research
∙
06/21/2023
A Finite Expression Method for Solving High-Dimensional Committor Problems
Transition path theory (TPT) is a mathematical framework for quantifying...
share
research
∙
05/16/2023
Spectral Clustering via Orthogonalization-Free Methods
Graph Signal Filter used as dimensionality reduction in spectral cluster...
research
∙
05/15/2023
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives
This paper addresses the problem of nearly optimal Vapnik–Chervonenkis d...
research
∙
05/15/2023
Finite Expression Methods for Discovering Physical Laws from Data
Nonlinear dynamics is a pervasive phenomenon observed in various scienti...
research
∙
02/21/2023
Deep Learning via Neural Energy Descent
This paper proposes the Nerual Energy Descent (NED) via neural network e...
research
∙
02/09/2023
On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: a Riemannian optimization interpretation
In many applications, it is desired to obtain extreme eigenvalues and ei...
research
∙
02/05/2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
This paper analyzes the convergence rate of a deep Galerkin method for t...
research
∙
01/28/2023
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Deep neural networks (DNNs) have seen tremendous success in many fields ...
research
∙
12/08/2022
A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering
We develop a distributed Block Chebyshev-Davidson algorithm to solve lar...
research
∙
12/06/2022
What is the Solution for State-Adversarial Multi-Agent Reinforcement Learning?
Various methods for Multi-Agent Reinforcement Learning (MARL) have been ...
research
∙
08/07/2022
Accelerating Numerical Solvers for Large-Scale Simulation of Dynamical System via NeurVec
Ensemble-based large-scale simulation of dynamical systems is essential ...
research
∙
06/21/2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Designing efficient and accurate numerical solvers for high-dimensional ...
research
∙
06/08/2022
Reinforced Inverse Scattering
Inverse wave scattering aims at determining the properties of an object ...
research
∙
05/19/2022
Neural Network Architecture Beyond Width and Depth
This paper proposes a new neural network architecture by introducing an ...
research
∙
03/10/2022
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning
Discretization invariant learning aims at learning in the infinite-dimen...
research
∙
02/22/2022
Connecting Optimization and Generalization via Gradient Flow Path Length
Optimization and generalization are two essential aspects of machine lea...
research
∙
01/01/2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces
Learning operators between infinitely dimensional spaces is an important...
research
∙
11/15/2021
ReLU Network Approximation in Terms of Intrinsic Parameters
This paper studies the approximation error of ReLU networks in terms of ...
research
∙
09/09/2021
Stationary Density Estimation of Itô Diffusions Using Deep Learning
In this paper, we consider the density estimation problem associated wit...
research
∙
09/04/2021
Multiscale and Nonlocal Learning for PDEs using Densely Connected RNNs
Learning time-dependent partial differential equations (PDEs) that gover...
research
∙
09/01/2021
Simultaneous Neural Network Approximations in Sobolev Spaces
We establish in this work approximation results of deep neural networks ...
research
∙
07/06/2021
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons
This paper develops simple feed-forward neural networks that achieve the...
research
∙
06/12/2021
Solving PDEs on Unknown Manifolds with Machine Learning
This paper proposes a mesh-free computational framework and machine lear...
research
∙
05/18/2021
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions
Numerical approximation of the Boltzmann equation presents a challenging...
research
∙
03/21/2021
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation
Identifying hidden dynamics from observed data is a significant and chal...
research
∙
02/28/2021
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth
This paper concentrates on the approximation power of deep feed-forward ...
research
∙
01/13/2021
Reproducing Activation Function for Deep Learning
In this paper, we propose the reproducing activation function to improve...
research
∙
12/15/2020
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning
This paper proposes Friedrichs learning as a novel deep learning methodo...
research
∙
11/28/2020
Efficient Attention Network: Accelerate Attention by Searching Where to Plug
Recently, many plug-and-play self-attention modules are proposed to enha...
research
∙
10/25/2020
Neural Network Approximation: Three Hidden Layers Are Enough
A three-hidden-layer neural network with super approximation power is in...
research
∙
07/07/2020
Structure Probing Neural Network Deflation
Deep learning is a powerful tool for solving nonlinear differential equa...
research
∙
06/28/2020
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory
Deep learning has significantly revolutionized the design of numerical a...
research
∙
06/22/2020
Deep Network Approximation with Discrepancy Being Reciprocal of Width to Power of Depth
A new network with super approximation power is introduced. This network...
research
∙
04/23/2020
Rapid Application of the Spherical Harmonic Transform via Interpolative Decomposition Butterfly Factorization
We describe an algorithm for the application of the forward and inverse ...
research
∙
01/14/2020
SelectNet: Self-paced Learning for High-dimensional Partial Differential Equations
The residual method with deep neural networks as function parametrizatio...
research
∙
01/09/2020
Deep Network Approximation for Smooth Functions
This paper establishes optimal approximation error characterization of d...
research
∙
10/13/2019
Machine Learning for Prediction with Missing Dynamics
This article presents a general framework for recovering missing dynamic...
research
∙
10/03/2019
Int-Deep: A Deep Learning Initialized Iterative Method for Nonlinear Problems
This paper focuses on proposing a deep learning initialized iterative me...
research
∙
08/25/2019
Multidimensional Phase Recovery and Interpolative Decomposition Butterfly Factorization
This paper focuses on the fast evaluation of the matvec g=Kf for K∈C^N× ...
research
∙
08/12/2019
Instance Enhancement Batch Normalization: an Adaptive Regulator of Batch Noise
Batch Normalization (BN) (Ioffe and Szegedy 2015) normalizes the feature...
research
∙
06/27/2019
Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem
We prove a theorem concerning the approximation of multivariate continuo...
research
∙
06/13/2019
Deep Network Approximation Characterized by Number of Neurons
This paper quantitatively characterizes the approximation power of deep ...
research
∙
05/25/2019
DIANet: Dense-and-Implicit Attention Network
Attention-based deep neural networks (DNNs) that emphasize the informati...
research
∙
05/23/2019
CASS: Cross Adversarial Source Separation via Autoencoder
This paper introduces a cross adversarial source separation (CASS) frame...
research
∙
05/23/2019
SelectNet: Learning to Sample from the Wild for Imbalanced Data Training
Supervised learning from training data with imbalanced class sizes, a co...
research
∙
02/26/2019
Nonlinear Approximation via Compositions
We study the approximation efficiency of function compositions in nonlin...
research
∙
11/14/2018
Drop-Activation: Implicit Parameter Reduction and Harmonic Regularization
Overfitting frequently occurs in deep learning. In this paper, we propos...
research
∙
05/21/2018
Non-Oscillatory Pattern Learning for Non-Stationary Signals
This paper proposes a novel non-oscillatory pattern (NOP) learning schem...
research
∙
01/31/2017
Interior Eigensolver for Sparse Hermitian Definite Matrices Based on Zolotarev's Functions
This paper proposes an efficient method for computing selected generaliz...
research
∙
10/12/2016