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04/14/2023
The Random Feature Method for Time-dependent Problems
We present a framework for solving time-dependent partial differential e...
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02/05/2023
MAC: A unified framework boosting low resource automatic speech recognition
We propose a unified framework for low resource automatic speech recogni...
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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...
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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 ...
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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...
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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...
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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...
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07/08/2021
Generalization Error of GAN from the Discriminator's Perspective
The generative adversarial network (GAN) is a well-known model for learn...
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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...
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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...
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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 ...
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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...
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11/29/2020
Generalization and Memorization: The Bias Potential Model
Models for learning probability distributions such as generative models ...
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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...
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10/11/2020
Interpretable Neural Networks for Panel Data Analysis in Economics
The lack of interpretability and transparency are preventing economists ...
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10/11/2020
The Knowledge Graph for Macroeconomic Analysis with Alternative Big Data
The current knowledge system of macroeconomics is built on interactions ...
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09/28/2020
A priori estimates for classification problems using neural networks
We consider binary and multi-class classification problems using hypothe...
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09/23/2020
Machine Learning and Computational Mathematics
Neural network-based machine learning is capable of approximating functi...
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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...
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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...
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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...
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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...
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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...
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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 ...
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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...
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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 ...
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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 ...
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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...
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06/10/2020
Representation formulas and pointwise properties for Barron functions
We study the natural function space for infinitely wide two-layer neural...
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06/04/2020
Integrating Machine Learning with Physics-Based Modeling
Machine learning is poised as a very powerful tool that can drastically ...
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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...
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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...
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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...
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03/07/2020
Machine learning based non-Newtonian fluid model with molecular fidelity
We introduce a machine-learning-based framework for constructing continu...
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12/30/2019
Machine Learning from a Continuous Viewpoint
We present a continuous formulation of machine learning, as a problem in...
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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...
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07/29/2019
A Mathematical Model for Linguistic Universals
Inspired by chemical kinetics and neurobiology, we propose a mathematica...
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06/27/2019
Deep neural network for Wannier function centers
We introduce a deep neural network (DNN) model that assigns the position...
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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09/26/2018
Monge-Ampère Flow for Generative Modeling
We present a deep generative model, named Monge-Ampère flow, which build...
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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...
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07/03/2018
A Mean-Field Optimal Control Formulation of Deep Learning
Recent work linking deep neural networks and dynamical systems opened up...
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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...
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02/27/2018
