一周活动预告（9.26-10.2）
请查收。
目录：
机理与数据融合的计算成像（董彬）
Deep Reinforcement Learning in Quantitative Trading（Yizheng Hu）
Graph Representation Learning: A Geometric Perspective（Rex Ying）
步态识别历史与发展趋势 （丁仕琪）
基于参数估计误差的自适应控制：理论及应用 （那靖）
Minimax optimal learning: adaptivity, model compression and limitation （Yuhong Yang）
From Weyl conjecture to fundamental gap conjecture and beyond (包维柱)
A deep adaptive sampling method for the approximation of high-dimensional PDEs （Xiaoliang Wan）
Adaptive nonlinear preconditioning for PDEs （刘璐璐）
Convergence analysis of a fully discrete scheme for incompressible vector potential MHD systems（毛士鹏）
PoS4MPC: Automated Security Policy Synthesis for Secure Multi-party Computation（Fu Song）
基于气象资料同化算法加速的研究（鞠国良）
High-Dimensional Challenges for Computational Finance（Xiaoqun Wang）
近场动力学问题模型简介及非局部发展模型的POD算法（聂玉峰）
Deep Learning Based Causal Inference with Combinatorial A/B Tests on Large-Scale Platforms（Philip Renyu Zhang）
Geometric Deep Learning: Grids, Graphs, Groups, Geodesics and Gauges (Petar Veličković)
High-order Gas-kinetic schemes under finite difference and spectral difference frameworks （Qing Xie）
High-dimensional Quantile Tensor Regression（Zhongyi Zhu）
Global Dynamics of a Predator-Prey Model in Open Advective Environments（聂华）
Data-driven optimization---integrating data sampling, learning and optimization (Wei Chen)
On preconditioned iteration methods for saddle point problems from Eddy current models (任志茹)
Randomized methods of matrix decompositions and its applications （任志茹）
How many PDE numerical eigenvalues can we trust, and how to get more out of it? （Zhimin Zhang）
Why spectral methods are preferred in PDE eigenvalue computations in some cases?（Zhimin Zhang）
1. 机理与数据融合的计算成像
Speaker: 董彬（北京国际数学研究中心）
Time: 2022-09-26 10:00-11:00
Venue: 腾讯会议ID: 691666024 密码: 304699
Info Source:
https://ins.sjtu.edu.cn/seminars/2156
Abstract:
计算成像关心的问题是如何有效的感知数据并重建高质量的图像以辅助人们进行决策，这包含了三个环节：图像感知、图像重建和图像分析。传统的图像感知以硬件设计为主，而图像重建和分析是数学与统计方法的主战场。长久以来这三个步骤的发展相对独立，融通性较弱，但在机器学习（尤其是深度学习）得以长足发展的今天，这一状况在逐渐的发生改变。本报告主要围绕深度学习给计算成像所带来的机遇与挑战展开，介绍如何将传统的图像重建算法与深度学习方法相结合来设计数据驱动与任务驱动的成像算法，从而实现计算成像三个环节的有机融合。
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2. Deep Reinforcement Learning in Quantitative Trading
报告人: Yizheng Hu (PKU)
报告时间: 2022-09-26 16:00-17:00
报告链接: 腾讯会议ID: 723 1564 5542
信息来源: https://www.math.pku.edu.cn/kxyj/xsbg/tlb/informationsciences/143202.htm
报告摘要:
Quantitative Trading (QT) has been vastly growing in recent years, especially in T+0 markets. In fact, it has been a research topic both in the area of finance and computer science for many decades. Classic QT methods, such as stochastic control, rely heavily on model assumptions about the market. In recent years, with the success of Deep Reinforcement Learning (DRL), many QT methods using DRL have been developed, which achieved state-of-the-art performance with few model assumptions.
In this talk, we will introduce recent DRL works on three QT tasks: vanilla QT or optimal execution, portfolio management, and market making. We will also discuss the challenges of DRL in QT and possible future research directions.
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3. Graph Representation Learning: A Geometric Perspective
Speaker: Rex Ying（Yale University）
Time: 2022-09-27 09:00-10:00
Venue:
Zoom Meeting ID: 885 6782 3248 Password: PSJAS0927
VooV Meeting ID: 904 526 516
Info Source:
https://ins.sjtu.edu.cn/seminars/2161
Abstract:
The talk focuses on geometric embedding approaches to representation learning on graph-structured data. We observe that certain inductive biases of graph data, such as hierarchies and transitive closures, can be modeled more effectively through different embedding geometries. We leverage hyperbolic embeddings, cone embeddings and order embeddings for incorporating these inductive biases of input graph data when learning node and graph representations for large-scale, heterogeneous graph data and other challenging tasks.
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4. 步态识别历史与发展趋势
报告人: 丁仕琪（南方科技大学）
报告时间: 2022-09-27 10:30
报告链接: 腾讯会议ID: 845 284 863
信息来源:
http://math.lzu.edu.cn/info/1065/3993.htm
报告摘要:
步态识别真的能用吗？现在步态识别技术发展到了什么程度？步态识别可以远远瞥一眼就能识别你是谁吗？这个报告将深入浅出地介绍步态识别发展历史，梳理出一个清晰的步态识别发展趋势，根据这个趋势你可以看到步态识别下一步的研究热点，以及未来步态识别达到的效果。
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5. 基于参数估计误差的自适应控制：理论及应用
报告人: 那靖（昆明理工大学）
报告时间: 2022-09-27 14:30-15:30
报告链接: 腾讯会议ID: 337 780 671
信息来源:
http://tianyuan.scu.edu.cn/portal/article/index/id/746/cid/3/p/7.html
报告摘要:
自适应控制是处理具有参数不确定性系统的有效方法, 从提出以来一直备受关注, 并逐渐形成了以梯度学习算法为 核心的理论体系。但与较为成熟的理论研究相比, 自适应技术在实际系统中应用推广较少。事实上, 自适应系统中在线学 习机制的引入使得系统性能分析及保障较为困难, 且围绕梯度算法构建的自适应系统中存在本质性的矛盾。本报告首先介 绍自适应估计和控制的基本思想; 在此基础上, 针对传统自适应学习方法的局限, 介绍了一类基于参数估计误差的新的学 习方法, 以及据此构建的快速自适应参数估计和控制系统设计和收敛性、鲁棒性分析理论, 并给出了持续激励条件的在线 判别方法; 最后, 介绍了该自适应方法在汽车、核聚变系统、海浪能转化系统、机器人等实际系统建模和控制中的应用宩 例。
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6. Minimax optimal learning: adaptivity, model compression and limitation
报告人: Yuhong Yang（University of Minnesota）
报告时间: 2022-09-27 15:00-16:00
报告链接: 腾讯会议ID: 956 802 903
信息来源:
https://math.cnu.edu.cn/xsbg/6d7a75b47be848408ad475dfb358d200.htm
报告摘要:
Minimax-rate optimallty plays a foundational role in theory of statistical and machine leaning. Besides the identification of minimax-rates of convergence and optimal learning procedures for various learning scenarlos. adaptive strategies have also been devised to work simultaneously well for multiple or even infinitely (countably or contlnuously, many possible scenarlos that may describe the underying distribution of the data. Going with the exciting successes of the modern regression leaming tool are questions/concerns/doubts on sparsity, model compressibility, instablity, robustness and rellability of the fancy automated algorithms. in this talk, we will first present on minimax optimal adaptive estimations for high dimensional regression learning under hard and soft sparsity setups, taking advantage of recent sharp sparse linear approdmation bounds. An application on mode compression in neural network leaming will be given. Then we will address the question that how adaptive and powerful any learning procedure really can be. We show that every procedure, no matter how it is constructed, can only work well for a limited set of regreson functions
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7. From Weyl conjecture to fundamental gap conjecture and beyond
报告人: 包维柱 (新加坡国立大学)
报告时间: 2022-09-27 16:00-17:00
报告链接: ZoomID: 833 1273 7137 密码: 202209
信息来源:
http://math.bnu.edu.cn/xzbg/zwxygzbg/247669.htm
报告摘要:
In this talk, I will begin with the Weyl's law and Weyl conjecture on the asymptotics of eigenvalues of the Laplacian and Schrodinger operators (LO/SO) on bounded domains with Dirichlet boundary condition. Based on our recent numerical results by using a spectral method, I report some information on the reminder in the Weyl conjecture for the LO/SO. In addition, a generalized Weyl's law for the fractional Schrodinger operator (FSO) is proposed. Then I review the fundamental gap conjecture -- difference between the first two smallest eigenvalues -- of the LO/SO. Again, based on our recent asymptotic and numerical results, we propose a gap conjecture on the fundamental gap of the FSO. In addition, different gaps of eigenvalues of the FSO are discussed and the ``unfolding'' gaps statistics of FSO is reported. Finally, fundamental gaps on energy and chemical potential of the Gross-Pitaevskii equation are studied asymptotically and numerically.
