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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：An inverse Lax-Wendroff procedure for finite difference schemes on the Cartesian grids
笛卡尔网格 有限差分格式 Lax-Wendroff逆过程
2023/11/13
In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in...
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：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：Machine learning methods for forward and inverse PDEs
正反向 偏微分方程 机器学习
2023/4/27
本报告介绍我们近期的两项工作。(1) 求解PDE的PINN方法在处理时间发展方程时往往遇到难以收敛的困难。我们发展了时间方向的预训练PINN方法及自适应步长方法，解决了收敛性困难，使PDE求解精度能够得到系统性提高。我们在一系列时间发展方程上获得了比文献报道更精确的训练结果。(2) 辐射调源问题是一个典型的反问题，要求调整辐射输运方程的边条件(源)，使解满足特定设计目标。我们针对辐射输运方程的时序...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problem for the harmonic measure
谐波测量 反问题 双曲群
2023/4/17
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problems for stochastic wave equations
随机波动方程 反问题 随机偏微分方程
2023/4/25
Stochastic wave equations describe wave motion in random environments that is common in realistic situations. In this talk, I will present our recent studies on the inverse source and potential proble...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse Problems on Piezoelectric Equations
压电方程 反问题 狄利克雷 诺依曼映射 有限子域
2023/4/26
In this talk, recent progress on inverse problems for piezoelectric equations is discussed. We show a uniqueness result on recovering coefficients of piecewise homogeneous piezoelectric equations from...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse optimal control based on output measurements
输出测量 逆优化控制 逆问题
2023/5/5
In this talk we discuss inverse optimal control for the case where only the output measurements are available. By considering the inverse problem as an identification problem, the focus of the talk is...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Inverse optimal control based on output measurements
输出测量 逆优化控制 逆问题
2023/5/5
In this talk we discuss inverse optimal control for the case where only the output measurements are available. By considering the inverse problem as an identification problem, the focus of the talk is...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep image prior for inverse problems: acceleration and probabilistic treatment
反问题 深度图像 加速 概率处理
2023/5/10
Since its first proposal in 2018, deep image prior has emerged as a very powerful unsupervised deep learning technique for solving inverse problems. The approach has demonstrated very encouraging empi...
2018年SIAM反问题暑期学校（Gene Golub SIAM Summer School 2018:Inverse Problems）
2018年 SIAM 反问题暑期 学校
2017/12/20
The summer school aims to introduce graduate students to the mathematical and computational aspects of inverse problems, particularly modern developments that emphasize the quantification of uncertain...