b'Weinan E'

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 ...

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...

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...

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...

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...

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...

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...

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 ...

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...

Weinan E, et al. ∙

research

∙ 11/29/2020

Generalization and Memorization: The Bias Potential Model

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

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...

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 ...

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 ...

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...

Weinan E, et al. ∙

research

∙ 09/23/2020

Machine Learning and Computational Mathematics

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

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...

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...

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...

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...

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...

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 ...

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...

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 ...

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 ...

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...

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...

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 ...

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...

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...

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...

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...

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...

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...

Weinan E, et al. ∙

research

∙ 07/29/2019

A Mathematical Model for Linguistic Universals

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

Lei Wu, et al. ∙

research

∙ 12/11/2017

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

Recent developments in many-body potential energy representation via dee...

Han Wang, et al. ∙

research

∙ 12/10/2017

Reinforced dynamics for enhanced sampling in large atomic and molecular systems. I. Basic Methodology

A new approach for efficiently exploring the configuration space and com...

Linfeng Zhang, et al. ∙

research

∙ 10/26/2017

Maximum Principle Based Algorithms for Deep Learning

The continuous dynamical system approach to deep learning is explored in...

Qianxiao Li, et al. ∙

Weinan E

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