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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence of the Planewave Approximations for Incommensurate Systems
不可测系统 平面波逼近 收敛性
2023/12/11
Incommensurate structures come from stacking the single layers of low-dimensional materials on top of one another with misalignment such as a twist in orientation. While these structures are of signif...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence in probability from moderate interacting SDE system to degenerate Keller-Segel systema
中度相互作用 SDE系统 凯勒-西格尔系统 概率收敛性
2023/4/13
In this talk I will present one of our recent work in rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system. We establish the classical solution theory of the degenerate parabol...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence and Implicit Regularization of Deep Learning Optimizers
深度学习 优化 收敛 隐式正则化
2023/4/13
In this talk, I will present our recent work on the convergence/generalization analysis for the popular optimizers in deep learning. (1) We establish the convergence for Adam under (L0,L1 ) smoothness...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the L2 rate of convergence in the limit from the Hartree to the Vlasov–Poisson Equation
哈特里到弗拉索夫 泊松方程 极限 L2收敛率
2023/4/13
We consider the semiclassical limit from the Hartree equation with Coulomb interaction potential to the Vlasov–Poisson equation. Using a new stability estimate for the difference of the square roots o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global and Local Convergence-Rate Analysis of an Inexact Newton Augmented Lagrangian Method for Zero-One Composite Optimization
零一复合优化 不精确 牛顿增强拉格朗日方法 收敛率分析
2023/4/14
Zero-One Composite Optimization (0/1-COP) is a prototype of nonsmooth, non- convex optimization problems and it has attracted much attention recently. Augmented Lagrangian Method (ALM) has stood out a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Linear Convergence of a Primal-dual Algorithm for Multi-agent Interval Optimization
多智能体 区间优化 原对偶算法 线性收敛
2023/4/21
In this talk, we consider a distributed interval optimization problem (DIOP) with uncertainties, whose global function is formed by local convex interval functions. In seeking Pareto solutions for dis...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence analysis of one-point large deviations rate functions of numerical methods for stochastic wave equations with small noise
小噪声 随机波动方程 数值方法 单点大偏差率 函数收敛分析
2023/4/21
In this talk, we present the pointwise convergence of one-point large deviations rate functions (LDRFs) of the spatial finite difference method and further the fully discrete method based on the tempo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence Thery of Deep Neural Networks: Arbitrary Activation Functions and Pooling
深度神经网络 激活函数 池化
2023/4/28
Deep neural networks, as a powerful system to represent high dimensional complex functions, play a key role in deep learning. Convergence of deep neural networks is a fundamental issue in building the...
The study of the spectrum of the Laplace operator has produced an extensive literature. (See [Cha] and the references therein.) Of special interest to recent applications has been the behavior of spec...
This paper studies Adaptive Finite Element Methods (AFEMs), based on piecewise liear elements and newest vertex bisection, for solving second order elliptic equations with
piecewise constant coeʂ...
QUASI-OPTIMAL CONVERGENCE RATE OF AN ADAPTIVE DISCONTINUOUS GALERKIN METHOD
Discontinuous Galerkin interior penalty nonconforming meshes
2015/12/11
We analyze an adaptive discontinuous finite element method (ADFEM) for symmetric
second order linear elliptic operators. The method is formulated on nonconforming meshes made
of simplices or q...
We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A − ∇div in H(div,Ω). For A being a
variab...
CONVERGENCE OF MOMENTS FOR DISPERSING BILLIARDS WITH CUSPS
Chaos decay of correlations Central Limit Theorem
2015/9/29
Dispersing billiards with cusps are deterministic dnamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic paterns.
The Hausdorff distance between a compact convex set K CRd and random sets
K c lRd iS studied. Basic inequalities are derived for the case of K being a convex
subset of K. If applied to special seq...
On quantitative convergence to quasi-stationarity。