一周活动预告（5.29-6.5）
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目录：
Modeling and optimization for interconnected control systems, and flexible manufacturing system（Yan Wang）
Some applications of optimal transportation （Jiakun Liu）
周期运动与能量守恒 （龙以明）
A general alternating-direction implicit framework with Gaussian process regression parameter prediction for large sparse linear systems （张娟）
Deep Learning Application in Gastrointestinal Cancer — From Diagnosis to Survival Prediction（Zhangsheng Yu）
Mean Field Description for Residual Neural Networks（Michael Herty）
Advances in Quantum Chemistry Simulation（Dominic Berry）
数学之美与应用 （丘成桐）
Understanding the Learning Paradigm of Non-Autoregressive Machine Translation（Hao Cheng）
A sequential discontinuous Galerkin method for two-phase flow in deformable porous media （Boqian Shen）
An SIR contact tracing model for randomly mixed populations （Junling Ma）
Compact exponential structure-preserving approaches for the Schrodinger-type equations （蔡加祥）
Machine Learning and LHC Event Generation (Anja Butter)
流形赋值的纵向形状数据分析（ 应时辉 ）
Quantum algorithms for nonlinear partial differential equations（金石）
A statistical learning perspective of data-driven model reduction （Fei Lu）
1. Modeling and optimization for interconnected control systems, and flexible manufacturing system
报告人: Yan Wang
报告时间: 2022-5.29 15:00-16:00
报告链接: 腾讯会议ID: 675 958 042
信息来源:
http://www.amss.cas.cn/mzxsbg/202205/t20220527_6454939.html
报告摘要:
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2. Some applications of optimal transportation
报告人: Jiakun Liu （University of Wollongong ）
报告时间: 2022-5.30 10:00-11:30
报告链接: 腾讯会议ID: 282 944 594
信息来源:
http://math.xjtu.edu.cn/info/1089/11310.htm
报告摘要:
In this talk, we will introduce some interesting applications of optimal transportation in various fields including a reconstruction problem in cosmology; a brief proof of isoperimetric inequality in geometry; and an application in image recognition relating to a transport between hypercubes. Our research focuses on the regularity theory for Monge-Ampere type equations, in particular the recent established global regularity results. This talk is based on a series of joint work with Shibing Chen, Xu-Jia Wang, and with Gregoire Loeper.
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3. 周期运动与能量守恒
报告人: 龙以明 （南开大学）
报告时间: 2022-5.30 15:00-16:00
报告链接: 腾讯会议ID: 895 395 833
信息来源:
http://tianyuan.scu.edu.cn/portal/article/index/id/612/pid/0/cid/3.html
报告摘要:
在此报告中，我将回顾由研究星体的周期运动产生的关于哈密顿系统的周期解轨道的研究近几百年来的发展，介绍目前关于能量曲面上的周期解轨道的研究现状。
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4. A general alternating-direction implicit framework with Gaussian process regression parameter prediction for large sparse linear systems
报告人: 张娟 （湘潭大学）
报告时间: 2022-5.31 10:00-11:00
报告链接: 腾讯会议ID: 345 773 4983
信息来源:
http://tmcc.whu.edu.cn/info/1102/1981.htm
报告摘要:
In this talk, we propose an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of the existing ADI methods can be viewed as particular schemes of the developed framework. Meanwhile the GADI framework can derive new ADI methods. Moreover, as the algorithm efficiency is sensitive to the splitting parameters, we offer a data-driven approach, the Gaussian process regression (GPR) method based on the Bayesian inference, to predict the GADI framework's relatively optimal parameters. The GPR method requires a small training data set to learning the regression prediction mapping, which has both sufficient accuracy and high generalization capability. It allows us to efficiently solve linear systems with a one-shot computation, and does not require any repeated computations to obtain relatively optimal splitting parameters. Finally, we use the three-dimensional convection-diffusion equation and continuous Sylvester matrix equation to examine the performance of our proposed methods. Numerical results demonstrate that the proposed framework is faster tens to thousands of times than the existing ADI methods, such as (inexact) Hermitian and skew-Hermitian splitting type methods in which the consumption of obtaining relatively optimal splitting parameters is ignored. Due to the efficiency of the developed methods, we can solve much large linear systems which these existing ADI methods have been not reached.
