (FTQC) requires resolving many challenges, both theoretical and practical. These challenges include tremendous resource overhead, low accuracy threshold, low connectivity between qubits, state leakage, et.al. In this talk, I will give a brief review of the development of the theory of fault-tolerant quantum computation and its recent developments on both theoretical and experimental sides.

**Bio：**

郑一聪，现任腾讯量子实验室(TQL) 量子计算专家研究员。在加入腾讯之前，他自2015年起在新加坡国立大学（NUS）量子技术中心（CQT）和耶鲁-国立大学学院(Yale-NUS College)做博士后工作。他分别于2013年和2015年在南加州大学 (USC) 获得了计算机科学硕士学位和电子工程博士学位。他的研究兴趣集中在容错量子计算架构、量子误差修正/缓解、量子电路编译，量子模拟，开放量子系统，量子计算的物理平台（如超导量子比特、量子点和中性原子）等相关理论和实验研究。

**Title：**Trace optimization and eigenvector-dependent nonlinear eigenvalue problems in data science

**Speaker：**Leihong Zhang（张雷洪), Soochow University

**Time：**Thur.,14:00-15:00,Nov.24th,2022

**Venue：**Tencent Meeting ID: 431642438

Join the meeting：https://meeting.tencent.com/dm/PyxmpJWoWQDb

**Abstract：**

Some recent applications of multivariate statistical analysis in data science need to optimize certain trace-related objective functions over the orthogonal constraints. In this talk, we shall first present some recent applications in data science and show that solving the optimization problems can be converted to eigenvector-dependent eigenvalue problems (NEPv) for which the self-consistent filed (SCF) iteration can be effectively applied. We then discuss recent developments of the general SCF on the local convergence rate and the level-shifted technique.

**Bio:**

张雷洪于2008年博士毕业于香港浸会大学，现为苏州大学数学科学学院教授。从事最优化理论与计算、数值线性代数、模式识别、数据挖掘等领域的研究。主持多项国家自科项目，参与国家自然科学基金重大研究计划。在《Math Program》、《Math. Comput.》、《Numer. Math.》、《IEEE TPAMI》以及SIAM期刊系列等发表六十多篇学术论文。曾获第四届“应用数值代数奖’’、2018和2019年两届世界华人数学家联盟最佳论文奖（若琳奖），及2019年上海市自然科学三等奖（第一完成人） 等。

**Title：**Recent advance on Nesterov acceleration

**Speaker**：Bin Shi, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

**Time：**(updated)Thur.,16:00-17:30, Nov. 24th,2022

**Venue**：(updated) Online Tencent ID：410-207-317

Join the meeting: https://meeting.tencent.com/dm/RpLiN266oVS7

**Abstract: **

Nesterov's accelerated gradient descent (NAG) is one of the milestones in the history of first-order algorithms. Until recently, it was not successfully uncovered by the high-resolution differential equation framework in [Shi et al., 2021] that the mechanism behind the acceleration phenomenon is due to the gradient correction term. Along this way, I present some recent advances about the high-resolution differential equation framework with focusing on the implicit-velocity scheme and proximal scheme.

**Bio: **

史斌，本科毕业于中国海洋大学数学系，之后分别在复旦大学和美国麻省大学达特茅斯分校获得基础数学和理论物理的硕士学位，于2018年在佛罗里达国际大学获得计算机科学的博士学位。2019年至2021年在加州大学伯克利分校跟随机器学习的先驱Michael I. Jordan从事博士后研究工作，于2021年6月入职中国科学院数学与系统科学研究院，任副研究员。

**Title: **Deep image prior for inverse problems: acceleration and probabilistic treatment

**Speaker：**Bangti Jin (金邦梯), The Chinese University of Hong Kong

**Time：**Mon.,14:00-15:00,Nov.21th,2022

**Venue：**Tencent Meeting ID: 431642438

Join the meeting：https://meeting.tencent.com/dm/PyxmpJWoWQDb

**Abstract:**

Since its first proposal in 2018, deep image prior has emerged as a very powerful unsupervised deep learning technique for solving inverse problems. The approach has demonstrated very encouraging empirical success in image denoising, deblurring, super-resolution etc. However, there are also several known drawbacks of the approach, notably high computational expense. In this talk, we describe some of our efforts: we propose to accelerate the training process by pretraining on synthetic dataset and further we propose a novel probabilistic treatment of deep image prior to facilitate uncertainty quantification.

**Bio:**

Bangti Jin received a PhD in Mathematics from the Chinese University of Hong Kong, Hong Kong in 2008. Previously, he was Lecturer and Reader, and Professor at Department of Computer Science, University College London (2014-2022), an assistant professor of Mathematics at the University of California, Riverside (2013–2014), a visiting assistant professor at Texas A&M University (2010–2013), an Alexandre von Humboldt Postdoctoral Researcher at University of Bremen (2009–2010). Currently he is Professor of Mathematics at the Chinese University of Hong Kong. His research interests include inverse problems, numerical analysis and machine learning. Currently he serves on the editorial board of five journals, including Inverse Problems and Journal of Computational Mathematics.

Time：10:00-11:00, Nov. 17th (Thur.) 2022

Venue：Zoom Meeting ID: 276 366 7254 Passcode: YMSC

Zoom Link：https://zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

Title：Deep learning of multi-scale PDEs based on data generated from particle methods

Speaker：Zhongjian Wang, The University of Chicago

Abstract: Solving multiscale PDEs is difficult in high dimensional and/or convection dominant cases. The Lagrangian computation, interacting particle method, is shown to outperform solving PDEs directly (Eulerian). Examples include computing effective diffusivities, KPP front speed, and asymptotic transport properties in topological insulators. However the particle simulation takes long before convergence and does not have a continuous model. In this regard, we introduce the DeepParticle methods, which learn the pushforward map from arbitrary distribution to IPM-generated distribution by minimizing the Wasserstein distance. In particular, we formulate an iterative scheme to find the transport map and prove the convergence. On the application side, in addition to KPP invariant measures, our method can also investigate the blow-up

behavior in chemotaxis models.

Bio: Zhongjian Wang is a William H. Kruskal Instructor in the Department of Statistics at the University of Chicago.

Time：15:30-16:30, Nov. 17th (Thur.) 2022

Venue：Tencent Meeting ID: 431642438

Join the meeting：https://meeting.tencent.com/dm/PyxmpJWoWQDb

Title：Electrically controlled self-similar evolution of viscous fingering patterns

Speaker：Meng Zhao（赵蒙), 华中科技大学数学中心

Abstract: Interfacial instabilities are prevalent in nature and engineering. In this talk, I will discuss the dynamics of a interface in a Hele-Shaw cell under an electric field. The coupling of the hydraulic and electric fields make the dynamics of the interface very complicated. We develop an efficient algorithm to investigate the nonlinear dynamics of the interface. Our nonlinear results reveal that the electric feild plays an important in controlling the interfacial instability. Finally, we construct an efficient controlling scheme for the interface.

Bio: 赵蒙，华中科技大学数学中心副教授，2011年本科毕业于华东理工大学，2013和2017年在Illinois Institute of Technology, Chicago 分别获得应用数学硕士和博士学位。2017至2021年在 University of California, Irvine担任访问助理教授和研究员。2021年加入华中科技大学数学中心。主要研究方向为Numerical Analysis, Scientific Computing (Sequential and Parallel), Methods for Interface Problems in Materials and Fluids, Hele-Shaw Flow, Computational Fluid Mechanics and Tumor Growth。

Time：16:00-17:00, 11月10日(星期四), Nov. 10th (Thur.) 2022

Venue：近春园西楼三层报告厅, Lecture hall, 3rd floor of Jin Chun Yuan West Building

Title：Partially adjoint discretizations of adjoint operators: preservation of strong dualities and closed range theorem

Speaker：Shuo Zhang（张硕）, LSEC, Chinese Academy of Sciences

Abstract: This talk concerns the discretizations in pair of adjoint operators so that the adjoint properties can be preserved. A theoretical framework and the formal construction of discretizations are presented; some new finite element schemes are stimulated. The main features are

• the adjoint properties concerned, particularly the closed range theorem and Poincar´e-Alexander-Lefschetz type strong dualities, are preserved;

• theory of partially adjoint operators serves as a framework to describe adjoint properties, which works for a family of infinitely-many finite-dimensional operators;

• a pair by a conforming discretization (CD) and an accompanied-by-conforming discretization (ABCD) for each of the operators serves as a general methodology to construct partially adjoint discretizations.

The validities of the theoretical framework and the formal construction of discretizations are illustrated by a systematic family of in-pair discretizations of the adjoint exterior differential operators. Some possible extensions can be mentioned.

Time：15:00-16:00, 11月3日(星期四), Nov. 3rd (Thur.) 2022

Venue：Tencent #腾讯会议：431-642-438 https://meeting.tencent.com/dm/PyxmpJWoWQDb

Title：Challenges and Opportunities in Turbulent Reactive Flow Simulations

Speaker：Zhuyin Ren （任祝寅） Center for Combustion Energy /Institute of Aero Engine， Tsinghua University

Abstract: Combustion modeling is now playing an important role in the design and optimization of advanced combustion devices. For high-fidelity combustion modeling, it is essential, though challenging, to resolve the highly nonlinear turbulence-chemistry interaction (TCI) and to predict the near-limit combustion phenomena. This talk will first give a review on the grand challenges for turbulent flame simulations. The implication of stiff chemical kinetics and TCI on numerical methods will be discussed. Then the talk will discuss the potential use of machine learning in some aspects of physical modeling and computational acceleration for turbulent flame simulations. Specific examples include efficient evaluation of the nonlinear reaction mapping, the use of neural ODE for mechanism optimization, and exploring the intrinsic active subspace in uncertainty quantification.

Bio：Dr. Zhuyin Ren received his Ph.D. in Mechanical Engineering from Cornell University in 2006. He has been a Professor of the Center for Combustion Energy /Institute of Aero Engine at Tsinghua University since 2013. His research interests include turbulent combustion modeling , numerical methods for high-fidelity engine simulations, advanced propulsion and power systems. He received the National Science Fund for Distinguished Young Scholars in 2020, and now serves as associate editors of Journal of Propulsion and Power, Combustion Theory and Modelling.

Time：16:00-17:00, 11月3日(星期四), Nov. 3rd (Thur.) 2022

Venue：近春园西楼三层报告厅, Lecture hall, 3rd floor of Jin Chun Yuan West Building

Title：A construction of C^r conforming finite element spaces in any dimension

Speaker：Jun Hu （胡俊）, Peking University

Abstract: This talk proposes a construction of C^r conforming finite element spaces with arbitrary r in any dimension. It is shown that if k ≥ 2^dr + 1 the space P_k of polynomials of degree ≤ k can be taken as the shape function space of Cr finite element spaces in d dimensions. This is the first work on constructing such C^r conforming finite elements in any dimension in a unified way.

Bio: 胡俊，北京大学数学科学学院党委书记、教授，北京大学重庆大数据研究院院长。兼任Adv Appl. Math. Mech.执行主编、多个期刊的编委、北京计算数学学会理事长、中国数学会常务理事、中国大坝工程学会大坝数值模拟专委会副主任委员、重庆市工业软件应用发展协会副会长、北大-华为数学联合实验室主任。主要从事非标准有限元方法的研究，特别是弹性力学问题、线性化Einstein-Bianchi方程组及相关问题的非标准有限元方法的构造与数值分析的研究，解决了弹性力学问题混合有限元方法的构造这个长期悬而未决的公开问题，首次构造了线性化Einstein-Bianchi方程组保结构的稳定有限元方法。曾获国家杰出青年基金、中国计算数学学会“首届青年创新奖”、冯康科学计算奖等荣誉。

Title：AI-for-Science – the next wave of artificial intelligence

Speaker: Tieyan Liu (刘铁岩)

Time：16：00-17：00, Oct. 27th (Thur.) 2022

Venue：近春园西楼三楼报告厅 Lecture Hall, Jin Chun Yuan West Bldg.; 腾讯会议：807-850-470

Abstract：

In the past decades, AI has achieved notable success in computer vision, speech recognition, and natural language understanding. However, mimicking human’s vision, speech, and language capabilities is just a shallow aspect of AI. It neglects the fact that we, as human beings, are unique because of our courage and ability to discover and change the world. AI-for-Science aims at building powerful tools to help natural scientists to better discover and change the world. Specifically, AI-for-Science assumes that the physical world can be theoretically characterized by fundamental scientific equations, usually at very large scale. It also acknowledges that there is always a gap between theory and reality, and the evidence of the gap can be found in experimental data. No one has the capability to efficiently solve all those complex scientific equations, analyze those massive experimental data, or create a closed loop between them. This is exactly where AI could play a disruptive role. As a showcase of such disruptions, I will introduce several research projects at MSR AI4Science, including Graphormer, an AI model for molecular dynamics simulation, DeepVortexNet, a neural PDE solver for fluid dynamics, SciGPT, an AI language model to automatically extract knowledge from scientific literature, and LorentzNet, and equivariant AI model to detect new particles from large-scale jet data. After introducing these works, I will also discuss some future trends of AI-for-Science research.

Bio：

刘铁岩博士，微软杰出首席科学家、微软亚洲研究院副院长、微软研究院科学智能中心亚洲区负责人。他是国际电气电子工程师学会（IEEE）会士、 国际计算机学会（ACM）会士、亚太人工智能学会（AAIA）会士。他被聘为清华大学、香港科技大学、中国科技大学、华中科技大学兼职教授、诺丁汉大学荣誉教授。

刘博士的先锋性研究促进了机器学习与信息检索之间的融合，被公认为“排序学习”领域的代表人物。近年来他在深度学习、强化学习、工业智能、科学智能等方面颇有建树，在顶级国际会议和期刊上发表论文数百篇，被引用数万次。他的研究工作多次获得最佳论文奖、最高引用论文奖、研究突破奖，并被广泛应用在微软的产品和在线服务中，如必应（Bing）搜索、微软广告、Windows、Xbox、Azure等。

刘博士曾担任WWW/WebConf、SIGIR、NeurIPS、ICLR、ICML、IJCAI、AAAI、KDD、ACL等十余个国际顶级学术会议的大会主席、程序委员会主席或（资深）领域主席；ACM TOIS、ACM TWEB、IEEE TPAMI等国际期刊副主编。

他的团队于2017年开源了LightGBM，目前已成为Kaggle比赛、KDD Cup和产业决策过程中最受欢迎的机器学习工具之一；于2018年在中英新闻翻译任务上达到了人类专家水平，并于次年获得WMT机器翻译比赛8项冠军；于2019年研发了麻将AI Suphx，在国际知名麻将平台“天凤”上荣升十段，稳定段位显著超越人类顶级选手；2021年发布了用于分子模拟的Graphormer模型，并在KDD Cup分子建模比赛和催化剂设计开放挑战赛中力拔头筹。

刘铁岩博士毕业于清华大学，先后获得电子工程系学士、硕士及博士学位。

Title：Geometry and topology in collective dynamics models

Speaker：Pierre Degond, Institut de Mathématiques de Toulouse CNRS & Université Paul Sabatier

Time：15:30-16:30, 10月20日(星期四), Oct. 20th (Thur.) 2022

Zoom Meeting ID: 276 366 7254 Passcode: YMSC

Zoom Link： https://zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

Abstract: Collective dynamics arises in systems of self-propelled particles and plays an important role in life sciences, from collectively migrating cells in an embryo to flocking birds or schooling fish. It has stimulated intense mathematical research in the last decade. Many different models have been proposed but most of them rely on point particles. In practice, particles often have more complex geometrical structures. Here, we will consider particles as rigid bodies whose body attitude is described by an orthonormal frame. Particles tend to align their frame with those of their neighbours. A hydrodynamic model will be derived when the number of particles is large. It will be used to exhibit solutions having non-trivial topology. We will investigate whether topology provides enhanced stability against perturbations, as observed in other systems such as topological insulators. This talk is based on recent results issued from collaborations with Antoine Diez, Amic Frouvelle, Sara Merino-Aceituno, Mingye Na and Ariane Trescases.

Bio: Prof. Degond was trained at the Ecole Normale Supérieure in Paris and his first appointment was in Ecole Polytechnique in Palaiseau in 1985 as a Junior Researcher at CNRS. He was then appointed a full Professor in Ecole Normale Superieure of Cachan in 1990. He joined back the CNRS in Toulouse as a Senior Researcher in 1993, where he founded the Applied Math group, and holds a permanent position. He has been a Chair Professor in Applied Mathematics at Imperial College in the period 2013-2020, and a Visiting Professor in Mathematics afterwards. He is interested in plasma physics, rarefied gas dynamics, semiconductor modeling, collective dynamics, decision making and self-organization in complex systems arising from biology and social sciences. His methods combine analysis, asymptotic theory and multiscale numerical techniques. He has been been an invited speaker at the 2018 International Congress of Mathematicians (ICM 2018). He was awarded the Jacques-Louis Lions prize 2013 of the French Academy of Sciences and a Royal Society Wolfson Research Merit Award holder in 2014-2018.

