第十二届国际青年学者东湖论坛-数学与统计学院分论坛

时  间：2023年12月26日14：30-18:00

地  点：东三十二楼115会议室

主持人：王保伟

议 程：

1、王文重书记致开幕辞，刘斌院长介绍学院学科建设发展情况和人才政策。

2、学者、学院教师学术汇报。

3、学院领导及相关学术骨干与学者互动交流。

学术汇报：

（一）

报告人： 刘常钰

个人简介：刘常钰，香港中文大学博士后研究员，主要从事Machine Learning,High-Dimensional Statistics,Survival Analysis和Graphical Model 研究，以一作作者在JASA, Statistica Sinica期刊上发表SCI论文, 且正在有一篇文章在Biometrika under major revision。其中JASA和Biometrika为统计领域顶刊。

报告题目：Conditional Generative Learning and Adversarial Risk

报告摘要：Censored data is frequently encountered in diverse fields such as modern medicine, econometrics and social science. Its partially observable characteristics present significant challenges for analysis, and existing methods often suffer from reduced efficiency and accuracy in complex settings due to misspecified underlying models and high dimensionality. To address this problem, we propose a novel deep generative approach for nonparametric estimation problem of censored data, requiring no explicit model assumption. The proposed method combines ideas from deep generative learning and classical nonparametric estimation in survival analysis, and is applied to estimate the conditional survival and hazard functions with right-censored data, as well as the conditional cumulative distribution function with current status data. We also study the convergence properties of the proposed estimator and establish its consistency. To provide a general theoretical understanding for the estimation framework, we link it with adversarial risk and propose a general approach to evaluate the performance of estimators based on adversarial losses under misspecified models.

（二）

报告人： 韩梦捷

个人简介：韩梦捷，达拉纳大学副教授，主要从事统计学、数据分析、优化等研究，以一作或通讯作者发表在Applied Soft Computing， Sustainable Cities and Socitey等期刊上发表SCI论文7余篇，其中A类2篇，累计他引（Google Scholar引用）1873次，单篇引用最高621次；主持EU项目1项，研究经费约130万人民币。

报告题目：PML-ED：A Method of Partial Multi-label Learning by Using Encoder-Decoder Framework

报告摘要：Partial multi-label learning (PML) addresses problems where each instance is assigned a candidate label set and only a subset of these candidate labels is correct. The major challenge of PML is that the training procedure can be easily misguided by noisy labels. Current studies on PML have revealed two significant drawbacks. First, most of them do not sufficiently explore complex label correlations, which could improve the effectiveness of label disambiguation. Second, PML models heavily rely on prior assumptions, limiting their applicability to specific scenarios. We propose a novel method of PML based on the Encoder-Decoder Framework (PML-ED) to address the drawbacks. PML-ED initially achieves the distribution of label probability through a KNN label attention mechanism.It then adopts Conditional Layer Normalization (CLN) to extract the high-order label correlation and relaxes the prior assumption of label noise by introducing a universal Encoder-Decoder framework. This approach makes PML-ED not only more efficient compared to the state-of-the-art methods, but also capable of handling the data with large noisy labels across different domains. Experimental results on 28 benchmark datasets demonstrate that the proposed PML-ED model, when benchmarked against nine leading-edge PML algorithms, achieves the highest average ranking across five evaluation criteria.

（三）

报告人：谈进

个人简介：谈进，CY Cergy Paris University博士后，主要从事流体力学和磁流体力学中偏微分方程的数学理论研究, 特别是 Navier-Stokes方程和带有霍尔效应的磁流体力学方程的定性和定量研究。在 Communications in Partial Differential Equations, Journal of Differential Equations,Communications in Contemporary Mathematics，Mathematical Models and Methods in Applied Sciences等期刊发表论文若干。

报告题目：Free boundary regularity of vacuum states for incompressibleviscous flows in unbounded domains

报告摘要：In a well-known book of P.-L. Lions, global existence results for finite energy weak solutions of the inhomogeneous incompressible Navier-Stokes equations (INS) were proved without assuming positive lower bounds on the initial density, hence allowing for vacuum. Uniqueness, regularity of Lions’ weak solutions and persistence of boundary regularity of density patches were listed as open problems. In the case where the fluid domain is either bounded or the torus, Lions’ problem has been understood well nowadays. However, the case of unbounded domains was left open. In this talk, I will present some regularity and uniqueness results of Lions’ weak solutions for (INS) with additional regularity only assumed for the initial velocity, in the whole space case. As an application, I will explain how these results imply persistence of boundary regularity of a density patch and a vacuum bubble in the whole space. The talk is based on a recent work with my mentor Christophe Prange (CY Cergy Paris University).

（四）

报告人：黄山林

个人简介：黄山林，18luck新利电竞 数学与统计学院副教授，研究方向为调和分析及其应用，目前主要从事不确定原理、薛定谔方程解的定量唯一性及有关控制问题的研究，相关关工作发表于AJM、CMP、Adv. Math、JFA、JDE等期刊。

报告题目：Uncertainty principle, unique continuation and control

报告摘要：The uncertainty principle, which describes the dual relationship between physical space and frequency space, is ubiquitous in Harmonic Analysis. In this talk, we are mainly concerned with its applications in unique continuation and control of solutions of PDEs. In particular, we focus on the Schrodinger equation with potentials and show that some variable coefficient versions of uncertainty principles play a key role. Finally, we review some recent progress on the Heisenberg uniqueness pair (HUP), which was first introduced by Hedenmalm and Montes-Rodriguez in 2011.

（五）

报告人：孟旭辉

个人简介：孟旭辉，2017年博士毕业于18luck新利电竞 能源与动力工程学院，2018年-2022年美国布朗大学应用数学系博士后，2022年3月至今任18luck新利电竞 数学与统计学院数学与应用学科交叉创新研究院副教授。主要研究方向为数据驱动的深度学习建模及其应用。截至目前已在JCP、CMAME、SIAM Review等期刊发表SCI论文20余篇，谷歌学术总引用3500余次，6篇ESI高被引论文；担任JCP、SISC、CMAME、Nat. Comput. Sci .等期刊审稿人。

报告题目：Machine learning for multi-fidelity data fusion with uncertainty quantification

报告摘要：The recent rapid developments in machine learning have also influenced the computational modeling of physical systems, e.g. in geosciences and engineering. Generally, large numbers of high-fidelity data sets are required for optimization of complex physical systems, which may lead to computationally prohibitive costs. On the other hand, inadequate high-fidelity data result in inaccurate approximations and possibly erroneous designs. Multi-fidelity modeling has been shown to be both efficient and effective in achieving high accuracy in diverse applications by leveraging both the low- and high-fidelity data. In this talk, I will introduce several newly developed machine learning algorithms for multi-fidelity data fusion as well as their applications: (1) a composite neural network that learns from multi-fidelity data; (2) multi-fidelity Bayesian neural networks for quantifying uncertainties in predictions; and (3) applications of the proposed machine learning algorithms in various scientific and engineering disciplines.