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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：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...
We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron,Hastie, Johnstone & Tibshirani (2004) it is proved that the le...
We also
study a condition under which the coefficient paths of the lasso are monotone, and hence the different algorithms coincide. Finally, we compare the
lasso and forward stagewise pro...
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
Local-in-space estimates initial time weak solutions of the Navier-Stokes equations forward self-similar solutions Analysis of PDEs
2012/4/18
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive time...
Forward-Backward Doubly Stochastic Differential Equations with Brownian Motions and Poisson Process
Forward-backward doubly stochastic differential equations stochastic analysis random measure Poisson process
2011/11/7
The existence and uniqueness for solution of backward doubly stochastic differential equations with Brownian motions and Poisson process and that of forward-backward doubly stochastic differential equ...
FORWARD-BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS
Forward-backward doubly stochastic differential equations equivalent norm, contraction mapping
2011/11/7
A type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. Under some natural monotonicity assumptions, the existence and uniqueness result is established.
Compress-and-Forward Scheme for a Relay Network: Approximate Optimality and Connection to Algebraic Flows
Compress-and-Forward Scheme Relay Network Approximate Optimality Connection Algebraic Flows
2011/1/17
We study a wireless relay network, with a single source and a single destination.Our main result is to show that an appropriate compress-and-forward scheme supports essentially the same reliable data ...
Connectivity statistics of store-and-forward inter-vehicle communication
Connectivity statistics store-and-forward inter-vehicle communication
2010/12/28
Inter-vehicle communication (IVC) enables vehicles to exchange messages within a limited broadcast range and thus self-organize into dynamical vehicular ad hoc networks. For
the foreseeable future, h...
Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation...
Towards a Low-Complexity Dynamic Decode-and-Forward Relay Protocol
Low-Complexity Dynamic Decode-and-Forward Relay Protocol
2011/1/17
The dynamic decode-and-forward (DDF) relaying protocol is a relatively new cooperative scheme
which has been shown to achieve promising theoretical results in terms of diversity-multiplexing gain tra...
Average Sum-Rate of Distributed Alamouti Space--Time Scheme in Two-Way Amplify-and-Forward Relay Networks
Average Sum-Rate Distributed Alamouti Space--Time Scheme Amplify-and-Forward Relay Networks
2010/11/11
In this paper, we propose a distributed Alamouti space-time code (DASTC) for two-way relay networks employing a single amplify-and-forward (AF) relay. We first derive closed-form expressions for the ...
On the weighted forward reduced Entropy of Ricci flow
the weighted forward reduced Entropy Ricci flow
2010/11/9
In this paper, we first introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which related to expanders of Ricci flow, is well-defined on noncompact manif...
Higher-order derivatives of the QR and of the real symmetric eigenvalue decomposition in forward and reverse mode algorithmic differentiation
univariate Taylor polynomial arithmetic higher-order derivatives QR decomposition real symmetric eigenvalue decomposition
2010/12/15
We address the task of higher-order derivative evaluation of computer programs that contain QR
decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate...