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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Inverse problems for elliptic PDE" (8)
椭圆偏微分方程 反问题 Calderón问题
2023/11/29
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Inverse problems for elliptic PDE" (7)
椭圆偏微分方程 反问题 Calderón问题
2023/11/29
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Direct sampling method to inverse wave-number-dependent source problems: determination of the support of a stationary source
反波数 相关源问题 直接采样 固定源
2023/11/29
This talk is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourie...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some new algorithm developments on highly stiff stable schemes and on a SAV based approach for optimization problems
高刚性稳定方案 基于SAV 优化方法 新算法发展
2023/11/29
In the first part, I shall present a new way to construct highly stiff stable schemes. Traditional time discretization schemes are usually based on Taylor expansions at $t_{n+\beta}$ with $\beta\in [0...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the construction of solutions to some inviscid free boundary problems
无粘 自由边界 解构造
2023/11/15
We will present our recent results on the local well-posedness of free boundary problems for some inviscid fluids. In particular, for each problem the solution is constructed as the vanishing viscosit...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： On the construction of solutions to some inviscid free boundary problems
无粘 自由边界 问题解 构造
2023/12/11
We will present our recent results on the local well-posedness of free boundary problems for some inviscid fluids. In particular, for each problem the solution is constructed as the vanishing viscosit...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient
VC-PINN 变系数 偏微分方程 正逆问题 变系数物理 知情神经网络
2023/11/13
The talk proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations-Variable Coefficient Physics-Informed Neural N...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Results on Partial Inverse Spanning Tree Problems
部分逆生成树 有权函数 非循环边子集
2023/11/6
Given a graph G with weight function w and an acyclic edge subset E', the partial inverse spanning tree problem on (G, w; E') is to find a new weight function w* so that E' can be extended to a maximu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals
光子晶体 线性非线性特征值问题 近似 计算
2023/5/15
In this talk, we discuss the approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals. We discretize the shifted Maxwell operator with edge finite elements a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse Problems and Their Applications
逆问题 系统辨识 正问题
2023/5/12
反问题和正问题是成对出现的。通常，学术界将已知原因（输入）、过程（模型）而探求结果（输出）的一类问题称为正问题。与此相对应，就有了两种反问题：已知模型、输出求未知输入的“溯源”问题和已知输入、输出来反求模型（或模型参数）的系统辨识问题。在现实社会和人类生活中，反问题无处不在；在关系国家命脉的经济生产和国防军事领域中反问题更是随处可见。例如，与人类健康福祉密切相关的无痛无损伤、在体表进行测量的医学诊...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Numerical PDEs for Fluid-Structure Interaction (FSI) Problems
流固耦合 数值 偏微分方程
2023/5/8
The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Capsule Aggregated Attention for Vehicle Routing Problems
车辆 路径问题 胶囊聚合 关注
2023/4/27
Deep learning based methods have shown great potential for solving Vehicle Routing Problems (VRPs) in recent years. In the current learning based models, attention mechanism plays an important role an...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville theorems for superlinear parabolic problems
超线性 抛物线问题 刘维尔定理
2023/4/21
We first consider positive classical solutions to a semilinear heat equation and discuss the associated Liouville-type theorems and their consequences on a priori estimates of solutions (in particular...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Liouville theorems for superlinear parabolic problems
超线性 抛物线问题 刘维尔定理
2023/4/23
We first consider positive classical solutions to a semilinear heat equation and discuss the associated Liouville-type theorems and their consequences on a priori estimates of solutions (in particular...