196 citations · 1.4k across the 75 of their papers we have counts for
14 papers · 1 filter
Machine Learning for Prediction with Missing Dynamics
John Harlim, Shixiao W. Jiang, Senwei Liang +1
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the pre…
Int-Deep: A Deep Learning Initialized Iterative Method for Nonlinear Problems
Jianguo Huang, Haoqin Wang, Haizhao Yang
This paper focuses on proposing a deep learning initialized iterative method (Int-Deep) for low-dimensional nonlinear partial differential equations (PDEs). The corresponding frame…
Instance Enhancement Batch Normalization: an Adaptive Regulator of Batch Noise
Senwei Liang, Zhongzhan Huang, Mingfu Liang +1
Batch Normalization (BN)(Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of…
Multidimensional Phase Recovery and Interpolative Decomposition Butterfly Factorization
Ze Chen, Juan Zhang, Kenneth L. Ho +1
This paper focuses on the fast evaluation of the matvec for , which is the discretization of a multidimensional oscillatory integral transform $…
Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem
Hadrien Montanelli, Haizhao Yang
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a co…
Deep Network Approximation Characterized by Number of Neurons
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper quantitatively characterizes the approximation power of deep feed-forward neural networks (FNNs) in terms of the number of neurons. It is shown by construction that ReLU…
Generative Imaging and Image Processing via Generative Encoder
Lin Chen, Haizhao Yang
This paper introduces a novel generative encoder (GE) model for generative imaging and image processing with applications in compressed sensing and imaging, image compression, deno…
CASS: Cross Adversarial Source Separation via Autoencoder
Yong Zheng Ong, Charles K. Chui, Haizhao Yang
This paper introduces a cross adversarial source separation (CASS) framework via autoencoder, a new model that aims at separating an input signal consisting of a mixture of multipl…
SelectNet: Learning to Sample from the Wild for Imbalanced Data Training
Yunru Liu, Tingran Gao, Haizhao Yang
Supervised learning from training data with imbalanced class sizes, a commonly encountered scenario in real applications such as anomaly/fraud detection, has long been considered a…
DIANet: Dense-and-Implicit Attention Network
Zhongzhan Huang, Senwei Liang, Mingfu Liang +1
Attention networks have successfully boosted the performance in various vision problems. Previous works lay emphasis on designing a new attention module and individually plug them…
Deep ReLU networks overcome the curse of dimensionality for bandlimited functions
Hadrien Montanelli, Haizhao Yang, Qiang Du
We prove a theorem concerning the approximation of bandlimited multivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome. Our theorem is ba…
Nonlinear Approximation via Compositions
Zuowei Shen, Haizhao Yang, Shijun Zhang
Given a function dictionary and an approximation budget , nonlinear approximation seeks the linear combination of the best terms $\{T_n\}_{1\le n\le…
A Hierarchical Butterfly LU Preconditioner for Two-Dimensional Electromagnetic Scattering Problems Involving Open Surfaces
Yang Liu, Haizhao Yang
This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations…
Fast Algorithms for the Multi-dimensional Jacobi Polynomial Transform
James Bremer, Qiyuan Pang, Haizhao Yang
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algori…