Time：15:30-16:30, Oct. 13th (Thur.) 2022

Venue：近春园西楼三层报告厅, Lecture hall, 3rd floor of Jin Chun Yuan West Building

Title：Computing quantum dynamics: towards fighting against multiscales and high dimensionality

Speaker：Zhennan Zhou （周珍楠）, Peking University

Abstract: We develop a Monte Carlo algorithm named the Frozen Gaussian Sampling (FGS) to solve the semiclassical Schrodinger equation based on the frozen Gaussian approximation. Due to the highly oscillatory structure of the wave function, traditional mesh-based algorithms suffer from ”the curse of dimensionality”, which gives rise to more severe computational burden when the semiclassical parameter ε is small. The Frozen Gaussian sampling outperforms the existing algorithms in that it is mesh-free in computing the physical observables and is suitable for high dimensional problems. We also discussion the extension of the FGS approach to the mixed quantum-classical dynamical models.

Bio: 周珍楠，北京大学北京国际数学研究中心助理教授、博士生导师。2014 年在美国威斯康辛大学麦迪逊分校获得博士学位，2014-2017 年在美国杜克大学担任助理研究教授，2017 年加入北京大学北京国际数学研究中心。主要研究领域为微分方程的应用分析，微分方程数值解，应用随机分析，随机模拟等，特别是关注来源于自然科学的应用数学问题。入选中组部第十四批“千人计划”青年人才项目（2018）。

Title: Learning for the Future Power Grid

Speaker：Chenye Wu (吴辰晔), CUHK (Shenzhen)

Time：16:00-17:15, Oct. 6th (Thur.) 2022

Tencent: 511 466 354

Abstract: Advanced learning frameworks are reshaping the landscape of power grid operation and the electricity market design.This talk shares two stories, both of which seek to use learning frameworks to enhance the future power grid. The first one investigates the storage control problem for consumers. Specifically, we consider that consumers face dynamic electricity prices and seek to use storage to reduce their electricity bills. The challenges come from the uncertainty in the electricity price and consumers' demand.We propose a practical learning-based online storage control policy. The second story studies a classical procedure in the electricity market,the economic dispatch problem, i.e., matching the electricity supply and demand at the minimal generation cost. The critical challenge is again from the uncertainty in the system demand. Hence, the conventional approach is to conduct the dispatch based on predicted demand.However, we submit that this conventional approach can be suboptimal, and we propose a model-free algorithm for economic dispatch based on the end-to-end learning framework.

Bio: Dr. Chenye Wu is currently an Assitant Professor and the presidential young fellow at the School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen. Dr. Wu received his bachelor's degree in electronic engineering from Tsinghua University in 2009 and his Ph.D. degree in computer science and engineering from Tsinghua University in 2013, advised by Prof. Andrew Yao, the Turing Award Laurant. Dr. Wu's research interests span from power system control to the electricity market design, emphasizing the emerging business model design for the energy sector, the market power analysis for the electricity market, the AI-driven power system control and operation. Dr. Wu has published over 70 research articles in top journals and leading conferences in the field, including IEEE Transactions on Power Systems, IEEE Transactions on Smart Grid, IEEE Transactions on Sustainable Energy, ACM e-Energy. He is a member of the FinTech special interest group, China Society for Industrial and Applied Mathematics, and a member of the special interest group, China Energy Society. Dr. Wu has been an Editorial Board Member for IEEE Systems Journal as an Associate Editor since February 2022. He is the symposium co-Chair for IEEE SmartGridComm 2022 and the digital conference co-Chair for ACM e-Energy 2022. Dr. Wu is the co-recipients of the three best paper awards, including the best paper award for IEEE SmartGridComm 2012 and IEEE PES General Meeting 2013 and 2020.

时间 Time：14:00-15:30, 9月30日(星期五), Sep. 30th (Fri.) 2022

地点 Venue：近春园西楼三层报告厅, Lecture hall, 3rd floor of Jin Chun Yuan West Building

Title： Modulated Free Energy and Mean Field Limit

Speaker: Zhenfu Wang (王振富), 北京大学北京国际数学研究中心 Beijing International Center for Mathematical Research, Peking University

Abstract: We prove the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the Patlak-Keller-Segel model in optimal subcritical regimes is obtained for the first time. To give an answer to this longstanding problem, we take advantage of a new modulated free energy and we prove some precise large deviation estimates encoding the competition between diffusion and attraction. This modulated free energy approach can also treat the systems with a wide range of repulsive kernels, including the vanishing viscosity case. Based on joint works with D. Bresch and P.-E. Jabin.

