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徐文青

教授
博士生导师

数学统计学与力学学院

徐文青，教授、博士生导师。 1992年 中国科学技术大学数学系 获学士学位。 1995年 中国科学院数学研究所 获硕士学位。 1999年 美国纽约大学库朗数学科学研究所 获应用数学博士学位。 1999-2002 美国麻州州立大学 做博士后。 2002年 起在美国加州州立大学长滩分校任教 先后任职助理教授、副教授、教授。 2012年 入选北京市第八批“海聚”工程（全职类）。 2013年 加入北京工业大学。 主要从事应用数学及相关交叉学科的研究工作(涉及偏微分方程，数值分析， 概率及随机过程，编码及信息论等研究方向)。

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A game-theoretic perspective of deep neural networks SCIE
期刊论文 | 2023 , 939 , 48-62 | THEORETICAL COMPUTER SCIENCE
Ren, Chunying | Wu, Zijun | Xu, Dachuan | Xu, Wenqing Unfold
Article has an altmetric score of 1
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Abstract ：

We devote this paper to a theoretic analysis of deep neural networks from a gametheoretical perspective. We consider a general deep neural network D with linear activation functions f (x) = x + b. We show that the deep neural network can be transformed into a non-atomic congestion game, regardless whether it is fully connected or locally connected. Moreover, we show that learning the weight and bias vectors of D for a training set H is equivalent to computing an optimal solution of the corresponding non-atomic congestion game. In particular, when D is a deep neural network for a classification task, then the learning is equivalent to computing a Wardrop equilibrium of the corresponding non-atomic congestion game. (c) 2022 Elsevier B.V. All rights reserved.

Keyword ：

Wardrop equilibria Wardrop equilibria Local minima Local minima Deep neural networks Deep neural networks Non -atomic congestion game Non -atomic congestion game

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GB/T 7714 Ren, Chunying , Wu, Zijun , Xu, Dachuan et al. A game-theoretic perspective of deep neural networks [J]. | THEORETICAL COMPUTER SCIENCE , 2023 , 939 : 48-62 .
MLA Ren, Chunying et al. "A game-theoretic perspective of deep neural networks" . | THEORETICAL COMPUTER SCIENCE 939 (2023) : 48-62 .
APA Ren, Chunying , Wu, Zijun , Xu, Dachuan , Xu, Wenqing . A game-theoretic perspective of deep neural networks . | THEORETICAL COMPUTER SCIENCE , 2023 , 939 , 48-62 .
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Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity SCIE
期刊论文 | 2021 , 72 (3) | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Wang, Shasha | Xu, Wen-Qing | Liu, Jitao
Article has an altmetric score of 1
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Abstract ：

In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system by imposing natural boundary conditions and regularity assumptions on the initial data, without any compatibility condition.

Keyword ：

2D magneto-micropolar equations 2D magneto-micropolar equations Initial-boundary value problem Initial-boundary value problem Zero angular viscosity Zero angular viscosity

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GB/T 7714 Wang, Shasha , Xu, Wen-Qing , Liu, Jitao . Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity [J]. | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2021 , 72 (3) .
MLA Wang, Shasha et al. "Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity" . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 72 . 3 (2021) .
APA Wang, Shasha , Xu, Wen-Qing , Liu, Jitao . Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2021 , 72 (3) .
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INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION SCIE
期刊论文 | 2020 | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
Fan, Xiaoting | Wang, Shu | Xu, Wen-Qing
WoS CC Cited Count： 3
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Abstract ：

This article concerns the initial-boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with ill-prepared initial data. We consider a non-slip boundary condition for the velocity field and inhomogeneous Dirichlet boundary condition for the temperature. By means of multi-scale analysis and matched asymptotic expansion methods, we establish an accurate approximating solution for the viscous and diffusive Boussinesq system. We also study the convergence of the infinite Prandtl number limit.

Keyword ：

Rayleigh-Benard convection Rayleigh-Benard convection initial-boundary layer initial-boundary layer infinite Prandtl number limit infinite Prandtl number limit Boussinesq system Boussinesq system asymptotic expansion asymptotic expansion

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GB/T 7714 Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing . INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION [J]. | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS , 2020 .
MLA Fan, Xiaoting et al. "INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION" . | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (2020) .
APA Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing . INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION . | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS , 2020 .
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Boundary layer analysis for a 2-D Keller-Segel model SCIE
期刊论文 | 2020 , 18 , 1895-1914 | OPEN MATHEMATICS
Meng, Linlin | Xu, Wen-Qing | Wang, Shu
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Abstract ：

We study the boundary layer problem of a Keller-Segel model in a domain of two space dimensions with vanishing chemical diffusion coefficient. By using the method of matched asymptotic expansions of singular perturbation theory, we construct an accurate approximate solution which incorporates the effects of boundary layers and then use the classical energy estimates to prove the structural stability of the approximate solution as the chemical diffusion coefficient tends to zero.

Keyword ：

energy estimates energy estimates boundary layer phenomenon boundary layer phenomenon Keller-Segel model Keller-Segel model matched asymptotic expansions matched asymptotic expansions

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GB/T 7714 Meng, Linlin , Xu, Wen-Qing , Wang, Shu . Boundary layer analysis for a 2-D Keller-Segel model [J]. | OPEN MATHEMATICS , 2020 , 18 : 1895-1914 .
MLA Meng, Linlin et al. "Boundary layer analysis for a 2-D Keller-Segel model" . | OPEN MATHEMATICS 18 (2020) : 1895-1914 .
APA Meng, Linlin , Xu, Wen-Qing , Wang, Shu . Boundary layer analysis for a 2-D Keller-Segel model . | OPEN MATHEMATICS , 2020 , 18 , 1895-1914 .
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Boundary layers associated with the 3-D Boussinesq system for Rayleigh-Benard convection SCIE
期刊论文 | 2020 , 99 (12) , 2026-2044 | APPLICABLE ANALYSIS
Fan, Xiaoting | Xu, Wen-Qing | Wang, Shu | Wang, Wei Unfold
WoS CC Cited Count： 2
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Abstract ：

We investigate the boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with vanishing diffusivity limit. By adopting the multi-scale analysis and the asymptotic expansion methods of singular perturbation theory, we construct an exact approximating solution for the viscous and diffusive Boussinesq system with well-prepared initial data. In addition, we obtain the convergence result of the vanishing diffusivity limit.

Keyword ：

vanishing diffusivity limit vanishing diffusivity limit boundary layers boundary layers Rayleigh-Benard convection Rayleigh-Benard convection Boussinesq system Boussinesq system asymptotic expansion asymptotic expansion Ming Mei Ming Mei

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GB/T 7714 Fan, Xiaoting , Xu, Wen-Qing , Wang, Shu et al. Boundary layers associated with the 3-D Boussinesq system for Rayleigh-Benard convection [J]. | APPLICABLE ANALYSIS , 2020 , 99 (12) : 2026-2044 .
MLA Fan, Xiaoting et al. "Boundary layers associated with the 3-D Boussinesq system for Rayleigh-Benard convection" . | APPLICABLE ANALYSIS 99 . 12 (2020) : 2026-2044 .
APA Fan, Xiaoting , Xu, Wen-Qing , Wang, Shu , Wang, Wei . Boundary layers associated with the 3-D Boussinesq system for Rayleigh-Benard convection . | APPLICABLE ANALYSIS , 2020 , 99 (12) , 2026-2044 .
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Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane SCIE
期刊论文 | 2019 , 49 , 355-367 | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Liu, Jitao | Xu, Wen-Qing
WoS CC Cited Count： 1
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Abstract ：

In this paper, we study the asymptotic behavior of solutions to second grade fluid equations, a model for viscoelastic fluids, in an expanding domain. We prove that, the solutions converge to a solution of the incompressible Euler equations in the whole plane, as the elastic response alpha and the viscosity nu vanish, and the radius of domain becomes infinite. Meanwhile, we also establish precise convergence rates in terms of nu, alpha and the radius of the family of spatial domains. (C) 2019 Elsevier Ltd. All rights reserved.

Keyword ：

Expanding domain Expanding domain Vanishing viscosity limits Vanishing viscosity limits Vanishing alpha limits Vanishing alpha limits Second grade fluid equations Second grade fluid equations

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GB/T 7714 Liu, Jitao , Xu, Wen-Qing . Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane [J]. | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2019 , 49 : 355-367 .
MLA Liu, Jitao et al. "Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane" . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 49 (2019) : 355-367 .
APA Liu, Jitao , Xu, Wen-Qing . Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2019 , 49 , 355-367 .
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Random Polygons and Estimations of pi SCIE
期刊论文 | 2019 , 17 , 575-581 | OPEN MATHEMATICS
Xu, Wen-Qing | Meng, Linlin | Li, Yong
WoS CC Cited Count： 1
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Abstract ：

In this paper, we study the approximation of pi through the semiperimeter or area of a random n-sided polygon inscribed in a unit circle in R-2. We show that, with probability 1, the approximation error goes to 0 as n -> infinity, and is roughly sextupled when compared with the classical Archimedean approach of using a regular n-sided polygon. By combining both the semiperimeter and area of these random inscribed polygons, we also construct extrapolation improvements that can significantly speed up the convergence of these approximations.