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8. A deep adaptive sampling method for the approximation of high-dimensional PDEs
信息来源:
https://hkumath.hku.hk/web/event/event-seminar.php
9. Adaptive nonlinear preconditioning for PDEs
报告人: 刘璐璐 (南京理工大学)
报告时间: 2022-09-28 10:00
报告链接: 腾讯会议ID: 784 158 870
信息来源:
http://tianyuan.xmu.edu.cn/cn/letures/903.html
报告摘要:
Nonlinear preconditioning is a globalization technique for Newton's method applied to systems of equations with unbalanced nonlinearities, in which nonlinear residual norm reduction stagnates due to slowly evolving subsets of the degrees of freedom. Even though the Newton corrections may effectively be sparse, a standard Newton method still requires large ill-conditioned linear systems resulting from global linearizations of the nonlinear residual to be solved at each step. Nonlinear preconditioners may enable faster global convergence by shifting work to where it is most strategic, on subsets of the original system. They require additional computation per outer iteration while aiming for many fewer outer iterations and correspondingly fewer global synchronizations. In this work, we improve upon previous nonlinear preconditioning implementations by introducing parameters that allow turning off nonlinear preconditioning during outer Newton iterations where it is not needed. Numerical experiments show that the adaptive nonlinear preconditioning algorithm has performance similar to monolithically applied nonlinear preconditioning, preserving robustness for some challenging problems representative of several PDE-based applications while saving work on nonlinear subproblems.
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10. Convergence analysis of a fully discrete scheme for incompressible vector potential MHD systems
报告人: 毛士鹏（中国科学院数学与系统科学研究院）
报告时间: 2022-09-28 10:00-11:00
报告链接: 腾讯会议ID: 722-868-209 密码: 220921
信息来源:
https://math.sustech.edu.cn/seminar_all/12476.html
报告摘要:
We investigate a fully discrete finite element scheme for the three dimensional incompressible magnetohydrodynamic problem based on magnetic vector potential formulation. The formulation enjoys the novel feature that it can always produce an exactly divergence-free magnetic induction discretized solution. Using a mixed finite element approach, we discretize the model by the fully discrete semi-implicit Euler scheme with the velocity and the pressure approximated by stable MINI finite elements and the magnetic vector potential by Nedelec edge elements. Convergence analysis and error estimates for the velocity and the magnetic vector potential are rigorously established. Finally, several numerical experiments are presented to illustrate the convergence properties of the numerical scheme.
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11. PoS4MPC: Automated Security Policy Synthesis for Secure Multi-party Computation
报告人: Fu Song (Shanghai Tech Univ.)
