Applied and Computational Math Colloquium

报告人 Speaker:Zheng Yicong (TQL)
组织者 Organizer:应用与计算数学团队
时间 Time:Thur.,14:00-15:00,Dec.1st,2022
地点 Venue:Online

Upcoming Talks:

 

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。

 

 



Past Talks:  



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.