Keyword ：

random polygon random polygon random division random division Borel-Cantelli lemma Borel-Cantelli lemma extrapolation extrapolation Archimedean polygon Archimedean polygon

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GB/T 7714 Xu, Wen-Qing , Meng, Linlin , Li, Yong . Random Polygons and Estimations of pi [J]. | OPEN MATHEMATICS , 2019 , 17 : 575-581 .
MLA Xu, Wen-Qing et al. "Random Polygons and Estimations of pi" . | OPEN MATHEMATICS 17 (2019) : 575-581 .
APA Xu, Wen-Qing , Meng, Linlin , Li, Yong . Random Polygons and Estimations of pi . | OPEN MATHEMATICS , 2019 , 17 , 575-581 .
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On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model SCIE
期刊论文 | 2019 , 43 (2) , 920-938 | MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Meng, Linlin | Xu, Wen-Qing | Wang, Shu
WoS CC Cited Count： 2
Abstract&Keyword Cite

Abstract ：

In this paper, we consider the vanishing viscosity limit problem for a system arising from the Keller-Segel equations in three space dimensions. First, we construct an accurate approximate solution that incorporates the effects of boundary layers. Then, we prove the structural stability of the approximate solution as the chemical diffusion coefficient tends to zero. Our approach is based on the method of matched asymptotic expansions of singular perturbation theory and the classical energy estimates.

Keyword ：

matched asymptotic expansions matched asymptotic expansions energy estimates energy estimates boundary layer phenomenon boundary layer phenomenon chemotaxis chemotaxis Keller-Segel model Keller-Segel model

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GB/T 7714 Meng, Linlin , Xu, Wen-Qing , Wang, Shu . On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2019 , 43 (2) : 920-938 .
MLA Meng, Linlin et al. "On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 43 . 2 (2019) : 920-938 .
APA Meng, Linlin , Xu, Wen-Qing , Wang, Shu . On the vanishing viscosity limit for a 3-D system arising from the Keller-Segel model . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2019 , 43 (2) , 920-938 .
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Initial layer problem of the Boussinesq system for Rayleigh-Benard convection with infinite Prandtl number limit SCIE
期刊论文 | 2018 , 16 , 1145-1160 | OPEN MATHEMATICS
Fan, Xiaoting | Wang, Shu | Xu, Wen-Qing | Liu, Mingshuo Unfold
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Abstract ：

The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Benard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates O (epsilon(3/2)) and O(epsilon(2)).

Keyword ：

Rayleigh-Benard convection Rayleigh-Benard convection Asymptotic expansion Asymptotic expansion Infinite Prandtl number limit Infinite Prandtl number limit Boussinesq system Boussinesq system Initial layers Initial layers Two-time-scale approach Two-time-scale approach

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GB/T 7714 Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing et al. Initial layer problem of the Boussinesq system for Rayleigh-Benard convection with infinite Prandtl number limit [J]. | OPEN MATHEMATICS , 2018 , 16 : 1145-1160 .
MLA Fan, Xiaoting et al. "Initial layer problem of the Boussinesq system for Rayleigh-Benard convection with infinite Prandtl number limit" . | OPEN MATHEMATICS 16 (2018) : 1145-1160 .
APA Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing , Liu, Mingshuo . Initial layer problem of the Boussinesq system for Rayleigh-Benard convection with infinite Prandtl number limit . | OPEN MATHEMATICS , 2018 , 16 , 1145-1160 .
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Random cyclic polygons from Dirichlet distributions and approximations of pi SCIE
期刊论文 | 2018 , 140 , 84-90 | STATISTICS & PROBABILITY LETTERS
Wang, Shasha | Xu, Wen-Qing
WoS CC Cited Count： 3
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Abstract ：

The classical Archimedean approximation of pi uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R-2. When n vertices are independently and uniformly randomly selected on the circle, a random inscribed or circumscribing polygon can be constructed and it is known that their semiperimeter and area both converge to pi almost surely as n -> infinity and their distributions are also asymptotically Gaussian. In this paper, we extend these results to the case of random cyclic polygons generated from symmetric Dirichlet distributions and show that as n -> infinity, similar convergence results hold for the semiperimeters or areas of these random polygons. Additionally, we also present some extrapolation estimates with faster rates of convergence. (C) 2018 Elsevier B.V. All rights reserved.

Keyword ：

Dirichlet distributions Dirichlet distributions Random cyclic polygons Random cyclic polygons Central limit theorems Central limit theorems Extrapolation Extrapolation Approximations of pi Approximations of pi

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GB/T 7714 Wang, Shasha , Xu, Wen-Qing . Random cyclic polygons from Dirichlet distributions and approximations of pi [J]. | STATISTICS & PROBABILITY LETTERS , 2018 , 140 : 84-90 .
MLA Wang, Shasha et al. "Random cyclic polygons from Dirichlet distributions and approximations of pi" . | STATISTICS & PROBABILITY LETTERS 140 (2018) : 84-90 .
APA Wang, Shasha , Xu, Wen-Qing . Random cyclic polygons from Dirichlet distributions and approximations of pi . | STATISTICS & PROBABILITY LETTERS , 2018 , 140 , 84-90 .
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