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第七届电子科技大学国际青年学者论坛-数学科学分论坛

时间:2019-12-13 17:00      来源:新皇冠体育

第七届电子科技大学国际青年学者论坛

数学科学分论坛日程

 


附:学术报告详情


报告一:Data-driven reduced order modelling and its applications

报告人:英国斯旺西大学 肖敦辉

摘要:计算模拟是人类认识自然界和地球复杂系统的重要手段。计算模拟是通过计算机求解描述自然或地球科学问题的偏微分方程来实现。由于地球系统的复杂、混沌、非线性以及高维度,求解此类偏微分方程的计算模型涉及到大量的数据以及矩阵运算,就连最先进的计算机也无法准确而快速的进行模拟。降阶模型为这个问题提高了解决途径。降阶模型能显著提高计算效率100-10000倍同时又保证了精度。降阶模型让各种需要运行计算模型成千上万次的应用问题比如飞机形体设计,参数敏感性分析、不确定性分析等问题成为可能。

近年来,数据科学以及深度学习的快速发展为模拟复杂非线性等问题提供了重要基础。本报告将探讨基于数据驱动降阶模型的理论以及地球科学以及工程科学领域如空气污染、洪水、城市流体、石油油藏模型等的应用。

报告人简介:

肖敦辉,男,目前就职于英国斯旺西大学有限元方法之父的Zienkiewicz工程计算中心担任讲师(助理教授),博士生导师。肖敦辉博士2013年获帝国理工全奖开始攻读计算流体力学博士,于2016年获博士学位。之后在帝国理工地球科学系和数据科学所从事博士后研究,于201810月开始在斯旺西大学担任讲师,博士生导师。肖博士以第一作者或通讯作者身份发表SCI 论文20篇,其中大多数都发表在计算力学领域顶级期刊上。

肖博士一直致力于地球科学领域基础计算方法研究。在帝国理工学习工作的七年多时间里,肖博士在基于数据驱动的计算模型领域取得了一系列的成果。由于在此领域的贡献,肖博士曾被帝国理工授予了最佳科研博士生(一年只授予一个学术最佳的博士生,经常空缺)。近年来,肖博士逐步从传统的计算模型降阶算法研究转向数据驱动的偏微分方程描述,并开发了一套数据驱动模型降阶理论以解决传统物理问题低维描述过程中一些长期悬而未决的问题如稳定性与非线性低效问题。


报告二:Toda-type lattices and their applications

报告人:墨尔本大学 李世豪

摘要:Fifty years ago, Morikazu Toda considered the interactions between the neighbouring lattices of the string by the exponential potential and found the celebrated Toda lattice. Later on, its classical integrability and explicit solutions were obtained and many applications of the Toda lattice were made. Its interplays with the orthogonal polynomials, matrix models and 2d gravity have attracted many scholars' attention. Besides, it relates to many branches of mathematical theories such as integrable geometry, integrable combinatorics, integrable probability and so on. In this talk, I will firstly discuss about the integrable property of the Toda lattice and its connections with other subjects, then give a brief introduction to my own works, mainly on the discoveries about the other types of Toda lattices as well as their interplays with other subjects.

报告人简介:

李世豪,2018年于中国科学院数学与系统科学研究院获得理学博士学位。现在在墨尔本大学从事博士后研究。专业方向为数学物理,尤其是可积系统,随机矩阵理论与特殊函数理论的研究。研究结果发表在Comm. Math. Phys., Adv. Math., Trans. AMS, IMRN, J. Nonlinear Sci., Nonlinearity, J. Diff. Equations等期刊上。


报告三:Second law of thermodynamics and bounded entropy solutions in the compressible Navier-Stokes system

报告人: Freie Universitaet Berlin 刘欣

摘要: Our goal is to investigate the existence of global-in-time solutions to the compressible Navier-Stokes system. Previous study of Cauchy problems motivates the free boundary problem, where the flows connect to vacuum with continuous density on the moving boundary. We mainly focus on the spherically symmetric solutions. A class of self-similar solutions are presented, and the bounded entropy solutions are obtained with initial data perturbed around such self-similar data.