报告时间: 2022-09-28 10:00-12:00
报告链接: 腾讯会议ID: 959-118-326
信息来源: https://www.math.pku.edu.cn/kxyj/xsbg/tlb/informationsciences/143170.htm
报告摘要:
Secure multi-party computation (MPC) is a promising technique for privacy-persevering applications. A number of MPC frameworks have been proposed to reduce the burden of designing customized protocols, allowing non-experts to quickly develop and deploy MPC applications. To improve performance, recent MPC frameworks allow users to declare variables secret only for these which are to be protected. However, in practice, it is usually highly non-trivial for non-experts to specify secret variables: declaring too many degrades the performance while declaring too less compromises privacy. To address this problem, in this work we propose an automated security policy synthesis approach to declare as few secret variables as possible but without compromising security. Our approach is a synergistic integration of type inference and symbolic reasoning. The former is able to quickly infer a sound—but sometimes conservative—security policy, whereas the latter allows to identify secret variables in a security policy that can be declassified in a precise manner. Moreover, the results from symbolic reasoning are fed back to type inference to refine the security types even further. We implement our approach in a new tool PoS4MPC. Experimental results on five typical MPC applications confirm the efficacy of our approach.
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12. 基于气象资料同化算法加速的研究
报告人: 鞠国良 博士（国家超级计算深圳中心）
报告时间: 2022-9-28 15:00-16:30
报告链接: 腾讯会议ID: 917-322-980
获取会议密码请联系汪老师：xcwang@hit.edu.cn
信息来源:
http://math.hit.edu.cn/2022/0921/c10234a281348/page.htm
报告摘要:
资料同化是数值天气预报的关键技术之一，它可以有效地将时空分布不均匀、不同来源及不同观测误差的常规和非常规观测资料有效地融入数值模式中，为数值预报天气预报提供更准确初值。然而当前资料同化存在着计算效率低、速度慢的缺点，使得业务化运行难以展开。为了克服这一难题，我们对LETKF算法的性能进行了优化。通过对LETKF算法的计算时间复杂度进行分析，发现在并行计算环境下，CPU计算量分配不均是影响计算效率的直接原因。为解决这一问题，我们设计了基于区域分解的动态调度算法，实现了负载均衡，提升了计算的效率，该算法具有很强的可扩展性与可移植性，目前已经应用到业务模式中。
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13. High-Dimensional Challenges for Computational Finance
报告人: Xiaoqun Wang (Tsinghua University)
报告时间: 2022-09-29 14:00-15:30
报告链接: Tencent Meeting ID: 372-572-945
信息来源: https://www.math.pku.edu.cn/kxyj/xsbg/tlb/financialmath/143367.htm
报告摘要:
Many problems in mathematical finance (such as the pricing and hedging of complex financial derivatives) can be formulated as high-dimensional integration with dimension as high as hundreds or even thousands. In this talk I will discuss the advances for tackling such high-dimensional problems in mathematical finance. It is shown how the curse of dimensionality can be broken with the optimal convergence rate by using low discrepancy sequences and by properly introducing weights to characterize the importance of variables. I also try to answer why high-dimensional problems in mathematical finance are often of low effective dimension. The necessity and the methods for choosing the right weights in constructing good lattice rules and the methods for dimension reduction are highlighted.
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14. 近场动力学问题模型简介及非局部发展模型的POD算法
信息来源:
https://www.math.sdu.edu.cn/info/1020/17615.htm
15. Deep Learning Based Causal Inference with Combinatorial A/B Tests on Large-Scale Platforms
报告人: Philip Renyu Zhang（The Chinese University of Hong Kong）
报告时间: 2022-09-29 15:10-17:00
报告链接: Tencent Meeting ID: 280-219-727
信息来源: https://www.math.pku.edu.cn/kxyj/xsbg/tlb/probabilityandstatistics/143386.htm
报告摘要:
Large-scale online platforms launch thousands of randomized experiments (a.k.a. A/B tests) every day to iterate their business operations. Consequently, each user of the platform might be treated by a lot of A/B tests simultaneously. This triggers important questions of both academic and practical interests for a platform to best leverage the power of A/B tests: (a) How to estimate and infer the overall treatment effect of multiple experiments on the platform? (b) Without observing the outcomes of all experiment combinations, how to identify the optimal treatment combination? We leverage a novel framework that combines deep learning (DL) and double machine learning (DML) to estimate the heterogeneous treatment effect (HTE) of any treatment combination for each user on the platform. Our proposed neural network architecture combines interpretable and flexible structural layers. Our framework (called debiased deep learning, DeDL) exploits Neyman orthogonality and yields consistent and asymptotically normal estimators, thus allowing for valid inference of the treatment effects and best-arm identification. Furthermore, we collaborate with a large-scale video-sharing platform (Platform O) and implement our framework for 3 independent A/B tests on Platform O. Our DeDL approach outperforms the linear-regression- and deep-learning-based benchmarks to accurately estimate and infer the average treatment effects of any treatment combination, and to correctly identify the best-arm. Our statistical framework is further validated with synthetic data, which demonstrates its robust performance under model misspecification. From an application standpoint, this is the first study in the literature to validate the practical strength of the theoretically elegant DML method for causal inference by leveraging data from large-scale field experiments.