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5. Deep Learning Application in Gastrointestinal Cancer — From Diagnosis to Survival Prediction
Speaker: Zhangsheng Yu（Shanghai Jiao Tong University）
Time: 2022-05-31 10:00-11:00
Venue:
Zoom Meeting ID: 826 7530 1781 Password: 123456
Tencent Meeting ID: 629-991-968 Password: 189114
Info Source:
https://ins.sjtu.edu.cn/seminars/2098
Abstract:
In this talk, I will first present deep learning algorithm for liver cancer diagnosis. Liver cancers are most diagnosed through multi-phase contrast enhanced CT imaging. We propose a Spatial Extractor-Temporal Encoder-Integration-Classifier design to integrate the temporal information of multi-phase contrast enhanced CT imaging for liver cancer. Through this model, we incorporate the clinical and imaging information and utilized the temporal pattern of CT imaging to enhance the accuracy of diagnosis to a similar level of radiologists with 5-year experience. I will also present a survival prediction model of liver cancer patients by integrating the clinical, genetic, and pathology image. For the survival model with a cure rate, we develop a cure rate model with imaging input using neural network.
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6. Mean Field Description for Residual Neural Networks
Speaker: Michael Herty（RWTH Aachen University）
Time: 2022-05-31 16:00-17:00
Venue: VooV Meeting ID: 388853031 Password: 188279
Info Source:
https://ins.sjtu.edu.cn/seminars/2108
Abstract:
Nowadays, neural networks are widely used in many applications as artificial intelligence models for learning tasks. Since typically neural networks process a very large amount of data, it is convenient to formulate them within the mean-field and kinetic theory. In this work we focus on a particular class of neural networks, i.e. the residual neural networks, assuming that each layer is characterized by the same number of neurons N, which is fixed by the dimension of the data. This assumption allows to interpret the residual neural network as a time-discretized ordinary differential equation, in analogy with neural differential equations. The mean-field description is then obtained in the limit of infinitely many input data. This leads to a Vlasov-type partial differential equation which describes the evolution of the distribution of the input data. We analyze steady states and sensitivity with respect to the parameters of the network, namely the weights and the bias. In the simple setting of a linear activation function and one-dimensional input data, the study of the moments provides insights on the choice of the parameters of the network. Furthermore, a modification of the microscopic dynamics, inspired by stochastic residual neural networks, leads to a Fokker-Planck formulation of the network, in which the concept of network training is replaced by the task of fitting distributions. The performed analysis is validated by artificial numerical simulations. In particular, results on classification and regression problems are presented.
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7. Advances in Quantum Chemistry Simulation
Speaker: Dominic Berry（Macquarie University）
Time: 2022-06-01 14:00-15:00
Venue: Tencent Meeting ID: 666587839 Password: 187521
Info Source:
https://ins.sjtu.edu.cn/seminars/2114
Abstract:
Simulation of quantum chemistry is a leading potential application of quantum computers, because it provides a natural speedup over classical computing, and can provide information of tremendous value. For example, FeMoco is a biological chemical involved in nitrogen fixing, but is beyond classical computing capability. Nitrogen fixing is used on a grand scale for producing fertiliser, and has an inefficient industrial process. Better understanding of the biological process could lead to more efficient fertiliser production. Initial quantum algorithms for simulation were very slow, and led to predicted computation times of many years even on large-scale quantum computers. We have introduced a wide range of new methods that greatly reduce the computation time over these initial algorithms, by more than a factor of 1000.
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8. 数学之美与应用
信息来源:
https://math.seu.edu.cn/2022/0524/c16339a408669/page.htm
9. Understanding the Learning Paradigm of Non-Autoregressive Machine Translation
报告人: Hao Cheng (PKU)
报告时间: 2022-06-01 15:10-16:10
报告地点: 腾讯会议ID: 723 1564 5542
信息来源: https://www.math.pku.edu.cn/kxyj/xsbg/tlb/informationsciences/140684.htm
报告摘要:
Non-autoregressive machine translation (NAT) models generate the entire target sentence in parallel by removing the dependency between target tokens to improve the inference speed. However, this strong independence assumption between target tokens also brings many problems and increases the difficulty of the task. There is still a certain gap between NAT models and state-of-the-art autoregressive models. In this talk, we will start from the background of NAT, then we will focus on the learning paradigm in NAT, including objective functions and learning strategies. The former alleviates the limitation of cross-entropy in NAT, and the latter simplifies the difficulty of NAT task learning.
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10. A sequential discontinuous Galerkin method for two-phase flow in deformable porous media
报告人: Boqian Shen （King Abdullah University）
报告时间: 2022-6-1 19:30-20:30
报告链接: 腾讯会议ID: 463 7874 0598
信息来源:
http://www.cc.ac.cn/news/seminars.html
报告摘要:
We formulate a numerical method for solving the two-phase flow poroelasticity equations. The scheme employs the interior penalty discontinuous Galerkin method and a sequential time-stepping method. The unknowns are the phase pressures and the displacement. Existence of the solution is proved. Three-dimensional numerical results show the accuracy and robustness of the proposed method.
