196 citations · 1.4k across the 75 of their papers we have counts for
78 papers
Finite Expression Approximation of High-Dimensional PDEs Without the Curse of Dimensionality
Zhi Heng Liu, Haizhao Yang
We establish that finite expressions form a symbolic representation class capable of overcoming the curse of dimensionality for several classes of high-dimensional partial differen…
Optimal Tradeoffs Between Network Size and Parameter Magnitude in Neural Approximation and Minimax Regression
Baicheng Li, Zuowei Shen, Haizhao Yang +1
The statistical accuracy of neural networks depends on both their approximation power and the complexity of the class fitted from data. While increasing network size is a natural w…
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…
A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering
Qiyuan Pang, Haizhao Yang
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of…
What is the Solution for State-Adversarial Multi-Agent Reinforcement Learning?
Songyang Han, Sanbao Su, Sihong He +4
Various methods for Multi-Agent Reinforcement Learning (MARL) have been developed with the assumption that agents' policies are based on accurate state information. However, polici…
The Lottery Ticket Hypothesis for Self-attention in Convolutional Neural Network
Zhongzhan Huang, Senwei Liang, Mingfu Liang +3
Recently many plug-and-play self-attention modules (SAMs) are proposed to enhance the model generalization by exploiting the internal information of deep convolutional neural netwo…
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Senwei Liang, Haizhao Yang
Designing efficient and accurate numerical solvers for high-dimensional partial differential equations (PDEs) remains a challenging and important topic in computational science and…
Reinforced Inverse Scattering
Hanyang Jiang, Yuehaw Khoo, Haizhao Yang
Inverse wave scattering aims at determining the properties of an object using data on how the object scatters incoming waves. In order to collect information, sensors are put in di…
Neural Network Architecture Beyond Width and Depth
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper proposes a new neural network architecture by introducing an additional dimension called height beyond width and depth. Neural network architectures with height, width,…
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning
Yong Zheng Ong, Zuowei Shen, Haizhao Yang
Discretization invariant learning aims at learning in the infinite-dimensional function spaces with the capacity to process heterogeneous discrete representations of functions as i…
From Optimization Dynamics to Generalization Bounds via Łojasiewicz Gradient Inequality
Fusheng Liu, Haizhao Yang, Soufiane Hayou +1
Optimization and generalization are two essential aspects of statistical machine learning. In this paper, we propose a framework to connect optimization with generalization by anal…
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces
Hao Liu, Haizhao Yang, Minshuo Chen +2
Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and…
Deep Network Approximation in Terms of Intrinsic Parameters
Zuowei Shen, Haizhao Yang, Shijun Zhang
One of the arguments to explain the success of deep learning is the powerful approximation capacity of deep neural networks. Such capacity is generally accompanied by the explosive…
Stationary Density Estimation of Itô Diffusions Using Deep Learning
Yiqi Gu, John Harlim, Senwei Liang +1
In this paper, we consider the density estimation problem associated with the stationary measure of ergodic Itô diffusions from a discrete-time series that approximate the solution…
Multiscale and Nonlocal Learning for PDEs using Densely Connected RNNs
Ricardo A. Delgadillo, Jingwei Hu, Haizhao Yang
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this…
Simultaneous Neural Network Approximation for Smooth Functions
Sean Hon, Haizhao Yang
We establish in this work approximation results of deep neural networks for smooth functions measured in Sobolev norms, motivated by recent development of numerical solvers for par…