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16. Geometric Deep Learning: Grids, Graphs, Groups, Geodesics and Gauges
Speaker: Petar Veličković (DeepMind and University of Cambridge)
Time: 2022-9-29, 17:00-18:00 Libson time
Registration Link and Info Source:
https://mpml.tecnico.ulisboa.pt/seminars?id=6632
Abstract:
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach — such as computer vision, playing Go, or protein folding — are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation.
While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This talk is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications.
Such a 'geometric unification' endeavour in the spirit of Felix Klein's Erlangen Program serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.
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17. High-order Gas-kinetic schemes under finite difference and spectral difference frameworks
信息来源:
https://www.math.hkust.edu.hk/events/?date=9/24/2022
18. High-dimensional Quantile Tensor Regression
报告人: Zhongyi Zhu (Fudan University)
报告时间: 2022-09-30 10:00-11:00
报告链接: Tencent Meeting ID: 511-589-604
信息来源: https://www.math.pku.edu.cn/kxyj/xsbg/tlb/probabilityandstatistics/143389.htm
报告摘要:
Tensor data refers to data in the form of multidimensional arrays, which are widely available in many fields such as medical research, image analysis, recommendation systems, signal processing, network data, etc. In this talk, we study high-dimensional quantile regression with tensor covariates and proposed an estimator based on convex regularization and an estimator based on tensor decomposition. We also propose an alternating update algorithm combined with alternating direction method of multipliers (ADMM). The asymptotic properties of the estimators are established under suitable conditions. The numerical performances are demonstrated via simulations and an application to a crowd density estimation problem.
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19. Global Dynamics of a Predator-Prey Model in Open Advective Environments
报告人: 聂华（陕西师范大学）
报告时间: 2022-09-30 10:30-11:30
报告链接: 腾讯会议ID: 570-101-854
信息来源:
https://math.sustech.edu.cn/seminar_all/12480.html
报告摘要:
We discuss a system of reaction-diffusion-advection equations for a generalist predator-prey model in open advective environments, subject to an unidirectional flow. In contrast to the specialist predator-prey model, the dynamics of this system is more complex. It turns out that there exist some critical advection rates and predation rates, which classify the global dynamics of the generalist predator-prey system into three or four scenarios: (i) coexistence; (ii) persistence of prey only; (iii) persistence of predators only; and (iv) extinction of both species. Moreover, the results reveal significant differences between the specialist predator-prey system and the generalist predator-prey system, including the evolution of the critical predation rates with respect to the ratio of the flow speeds; the take-over of the generalist predator; and the reduction in parameter range for the persistence of prey species alone. These findings may have important biological implications on the invasion of generalist predators in open advective environments.
