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no code implementations • 5 Feb 2023 • Yuling Jiao, Yanming Lai, Yang Wang, Haizhao Yang, Yunfei Yang

This paper analyzes the convergence rate of a deep Galerkin method for the weak solution (DGMW) of second-order elliptic partial differential equations on $\mathbb{R}^d$ with Dirichlet, Neumann, and Robin boundary conditions, respectively.

no code implementations • 28 Jan 2023 • Ke Chen, Chunmei Wang, Haizhao Yang

Deep neural networks (DNNs) have seen tremendous success in many fields and their developments in PDE-related problems are rapidly growing.

no code implementations • 8 Dec 2022 • 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.

1 code implementation • 6 Dec 2022 • Songyang Han, Sanbao Su, Sihong He, Shuo Han, Haizhao Yang, Fei Miao

Additionally, we propose a Robust Multi-Agent Adversarial Actor-Critic (RMA3C) algorithm to learn robust policies for MARL agents under state uncertainties.

Multi-agent Reinforcement Learning
reinforcement-learning
**+1**

1 code implementation • 7 Aug 2022 • Zhongzhan Huang, Senwei Liang, Hong Zhang, Haizhao Yang, Liang Lin

Conventional numerical solvers used in the simulation are significantly limited by the step size for time integration, which hampers efficiency and feasibility especially when high accuracy is desired.

no code implementations • 16 Jul 2022 • Zhongzhan Huang, Senwei Liang, Mingfu Liang, wei he, Haizhao Yang, Liang Lin

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 networks (CNNs).

1 code implementation • 21 Jun 2022 • 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 engineering, mainly due to the "curse of dimensionality" in designing numerical schemes that scale in dimension.

no code implementations • 8 Jun 2022 • 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.

no code implementations • 19 May 2022 • Zuowei Shen, Haizhao Yang, Shijun Zhang

It is proved by construction that height-$s$ ReLU NestNets with $\mathcal{O}(n)$ parameters can approximate $1$-Lipschitz continuous functions on $[0, 1]^d$ with an error $\mathcal{O}(n^{-(s+1)/d})$, while the optimal approximation error of standard ReLU networks with $\mathcal{O}(n)$ parameters is $\mathcal{O}(n^{-2/d})$.

1 code implementation • 10 Mar 2022 • 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 inputs and/or outputs of a learning model.

no code implementations • 22 Feb 2022 • Fusheng Liu, Haizhao Yang, Soufiane Hayou, Qianxiao Li

Optimization and generalization are two essential aspects of statistical machine learning.

no code implementations • 1 Jan 2022 • Hao liu, Haizhao Yang, Minshuo Chen, Tuo Zhao, Wenjing Liao

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc.

no code implementations • 15 Nov 2021 • Zuowei Shen, Haizhao Yang, Shijun Zhang

Furthermore, we show that the idea of learning a small number of parameters to achieve a good approximation can be numerically observed.

no code implementations • 29 Sep 2021 • Fusheng Liu, Haizhao Yang, Qianxiao Li

Through our approach, we show that, with a proper initialization, gradient flow converges following a short path with an explicit length estimate.

no code implementations • 9 Sep 2021 • Yiqi Gu, John Harlim, Senwei Liang, Haizhao Yang

In this paper, we consider the density estimation problem associated with the stationary measure of ergodic It\^o diffusions from a discrete-time series that approximate the solutions of the stochastic differential equations.

no code implementations • 11 Jul 2021 • wei he, Zhongzhan Huang, Mingfu Liang, Senwei Liang, Haizhao Yang

One filter could be important according to a certain criterion, while it is unnecessary according to another one, which indicates that each criterion is only a partial view of the comprehensive "importance".

no code implementations • 6 Jul 2021 • 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.

no code implementations • 12 Jun 2021 • Senwei Liang, Shixiao W. Jiang, John Harlim, Haizhao Yang

The resulting numerical method is to solve a highly non-convex empirical risk minimization problem subjected to a solution from a hypothesis space of neural networks.

no code implementations • 21 Mar 2021 • Qiang Du, Yiqi Gu, Haizhao Yang, Chao Zhou

We put forward error estimates for these methods using the approximation property of deep networks.

no code implementations • 28 Feb 2021 • 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.

no code implementations • 13 Jan 2021 • Senwei Liang, Liyao Lyu, Chunmei Wang, Haizhao Yang

We propose reproducing activation functions (RAFs) to improve deep learning accuracy for various applications ranging from computer vision to scientific computing.

no code implementations • 15 Dec 2020 • Fan Chen, Jianguo Huang, Chunmei Wang, Haizhao Yang

This paper proposes Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via a minmax formulation, which transforms the PDE problem into a minimax optimization problem to identify weak solutions.

1 code implementation • 28 Nov 2020 • Zhongzhan Huang, Senwei Liang, Mingfu Liang, wei he, Haizhao Yang

Recently, many plug-and-play self-attention modules are proposed to enhance the model generalization by exploiting the internal information of deep convolutional neural networks (CNNs).

no code implementations • 25 Oct 2020 • Zuowei Shen, Haizhao Yang, Shijun Zhang

A three-hidden-layer neural network with super approximation power is introduced.

no code implementations • 28 Jun 2020 • Tao Luo, Haizhao Yang

The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solutions.

no code implementations • 22 Jun 2020 • Zuowei Shen, Haizhao Yang, Shijun Zhang

More generally for an arbitrary continuous function $f$ on $[0, 1]^d$ with a modulus of continuity $\omega_f(\cdot)$, the constructive approximation rate is $\omega_f(\sqrt{d}\, N^{-\sqrt{L}})+2\omega_f(\sqrt{d}){N^{-\sqrt{L}}}$.

no code implementations • 9 Jan 2020 • Jianfeng Lu, Zuowei Shen, Haizhao Yang, Shijun Zhang

This paper establishes the (nearly) optimal approximation error characterization of deep rectified linear unit (ReLU) networks for smooth functions in terms of both width and depth simultaneously.

no code implementations • 13 Oct 2019 • John Harlim, Shixiao W. Jiang, Senwei Liang, Haizhao Yang

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques.

2 code implementations • 12 Aug 2019 • Senwei Liang, Zhongzhan Huang, Mingfu Liang, Haizhao Yang

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 the training loss.

no code implementations • 27 Jun 2019 • 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.

no code implementations • 13 Jun 2019 • 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.

3 code implementations • 25 May 2019 • Zhongzhan Huang, Senwei Liang, Mingfu Liang, Haizhao Yang

Attention networks have successfully boosted the performance in various vision problems.

Ranked #132 on Image Classification on CIFAR-100

no code implementations • 23 May 2019 • 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 significant challenge in machine learning.

no code implementations • 23 May 2019 • 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, denoising, inpainting, deblurring, and super-resolution.

no code implementations • 23 May 2019 • 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 multiple components into individual components defined via adversarial learning and autoencoder fitting.

no code implementations • 26 Feb 2019 • Zuowei Shen, Haizhao Yang, Shijun Zhang

In particular, for any function $f$ on $[0, 1]$, regardless of its smoothness and even the continuity, if $f$ can be approximated using a dictionary when $L=1$ with the best $N$-term approximation rate $\varepsilon_{L, f}={\cal O}(N^{-\eta})$, we show that dictionaries with $L=2$ can improve the best $N$-term approximation rate to $\varepsilon_{L, f}={\cal O}(N^{-2\eta})$.

2 code implementations • 14 Nov 2018 • Senwei Liang, Yuehaw Khoo, Haizhao Yang

Overfitting frequently occurs in deep learning.

Ranked #10 on Image Classification on SVHN

no code implementations • 21 May 2018 • Jieren Xu, Yitong Li, Haizhao Yang, David Dunson, Ingrid Daubechies

This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e. g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data.

1 code implementation • 12 Oct 2016 • Jieren Xu, Haizhao Yang, Ingrid Daubechies

This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes $\alpha_k(t)s_k(2\pi N_k\phi_k(t))$ from their superposition $\sum_{k=1}^K \alpha_k(t)s_k(2\pi N_k\phi_k(t))$.

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