个人简介：王振富，2012年本科毕业于南京大学，2017年获美国马里兰大学数学博士学位，博士导师为 Pierre-Emmanuel Jabin。2017年7月到2020年6月在美国宾夕法尼亚大学从事博士后研究工作。2020年10月入职北京大学，现任北京国际数学研究中心助理教授、研究员。主要研究领域为交互粒子系统的平均场极限和动理学方程的分析。

时间 Time：16:00-17:00, 9月29日(星期四), Sep. 29th (Thur.) 2022

地点 Venue：近春园西楼三层报告厅, Lecture hall, 3rd floor of Jin Chun Yuan West Building

Title： On splitting methods for the Dirac equation in the nonrelativistic limit regime

Speaker：Yongyong Cai (蔡勇勇), School of Mathematical Sciences, Beijing Normal University(北京师范大学)

Abstract: We establish error bounds of the Lie-Trotter splitting and Strang splitting for the Dirac equation in the nonrelativistic limit regime in the absence of external magnetic potentials. In this regime, the solution admits high frequency waves in time. Surprisingly, we find out that the splitting methods exhibit super-resolutions, i.e. the methods can capture the solutions accurately even if the time step size is much larger than the sampled wavelength. Lie splitting shows half order uniform convergence w.r.t temporal wave length. Moreover, if the time step size is non-resonant, Lie splitting would yield an improved uniform first order uniform error bound. In addition, we show Strang splitting is uniformly convergent with half order rate for general time step size and uniformly convergent with three half order rate for non-resonant time step size. We also discuss the case with external magnetic potentials, and splitting schemes also show superior performance among the commonly used numerical methods.

个人简介：蔡勇勇，北京师范大学教授，本科和硕士就读于北京大学，2012年在新加坡国立大学获得博士学位。他先后在威斯康辛大学麦迪逊分校、马里兰大学帕克分校和普渡大学从事博士后研究工作，从2016年至2019年在北京计算科学研究中心任特聘研究员。蔡勇勇博士的研究兴趣主要是偏微分方程的数值方法及其在量子力学等领域中的应用。

题目：Error statistics and scalability of quantum error mitigation formulas

Organizer / 组织者：魏朝晖

Speaker / 主讲人：Xiaodie Lin（清华大学）

Time / 时间：15:00-16:00pm, September 22 (Thur.) 2022

Venue / 地点：Ningzhai 宁斋S11

摘要：Quantum error mitigation is crucial for us to protect quantum computing against quantum errors before quantum error correction is truly available, which is still one or two decades away. Though some error mitigation protocols, like error extrapolation and error cancellation, have been demonstrated successfully in experiments using small scale quantum systems, whether they behave well on large scale quantum computers remains unclear. Recently, it has been found out that after error mitigation, the remaining error is roughly of order the square root of N, where N is the number of quantum gate number.

时间 Time：16:30-17:30, 9月22日(星期四), Sep. 22th (Thur.) 2022

地点 Venue：近春园西楼三层报告厅, Lecture hall, 3rd floor of Jin Chun Yuan West Building

Title：Optimization, Generalization and Implicit bias of Gradient Methods in Deep Learning

Speaker：Jian Li (李建), Institute for Interdisciplinary Information Sciences (IIIS), Tsinghua University.

Abstract: Deep learning has enjoyed huge empirical success in recent years. Although training a deep neural network is a highly nonconvex optimization problem,

simple (stochastic) gradient methods are able to produce good solutions that minimize the training error, and more surprisingly, can generalize well to out-of sample data, even when the number of parameters is significantly larger than the amount of training data. It is known that the optimization algorithms (various gradient-based methods) contribute greatly to the generalization properties of deep learning. However, recently, researchers have found that gradient methods (even gradient descent) may not converge to a stationary point, the loss graduately decreases but not necessarily monotonically, and the sharpness of the loss landscape (i.e., the max eigenvalue of the Hessian) may oscillate, entering a regime called edge of stability. These behaviors are inconsistent with several classical presumptions widely studied in the field of optimization. Moreover, what bias is introduced by the gradient-based algorithms in neural network training? What characteristics of the training ensures good generalization in deep learning? In this talk, we investigate these question from the perspective of the gradient based optimization methods. In particular, we attempt to explain some of the behaviors of the optimization trajectory (e.g., edge of stability), prove new generalization bounds and investigate the implicit bias of various gradient methods.