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20. Data-driven optimization---integrating data sampling, learning and optimization
报告人: Wei Chen（Microsoft research Asia）
报告时间: 2022-09-30 16:00-17:00
报告链接: ZoomID: 271 534 5558 密码: YMSC
信息来源:
https://ymsc.tsinghua.edu.cn/info/1056/2975.htm
报告摘要:
Traditionally machine learning and optimization are two different branches in computer science. They need to accomplish two different types of tasks, and they are studied by two different sets of domain experts. Machine learning is the task of extracting a model from the data, while optimization is to find the optimal solutions from the learned model. In the current era of big data and AI, however, such separation may hurt the end-to-end performance from data to optimization in unexpected ways. In this talk, I will introduce the paradigm of data-driven optimization that tightly integrates data sampling, machine learning, and optimization tasks. I will mainly explain two approaches in this paradigm, one is optimization from structured samples, which carefully utilizes the structural information from the sample data to adjust the learning and optimization algorithms; the other is combinatorial online learning, which adds feedback loop from the optimization result to data sampling and learning to improve the sample efficiency and optimization efficacy. I will illustrate these two approaches through my recent research studies in these areas.
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21. On preconditioned iteration methods for saddle point problems from Eddy current models
报告人: 任志茹 (中央财经大学)
报告时间: 2022-10-01 10:00-11:00
报告链接: 腾讯会议ID: 868 725 131
信息来源:
http://www.amss.cas.cn/mzxsbg/202209/t20220921_6515578.html
报告摘要:
For the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem, we present several different splitting preconditioners which are based on splittings of the saddle point matrix. We analyze the convergences of the corresponding splitting iteration methods, and discuss the computing procedures which is much easier to implement than
the existing preconditioners when they are used to accelerate the convergence rate of Krylov subspace methods such as GMRES. Numerical examples are given to show the effectiveness of our proposed preconditioners.
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22. Randomized methods of matrix decompositions and its applications
报告人: 任志茹 (中央财经大学)
报告时间: 2022-10-01 11:00-12:00
报告链接: 腾讯会议ID: 868 725 131
信息来源:
http://www.amss.cas.cn/mzxsbg/202209/t20220921_6515579.html
报告摘要:
Matrix decompositions are fundamental tools in the area of applied mathematics,statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital and widely used for data analysis, dimensionality reduction and data compression. Massive datasets, however, pose a computational challenge for traditional algorithms, placing significant constraints on both memory and processing power. Recently, the powerful concept of randomness has been introduced as a strategy to ease the computational load. In this talk, we will discuss randomized algorithms of some basic matrix decompositions and its applications.
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23. How many PDE numerical eigenvalues can we trust, and how to get more out of it?
报告人: Zhimin Zhang (Wayne state university)
报告时间: 2022-10-12 10:00-11:00
报告链接: 腾讯会议ID: 359 771 916
信息来源:
http://www.amss.cas.cn/mzxsbg/202209/t20220922_6516142.html
报告摘要:
When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element, it is common knowledge that only a small portion of numerical eigenvalues are reliable. However, this knowledge is only qualitative rather than quantitative in the literature. In this talk, we will investigate the number of "trusted" eigenvalues by the finite element(and the related finite difference method results obtained from mass lumping) approximation of 2mth order elliptic PDE eigenvalue problems. Our two model problems are the Laplace and bi-harmonic operators, for which a solid knowledge regarding magnitudes of eigenvalues are available in the literature. Combining this knowledge with a priori error estimates of the finite element method, we are able to figure out roughly how many "reliable" eigenvalues can be obtained from numerical approximation under a pre-determined convergence rate.
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24. Why spectral methods are preferred in PDE eigenvalue computations in some cases?
报告人: Zhimin Zhang (Wayne state university)
报告时间: 2022-10-12 11:00-12:00
报告链接: 腾讯会议ID: 359 771 916
信息来源:
http://www.amss.cas.cn/mzxsbg/202209/t20220922_6516144.html
报告摘要:
We know that only a small portion of numerical eigenvalues are reliable when approximating PDE eigenvalue problems by finite difference and finite element methods. As a comparison, spectral methods may perform extremely well in some situation, especially for 1-D problems. In addition, we demonstrate that
spectral methods can outperform traditional methods and the state-of-the-art method in 2-D problems even with singularities.
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