报告人简介:

刘欣, 2017年博士毕业于香港中文大学. 2017--2019年于 Texas A&M 任博士后/Visiting assistant professor. 现为 Freie Universitaet Berlin 博士后. 专业方向: 流体方程. 应用范围: well-posedness of compressible Navier-Stokes system; asymptotic stability; well-posedness of geophysics equations; asymptotic limits, etc. 发表学术论文: SIAM J. Math. Anal., Nonlinear Analysis, Nonlinearity, JDE, M3AS, etc.


报告四:Rational curves on hypersurfaces

报告人:美国西北大学 王远

摘要:It is a well known fact that a general hyperplane of degree d in Pn is rationally connected if d ≤ n, but contains very few curves if d ≥ n+1. More generally let X be a smooth projective variety and H a hypersurface of X such that KX +H is anti-ample, then by the adjunction formula and a classical result we know that H is rationally connected. We use the minimal model program as well as other techniques in birational geometry to study further how the behavior of rational curves on X as well as the positivity of (KX + H) and H influence the behavior of rational curves on H. In this talk I will present several results and examples of this kind. In particular we will see criteria for uniruledness and rational connectedness of H.

报告人简介:

王远,2017年于美国犹他大学获得数学博士。现在在美国西北大学数学系任职Boas Assistant Professor。专业方向:代数几何(双有理几何,极小模型),计算几何(拓扑数据分析,流形学习)。在Trans. Amer. Math Soc., Michigan Math J. 等期刊发表了学术论文5篇。


报告五:Collapsing of Non-Centred Parameterised MCMC Algorithms with Application to Epidemic Models

报告人:英国约克圣约翰大学 相斐

摘要:Data augmentation is required for the implementation of many Markov chain Monte Carlo (MCMC) algorithms. The inclusion of augmented data can often lead to conditional distributions from well-known probability distributions for some of the parameters in the model. In such cases, collapsing (integrating out parameters) has been shown to improve the performance of MCMC algorithms. We show how integrating out the infection rate parameter in epidemic models leads to an efficient MCMC algorithm for final outcome data from a multitype SIR epidemic.

报告人简介:相斐, 2012年于英国肯特大学获得统计学博士。之后于英国布里斯托大学,兰卡斯特大学,剑桥大学从事博士后研究。现任英国约克圣约翰大学Senior lecturer。专业方向:生物统计,计算统计。应用范围:高效率马尔可夫链蒙特卡罗(MCMC)算法的构建和疫病数据的应用, 病毒进化与传染统计推断工具的开发。所授课程包括概率论与数理统计,数据科学,R程序。报告人在 Computational Statistics & Data Analysis, Scandinavian Journal of Statistics等统计学术期刊和Virus Evolution等应用期刊上发表学术论文6篇。


报告六:A frequency/time hybrid integral solver for wave propagation in a bounded domain

报告人:美国加州理工学院 殷涛

摘要:In this talk, a fast and high-order frequency/time hybrid integral solver will be introduced for solving the wave equation problems in a bounded domain. A novel multiple scattering strategy is developed to reduce the original problem into a coupling of scattering problems in semi-infinity waveguides. Based on the eigenmode expansion, an integral equation method is proposed for the frequency-domain waveguide problems and as a result, high accuracy can be achieved for all frequencies (far/near eigenvalues). Combining with forward/backward Fourier transform and appropriate quadrature rules leads to a frequency/time hybrid integral solver whose efficiency and accuracy will be showed via several numerical examples.

报告人简介:

殷涛,美国加州理工学院计算与数学科学系博士后。2011年和2015年分别本科、博士毕业于重庆大学,期间受国家基金委资助在德国柏林工业大学联合培养。曾在浙江大学和法国格勒诺布尔大学从事博士后研究工作。主要研究兴趣包括声波、弹性波正反散射问题的数学理论和数值方法,边界积分方程科学计算等,已在SIAM系列(SINUM,SISC,SIAP,JCP,J. Math. Pure Appl.,Inverse Problems,Comput. Meth. Appl. Mech. Eng.等期刊发表14篇论文。




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