Bio：Jian Li is currently a tenured associate professor at Institute for Interdisciplinary Information Sciences (IIIS), Tsinghua University, headed by Prof. Andrew Yao. He got his BSc degree from Sun Yat-sen (Zhongshan) University, China, MSc degree in computer science from Fudan University, China and PhD degree in the University of Maryland, USA. His major research interests lie in theoretical computer science, machine learning, databases and finance. He co-authored several research papers that have been published in major computer science conferences and journals. He received the best paper awards at VLDB 2009 and ESA 2010, best newcomer award at ICDT 2017.

**Title：**Computational Quantum Mechanics in Phase Space — An Attempt to Break the Curse of Dimensionality

**Speaker：**Sihong Shao (邵嗣烘) ，School of Mathematical Sciences, Peking University, sihong@math.pku.edu.cn

**Time: **14:30-15:30, September 16th(Fri.) 2022

**Venue：**近春园西楼三层报告厅

**Abstract：**

The Wigner function has provided an equivalent and convenient way to render quantum mechanics in phase space. It allows one to express macroscopically measurable quantities, such as currents and heat fluxes, in statistical forms as usually does in classical statistical mechanics, thereby facilitating its applications in nanoelectronics, quantum optics and etc. Distinct from the Schrödinger equation, the most appealing feature of the Wigner equation, which governs the dynamics of the Wigner function, is that it shares many analogies to the classical mechanism and simply reduces to the classical counterpart when the reduced Planck constant vanishes. Despite the theoretical advantages, numerical resolutions for the Wigner equation is notoriously difficult and remains one of the most challenging problems in computational physics, mainly because of the high dimensionality and nonlocal pseudo-differential operator. On one hand, the commonly used finite difference methods fail to capture the highly oscillatory structure accurately. On the other hand, all existing stochastic algorithms, including the affinity-based Wigner Monte Carlo and signed particle Wigner Monte Carlo methods, have been confined to 2D phase space. Few results have been reported for higher dimensional simulations. My group has made substantial progress in both aspects.

We attempted to solve the Wigner equation in 4-D and 6-D phase space with gird-based deterministic methods by exploiting its intriguing mathematical structure. For 4-D simulations, we succeeded to detail the quantum dynamics of a Helium-like system and the quantum interference fringes in the double-slit experiment. For the 6-D Wigner-Coulomb system, we proposed a massively parallel solver, termed the characteristic-spectral-mixed scheme (CHASM), which utilizes the locally distributed cubic B-spline basis to interpolate the local spatial advection and the truncated kernel method to approximate the pseudodifferential operator with weakly singular symbol under the Coulomb interaction. Several typical numerical experiments demonstrate the accuracy and efficiency of CHASM, as well as its scalability up to 16000 cores.

On the other hand, we built the bridge between the Wigner equation and a stochastic particle method in a rigorous manner and proposed a SPA (Stationary Phase Approximation) + SPADE (Sequential-clustering Particle Annihilation via Discrepancy Estimation) strategy to overcome the sign problem where the curse of dimensionality which causes the unattainable exponential wall is translated into the NP-hard problems that may have approximate solutions. SPADE follows a divide-and-conquer strategy: Adaptive clustering of particles via controlling their number-theoretic discrepancies and independent random matching in each group, and it may learn the minimal amount of particles that can accurately capture the non-classicality of the Wigner function. A thorough performance benchmark of SPADE is provided with the reference solutions in 6-D phase space produced by CHASM under a 73^3*80^3 uniform grid, which fully explores the limit of grid-based deterministic Wigner solvers. Simulations of the proton-electron couplings in 6-D and 12-D phase space demonstrate the accuracy and the efficiency of our particle-based stochastic methods.

As a permanent goal and a tireless direction of computational mathematics, developing an accurate and stable high-dimensional solver has been attracting more and more attentions in recent years due to the urgent need in e.g., quantum science and high energy density physics. This talk represents our recent attempts to break the curse of dimensionality which poses a fundamental obstacle to high-dimensional numerical simulations.

邵嗣烘，北京大学数学科学学院副教授，毕业于北京大学数学科学学院并获得理学学士和博士学位，先后到访过北卡罗莱那大学夏洛特分校，香港科技大学，普林斯顿大学、塞维利亚大学和香港中文大学等。主要开展面向智能、量子和计算的交叉融合研究，落脚点在基础的数学理论和高效的算法设计，强调离散数学结构的设计、分析和应用。具体研究领域包括：高维问题的数值方法、组合优化、计算量子力学、图（网络）上的数学及其算法、微分方程数值解和脑科学等，获国家自然科学基金青年，面上和优青连续资助。2019年入选北京智源人工智能研究院“智源青年科学家”。2020年获北京大学优秀博士学位论文指导老师。2021年获北京大学黄廷芳/信和青年杰出学者奖。曾获中国计算数学学会优秀青年论文一等奖，北京大学学术类创新奖，北京大学优秀博士学位论文三等奖，宝洁教师奖和北京大学优秀班主任等。

Title/题目：Universal cost bound of quantum error mitigation based on quantum estimation theory

Organizer/组织者：魏朝晖

Speaker/主讲人：Weixiao Sun（清华大学）

Time/时间：15:00-16:00pm, September 8th(Thur.) 2022

Venue/地点：Ningzhai 宁斋S11；Tencent Meeting ID: 235-622-864

Abstract/摘要：Quantum error mitigation is very important for us to protect quantum computing from errors before we have sufficient computational resources to apply quantum error correction. Though quite a few techniques have been proposed for this purpose, little is known about their fundamental aspects, say the limitation of their power. Recently, a new approach that analyzes the cost of quantum error mitigation using the quantum estimation theory has been proposed, where by proving that the quantum Fisher information decays exponentially with the circuit depth, it has been shown that unbiased estimation of an observable encounters an exponential growth in the lower bound on the measurement cost, or more precisely the required number of copies of noisy quantum state.

**题目：**重思遥感图像复原的基本方法论

**报告人：**孟德宇 （西安交通大学）

**时间：**2022/08/26 10:00-11:30am

**#腾讯会议：**521-250-349

**摘要：**针对遥感图像复原问题，传统方法论主要分为模型驱动与数据驱动两类。其中模型驱动主要通过认识数据，预先设计合理的损失与正则项，从而达到良好复原效果。而数据驱动主要通过借鉴计算机视觉领域通用有效深度网络的构建技巧，通过端到端机器学习的方式来获得针对退化遥感图像的显式复原函数，从而便于泛化使用。然而，针对遥感图像的特殊内涵，两种方法论均存在内在的缺陷。本报告中，将尝试对已有底层遥感图像技术进行内在功能的分析，从而反思其局限性，进而讨论如何对遥感图像能够更加合理设计方法论的可能策略。

**Title: **Data-driven computational multiscale methods and applications

**Speaker:** Eric T. Chung (The Chinese University of Hong Kong)

**Time:** 2022/07/19， 10am-11am

**Venue：**Lecture hall, 3rd floor of Jin Chun Yuan West Building；Tencent Meeting: 502-4821-2807

**Organizer: **Jie Du

**Abstract: **Many practical problems, especially those arising from geosciences, have multiscale features due to medium heterogeneities, nonlinearity and coupling of multiple models. The goal of multiscale methods or numerical upscaling techniques is to compute the solutions of these complicated problems efficiently by constructing coarse scale equations for some dominant components of the solutions. In this talk, we will present the latest development of a class of multiscale methods, which make use of solutions of local problems to obtain coarse scale equations and have rigorous convergence theories. For nonlinear problems, the macroscopic parameters in the coarse scale equations can be computed efficiently by the use of deep learning techniques. We will discuss the general concepts and present some applications.

**Bio: **Eric T. Chung is a Professor in the Department of Mathematics in The Chinese University of Hong Kong. He obtained PhD degree from University of California at Los Angeles. His Ph.D. thesis advisor is Prof. Bjorn Engquist. His research interests are Discontinuous Galerkin Methods, Computational Wave Propagation, Fluid Flow in Heterogeneous Media, Multiscale Model Reduction Techniques, Adaptivity for Multiscale Problems, Domain Decomposition Methods, Seismic Imaging and Travel Time Tomography.