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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs
HT-Net 分层变压器 多尺度 偏微分方程 算子学习模型
2023/5/6
Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major difficulties for the computer simulation of multiscale PDE models in areas such as reser...
中国地质大学科学技术发展院吴奕德，葛明峰*等，机电学院，Nonlinear Dynamics（2020），Task-space bipartite tracking of networked robotic systems via hierarchical finite-time control
非线性；动力学领域
2021/10/15
近日，机电学院葛明峰副教授团队硕士研究生吴奕德以第一作者在非线性动力学领域《Nonlinear Dynamics》期刊上刊发研究成果。该文设计了几种新的有限时间控制算法，成功解决了多机器人系统在多种情况下的竞争一致跟踪问题。
中国地质大学科学技术发展院梁昌铎，葛明峰*等，机电学院，IEEE Transactions on Cybernetics (2020)，Output Multiformation Tracking of Networked Heterogeneous Robotic Systems Via Finite-time Hierarchical Control
有限时间；分层控制；算法
2021/10/15
近日，机电学院葛明峰副教授团队硕士研究生梁昌铎以第一作者在控制领域《IEEE Transactions on Cybernetics》（IF=10.387）期刊上刊发研究成果。该文设计了几种新型的有限时间分层控制算法成功地解决了多机器人系统的多编队跟踪问题。此外，该文还提出的一套系统的稳定性分析方法，能为相关的多群集行为问题分析提供理论指导。
Sweeping Preconditioner for the Helmholtz Equation:Hierarchical Matrix Representation
Sweeping Preconditioner Helmholtz Equation Hierarchical Matrix Representation
2015/7/14
The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including veryhigh-frequency problems. The first cent...
Fast construction of hierarchical matrix representation from matrix–vector multiplication
Fast algorithm Hierarchical matrix construction Randomized singular value decomposition Matrix–vector multiplication Elliptic operator Green’s function
2015/7/14
We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses Oelog nT appl...
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
Elliptic equations Fast algorithms Nested dissection Hierarchical matrices Sparse matrix
2015/7/14
We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining...
Hierarchical Interpolative Factorization for Elliptic Operators:Integral Equations
Hierarchical Interpolative Factorization Elliptic Operators Integral Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions.This factorization takes the form of an...
Hierarchical Interpolative Factorization for Elliptic Operators:Differential Equations
Hierarchical Interpolative Factorization Elliptic Operators Differential Equations
2015/7/14
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an a...
A TECHNIQUE FOR UPDATING HIERARCHICAL SKELETONIZATION-BASED FACTORIZATIONS OF INTEGRAL OPERATORS
factorization updating local perturbations hierarchical factorizations integral equations
2015/7/14
We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geo...
ON HIERARCHICAL GENERALIZED LINEAR MODELS.
Fitting Longitudinal Data with Hierarchical Generalized Linear Models
H-likelihood L-N estimators Poisson-Gamma models
2015/3/18
We propose a class of hierarchical generalized linear models (HGLMs) with random dispersions in this paper, and focus on the properties of the L-N estimators for the fixed
effect β in the extended Po...
Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, and Hierarchical Multi-scale Models
Evolutionary games Hierarchical Multi-scale models
2014/12/8
Evolutionary game theory has recently emerged as a key paradigm in various behavioral science disciplines. In particular it provides powerful tools and a conceptual framework for the analysis of the t...
The importance of distinct modeling strategies for gene and gene-specific treatment effects in hierarchical models for microarray data
Diffierential expression EM algorithm hierarchical models random effects uncertainty
2012/11/23
When analyzing microarray data, hierarchical models are often used to share information across genes when estimating means and variances or identifying differential expression. Many methods utilize so...
Hierarchical control based output synchronization of coexisting attractor networks
Hierarchical control passive control composite Lyapunov function theNewton-Leipnik equation attractor
2012/8/10
This paper introduces the concept of hierarchical control based output
synchronization of coexisting attractor networks. Under the new framework, each
dynamical node is made passive through intra co...
Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
nonnegative matrix factorization algorithms multiplicative updates hierarchical alternating least squares
2011/9/21
Abstract: Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational ...