b'Weinan E'

research

∙ 04/14/2023

The Random Feature Method for Time-dependent Problems

We present a framework for solving time-dependent partial differential e...

0 Jingrun Chen, et al. ∙

research

∙ 02/05/2023

MAC: A unified framework boosting low resource automatic speech recognition

We propose a unified framework for low resource automatic speech recogni...

0 Zeping Min, et al. ∙

research

∙ 07/27/2022

Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method

One of the oldest and most studied subject in scientific computing is al...

0 Jingrun Chen, et al. ∙

research

∙ 01/09/2022

A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics

Machine learning has long been considered as a black box for predicting ...

13 Tianhan Zhang, et al. ∙

research

∙ 01/06/2022

A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics

A deep learning-based model reduction (DeePMR) method for simplifying ch...

8 Zhiwei Wang, et al. ∙

research

∙ 12/29/2021

DeePN^2: A deep learning-based non-Newtonian hydrodynamic model

A long standing problem in the modeling of non-Newtonian hydrodynamics i...

6 Lidong Fang, et al. ∙

research

∙ 12/29/2021

DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks

We propose an efficient, reliable, and interpretable global solution met...

8 Jiequn Han, et al. ∙

research

∙ 07/08/2021

Generalization Error of GAN from the Discriminator's Perspective

The generative adversarial network (GAN) is a well-known model for learn...

4 Hongkang Yang, et al. ∙

research

∙ 04/15/2021

An L^2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation

Reinforcement learning (RL) algorithms based on high-dimensional functio...

13 Jihao Long, et al. ∙

research

∙ 03/31/2021

The Expectation-Maximization Algorithm for Continuous-time Hidden Markov Models

We propose a unified framework that extends the inference methods for cl...

0 Qingcan Wang, et al. ∙

research

∙ 12/10/2020

On the emergence of tetrahedral symmetry in the final and penultimate layers of neural network classifiers

A recent numerical study observed that neural network classifiers enjoy ...

5 Weinan E, et al. ∙

research

∙ 12/02/2020

Some observations on partial differential equations in Barron and multi-layer spaces

We use explicit representation formulas to show that solutions to certai...

0 Weinan E, et al. ∙

research

∙ 11/29/2020

Generalization and Memorization: The Bias Potential Model

Models for learning probability distributions such as generative models ...

0 Hongkang Yang, et al. ∙

research

∙ 10/12/2020

Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning

It is not clear yet why ADAM-alike adaptive gradient algorithms suffer f...

46 Pan Zhou, et al. ∙

research

∙ 10/11/2020

Interpretable Neural Networks for Panel Data Analysis in Economics

The lack of interpretability and transparency are preventing economists ...

0 Yucheng Yang, et al. ∙

research

∙ 10/11/2020

The Knowledge Graph for Macroeconomic Analysis with Alternative Big Data

The current knowledge system of macroeconomics is built on interactions ...

0 Yucheng Yang, et al. ∙

research

∙ 09/28/2020

A priori estimates for classification problems using neural networks

We consider binary and multi-class classification problems using hypothe...

0 Weinan E, et al. ∙

research

∙ 09/23/2020

Machine Learning and Computational Mathematics

Neural network-based machine learning is capable of approximating functi...

0 Weinan E, et al. ∙

research

∙ 09/22/2020

Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

The purpose of this article is to review the achievements made in the la...

270 Weinan E, et al. ∙

research

∙ 09/16/2020

On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis

We study the approximation properties and optimization dynamics of recur...

1 Zhong Li, et al. ∙

research

∙ 09/14/2020

A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms

The dynamic behavior of RMSprop and Adam algorithms is studied through a...

27 Chao Ma, et al. ∙

research

∙ 09/06/2020

OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle

We propose a systematic method for learning stable and interpretable dyn...

0 Haijun Yu, et al. ∙

research

∙ 08/31/2020

Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning

In recent years, tremendous progress has been made on numerical algorith...

0 Weinan E, et al. ∙

research

∙ 08/13/2020

The Slow Deterioration of the Generalization Error of the Random Feature Model

The random feature model exhibits a kind of resonance behavior when the ...

45 Chao Ma, et al. ∙

research

∙ 08/01/2020

DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory

We propose a general machine learning-based framework for building an ac...

0 Yixiao Chen, et al. ∙

research

∙ 07/30/2020

On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics

We develop Banach spaces for ReLU neural networks of finite depth L and ...

