196 citations · 1.4k across the 75 of their papers we have counts for
9 papers · 1 filter
Hierarchical Interpolative Factorization for Self Green's Function in 3D Modified Poisson-Boltzmann Equations
Yihui Tu, Zhenli Xu, Haizhao Yang
The modified Poisson-Boltzmann (MPB) equations are often used to describe equilibrium particle distribution of ionic systems. In this paper, we propose a fast algorithm to solve MP…
A Finite Expression Method for Solving High-Dimensional Committor Problems
Zezheng Song, Maria K. Cameron, Haizhao Yang
Transition path theory (TPT) is a mathematical framework for quantifying rare transition events between a pair of selected metastable states and . Central to TPT is the comm…
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives
Yahong Yang, Haizhao Yang, Yang Xiang
This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural network…
Spectral Clustering via Orthogonalization-Free Methods
Qiyuan Pang, Haizhao Yang
While orthogonalization exists in current dimensionality reduction methods in spectral clustering on undirected graphs, it does not scale in parallel computing environments. We pro…
Finite Expression Methods for Discovering Physical Laws from Data
Zhongyi Jiang, Chunmei Wang, Haizhao Yang
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics…
Deep Learning via Neural Energy Descent
Wenrui Hao, Chunmei Wang, Xingjian Xu +1
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulate…
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
Yuling Jiao, Yanming Lai, Yang Wang +2
This paper analyzes the convergence rate of a deep Galerkin method for the weak solution (DGMW) of second-order elliptic partial differential equations on with Diric…
On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: a Riemannian optimization interpretation
Shixin Zheng, Haizhao Yang, Xiangxiong Zhang
In many applications, it is desired to obtain extreme eigenvalues and eigenvectors of large Hermitian matrices by efficient and compact algorithms. In particular, orthogonalization…
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Ke Chen, Chunmei Wang, Haizhao Yang
Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing. This paper provides an e…