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11. An SIR contact tracing model for randomly mixed populations
报告人: Junling Ma （University of Victoria）
报告时间: 2022-6.2 10:00-12:00
报告链接: 腾讯会议ID: 921 251 724 密码: 0602
信息来源:
http://math.xjtu.edu.cn/info/1089/11326.htm
报告摘要:
Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments.
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12. Compact exponential structure-preserving approaches for the Schrodinger-type equations
报告人: 蔡加祥 （淮阴师范学院）
报告时间: 2022-6.2 19:00-20:00
报告链接: 腾讯会议ID: 989 282 406
信息来源:
http://www.cc.ac.cn/news/seminars.html
报告摘要:
The energy and mass conservation/dissipation laws are important physical features of the Schrodinger-type equations. This talk is mainly concerned with some efficient exponential prediction-correction structure-preserving approaches for the equations. Numerical results demonstrate the power of the proposed methods in the simulations.
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13. Machine Learning and LHC Event Generation
Speaker: Anja Butter, ITP, University of Heidelberg
Time: 2022-6-2，17:00–18:00 Europe/Lisbon
Registration Link and Info Source:
https://mpml.tecnico.ulisboa.pt/seminars?id=6619
Abstract:
First-principle simulations are at the heart of the high-energy physics research program. They link the vast data output of multi-purpose detectors with fundamental theory predictions and interpretation. In the coming LHC runs, these simulations will face unprecedented precision requirements to match the experimental accuracy. New ideas and tools based on neural networks have been developed at the interface of particle physics and machine learning. They can improve the speed and precision of forward simulations and handle the complexity of collision data. Such networks can be employed within established simulation tools or as part of a new framework. Since neural networks can be inverted, they open new avenues in LHC analyses
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14. 流形赋值的纵向形状数据分析
报告人: 应时辉 教授（上海大学）
报告时间: 2022-6-4 9:00—12:00
报告地点: 腾讯会议ID: 234 599 930
信息来源:
http://math.hit.edu.cn/2022/0527/c10234a274757/page.htm
报告摘要:
（1）在现实应用领域中存在大量数据或者数据的观测分布在特定的低维流形上。因此，如何对这样的数据进行内蕴分析就成为一个重要问题。本报告在数据观测构成低维流形的假设下，从模型和数据双驱动的角度建立流形上的半参回归模型。
（2）针对部分线性模型，给出模型的渐进性分析。首先，通过引入随机因素，构建流形上的混合效应模型。在此基础上，提出一个异常点判断依据。最后，通过在多个流形观测实际问题上的数值实验验证所提模型有更高的逼近精度。
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15. Quantum algorithms for nonlinear partial differential equations
报告人: 金石 教授（上海交通大学）
报告时间: 2022-6-4 14:00-17:00
报告地点: 腾讯会议ID: 214 905 299
信息来源:
http://math.hit.edu.cn/2022/0527/c10234a274760/page.htm
报告摘要:
（1）Nonlinear partial differential equations (PDEs) are crucial to modelling important problems in science but they are computationally expensive and suffer from the curse of dimensionality. Since quantum algorithms have the potential to resolve the curse of dimensionality in certain instances, some quantum algorithms for nonlinear PDEs have been developed. However, they are fundamentally bound either to weak nonlinearities, valid to only short times, or display no quantum advantage. We construct new quantum algorithms--based on level sets --for nonlinear Hamilton-Jacobi and scalar hyperbolic PDEs that can be performed with quantum advantages on various critical numerical parameters, even for computing the physical observables, for arbitrary nonlinearity and are valid globally in time.
（2）PDEs are important for many applications like optimal control, machine learning, semi-classical limit of Schrodinger equations, mean-field games and many more. Depending on the details of the initial data, it can display up to exponential advantage in both the dimension of the PDE and the error in computing its observables. For general nonlinear PDEs, quantum advantage with respect to M, for computing the ensemble averages of solutions corresponding to M different initial data, is possible in the large $M$ limit.
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16. A statistical learning perspective of data-driven model reduction
报告人: Fei Lu （Johns Hopkins University）
报告时间: 2022-6.6 10:00-11:00
报告链接: 腾讯会议ID: 317 978 360
信息来源:
http://www.cc.ac.cn/news/seminars.html
报告摘要:
Fast simulations of differential equations(DE) are crucial for ensemble predictions in uncertainty quantification, with many applications ranging from weather forecasting to finance. However, classical numerical methods are often computationally prohibitive for such tasks, because these DEs are often high-dimensional and stiff. Data-driven reduced models have succeeded in such tasks by focusing computational resources on the quantities of interest with the help of data. In this talk, I will cast the data-driven reduced model as an inference-based approximation of the discrete-time flow map for the dynamics of the variables of interest. This flow map approximation framework presents fruitful connections between classical numerical methods and data-driven machine learning methods.
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