196 citations · 1.4k across the 75 of their papers we have counts for
12 papers · 1 filter
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…
Blending Pruning Criteria for Convolutional Neural Networks
Wei He, Zhongzhan Huang, Mingfu Liang +2
The advancement of convolutional neural networks (CNNs) on various vision applications has attracted lots of attention. Yet the majority of CNNs are unable to satisfy the strict re…
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper develops simple feed-forward neural networks that achieve the universal approximation property for all continuous functions with a fixed finite number of neurons. These…
Solving PDEs on Unknown Manifolds with Machine Learning
Senwei Liang, Shixiao W. Jiang, John Harlim +1
This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion…
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions
Jingwei Hu, Xiaodong Huang, Jie Shen +1
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic me…
Linear-Scaling Selected Inversion based on Hierarchical Interpolative Factorization for Self Green's Function for Modified Poisson-Boltzmann Equation in Two Dimensions
Yihui Tu, Qiyuan Pang, Haizhao Yang +1
This paper studies an efficient numerical method for solving modified Poisson-Boltzmann (MPB) equations with the self Green's function as a state equation to describe electrostatic…
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation
Qiang Du, Yiqi Gu, Haizhao Yang +1
Identifying hidden dynamics from observed data is a significant and challenging task in a wide range of applications. Recently, the combination of linear multistep methods (LMMs) a…
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper concentrates on the approximation power of deep feed-forward neural networks in terms of width and depth. It is proved by construction that ReLU networks with width $\ma…
Reproducing Activation Function for Deep Learning
Senwei Liang, Liyao Lyu, Chunmei Wang +1
We propose reproducing activation functions (RAFs) to improve deep learning accuracy for various applications ranging from computer vision to scientific computing. The idea is to e…