11 Weinan E, et al. ∙

research

∙ 07/19/2020

Coarse-grained spectral projection (CGSP): A scalable and parallelizable deep learning-based approach to quantum unitary dynamics

We propose the coarse-grained spectral projection method (CGSP), a deep ...

0 Pinchen Xie, et al. ∙

research

∙ 06/25/2020

The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models

A numerical and phenomenological study of the gradient descent (GD) algo...

6 Chao Ma, et al. ∙

research

∙ 06/10/2020

Representation formulas and pointwise properties for Barron functions

We study the natural function space for infinitely wide two-layer neural...

0 Weinan E, et al. ∙

research

∙ 06/04/2020

Integrating Machine Learning with Physics-Based Modeling

Machine learning is poised as a very powerful tool that can drastically ...

0 Weinan E, et al. ∙

research

∙ 05/21/2020

Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective

We prove that the gradient descent training of a two-layer neural networ...

51 Stephan Wojtowytsch, et al. ∙

research

∙ 05/21/2020

Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels

We establish a scale separation of Kolmogorov width type between subspac...

22 Weinan E, et al. ∙

research

∙ 04/24/2020

86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy

We present the GPU version of DeePMD-kit, which, upon training a deep ne...

0 Denghui Lu, et al. ∙

research

∙ 03/07/2020

Machine learning based non-Newtonian fluid model with molecular fidelity

We introduce a machine-learning-based framework for constructing continu...

12 Huan Lei, et al. ∙

research

∙ 12/30/2019

Machine Learning from a Continuous Viewpoint

We present a continuous formulation of machine learning, as a problem in...

33 Weinan E, et al. ∙

research

∙ 12/15/2019

On the Generalization Properties of Minimum-norm Solutions for Over-parameterized Neural Network Models

We study the generalization properties of minimum-norm solutions for thr...

10 Weinan E, et al. ∙

research

∙ 07/29/2019

A Mathematical Model for Linguistic Universals

Inspired by chemical kinetics and neurobiology, we propose a mathematica...

12 Weinan E, et al. ∙

research

∙ 06/27/2019

Deep neural network for Wannier function centers

We introduce a deep neural network (DNN) model that assigns the position...

0 Linfeng Zhang, et al. ∙

research

∙ 06/18/2019

Barron Spaces and the Compositional Function Spaces for Neural Network Models

One of the key issues in the analysis of machine learning models is to i...

1 Weinan E, et al. ∙

research

∙ 04/10/2019

Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections

The behavior of the gradient descent (GD) algorithm is analyzed for a de...

15 Weinan E, et al. ∙

research

∙ 04/08/2019

A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics

A fairly comprehensive analysis is presented for the gradient descent dy...

25 Weinan E, et al. ∙

research

∙ 03/06/2019

A Priori Estimates of the Population Risk for Residual Networks

Optimal a priori estimates are derived for the population risk of a regu...

6 Weinan E, et al. ∙

research

∙ 11/05/2018

Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations

We develop the mathematical foundations of the stochastic modified equat...

0 Qianxiao Li, et al. ∙

research

∙ 10/28/2018

Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation

An active learning procedure called Deep Potential Generator (DP-GEN) is...

0 Linfeng Zhang, et al. ∙

research

∙ 10/15/2018

A Priori Estimates of the Generalization Error for Two-layer Neural Networks

New estimates for the generalization error are established for the two-l...

0 Weinan E, et al. ∙

research

∙ 09/26/2018

Monge-Ampère Flow for Generative Modeling

We present a deep generative model, named Monge-Ampère flow, which build...

0 Linfeng Zhang, et al. ∙

research

∙ 08/10/2018

Model Reduction with Memory and the Machine Learning of Dynamical Systems

The well-known Mori-Zwanzig theory tells us that model reduction leads t...

0 Chao Ma, et al. ∙

research

∙ 07/03/2018

A Mean-Field Optimal Control Formulation of Deep Learning

Recent work linking deep neural networks and dynamical systems opened up...

0 Weinan E, et al. ∙

research

∙ 07/01/2018

Exponential Convergence of the Deep Neural Network Approximation for Analytic Functions

We prove that for analytic functions in low dimension, the convergence r...

0 Weinan E, et al. ∙

research

∙ 02/27/2018

Understanding and Enhancing the Transferability of Adversarial Examples

State-of-the-art deep neural networks are known to be vulnerable to adve...

0 Lei Wu, et al. ∙

Weinan E

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