Fetching the paper…
Reading the bibliography…
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.
Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
Earlier work this paper cites.
Neural-network-based Approximations for Solving Partial Differential Equations
M. W. M. G. Dissanayake and N. Phan-Thien · 1994
Earlier work this paper cites.
Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
I.E. Lagaris, A. Likas, and D. I. Fotiadis · 1998
Earlier work this paper cites.
A type of generalization error induced by initialization in deep neural networks
Y. Zhang, Z.-Q. J. Xu, T. Luo, and Z. Ma · 2006
Earlier work this paper cites.
Understanding machine learning: From theory to algorithms
S. Shalev-Shwartz and S. Ben-David · 2014
Earlier work this paper cites.
Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2015
Earlier work this paper cites.
A Constrained Integration (CINT) Approach to Solving Partial Differential Equations Using Artificial Neural Networks
K. Rudd and S. Ferrari · 2015
Earlier work this paper cites.
Deep Learning
I. Goodfellow, Y. Bengio, and A. Courville · 2016
Earlier work this paper cites.
Densely connected convolutional networks
Gao Huang, Zhuang Liu, and Kilian Q. Weinberger · 2016
Earlier work this paper cites.
Shiyu Liang and R. Srikant · 2016
Earlier work this paper cites.
Solving the Quantum Many-body Problem with Artificial Neural Networks
G. Carleo and M. Troyer · 2017
Earlier work this paper cites.
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
Weinan E, Jiequn Han, and Arnulf Jentzen · 2017
Earlier work this paper cites.
Why and when can deep—but not shallow—networks avoid the curse of dimensionality: A review
T. Poggio, H. N. Mhaskar, L. Rosasco, B. Miranda, and Q. Liao · 2017
Earlier work this paper cites.
Error bounds for approximations with deep ReLU networks
Dmitry Yarotsky · 2017
Earlier work this paper cites.
A Unified Deep Artificial Neural Network Approach to Partial Differential Equations in Complex Geometries
J. Berg and K. Nyström · 2018
Earlier work this paper cites.
Julius Berner, Philipp Grohs, and Arnulf Jentzen · 2018
Earlier work this paper cites.
Gradient descent finds global minima of deep neural networks
Simon S. Du, Jason D. Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai · 2018
Earlier work this paper cites.
The Deep Ritz Method: a Deep Learning-based Numerical Algorithm for Solving Variational Problems
W. E and B. Yu · 2018
Cited alongside, same era.
Exponential convergence of the deep neural network approximation for analytic functions
Weinan E and Qingcan Wang · 2018
Cited alongside, same era.
Solving High-dimensional Partial Differential Equations Using Deep Learning
J. Han, A. Jentzen, and W. E · 2018
Cited alongside, same era.
Convergence of the deep bsde method for coupled fbsdes
Jiequn Han and Jihao Long · 2018
Cited alongside, same era.
Neural tangent kernel: Convergence and generalization in neural networks
Arthur Jacot, Franck Gabriel, and Clément Hongler · 2018
Cited alongside, same era.
Deep ReLU networks overcome the curse of dimensionality for bandlimited functions
Hadrien Montanelli, Haizhao Yang, and Qiang Du · 2019
Later among the works it cites.
Exponential relu dnn expression of holomorphic maps in high dimension
Joost A.A. Opschoor, Christoph Schwab, and Jakob Zech · 2019
Later among the works it cites.
Physics-informed Neural Networks: a Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations
M. Raissi, P. Perdikaris, and G.E. Karniadakis · 2019
Later among the works it cites.
Nonlinear approximation via compositions
Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2019
Later among the works it cites.
Barron spaces and the compositional function spaces for neural network models
E. Weinan, Chao Ma, and Lei Wu · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A mean field view of the landscape of two-layer neural networks
Song Mei, Andrea Montanari, and Phan-Minh Nguyen · 2018
Cited alongside, same era.
DGM: a Deep Learning Algorithm for Solving Partial Differential Equations
J. Sirignano and K. Spiliopoulos · 2018
Cited alongside, same era.
Generalization bounds of stochastic gradient descent for wide and deep neural networks
Yuan Cao and Quanquan Gu · 2019
Cited alongside, same era.
A note on the expressive power of deep rectified linear unit networks in high-dimensional spaces
Liang Chen and Congwei Wu · 2019
Cited alongside, same era.
How much over-parameterization is sufficient to learn deep relu networks?
Zixiang Chen, Yuan Cao, Difan Zou, and Quanquan Gu · 2019
Cited alongside, same era.
Gradient descent provably optimizes over-parameterized neural networks
Simon S. Du, Xiyu Zhai, Barnabas Poczos, and Aarti Singh · 2019
Cited alongside, same era.
A priori estimates of the population risk for residual networks
Weinan E, Chao Ma, and Qingcan Wang · 2019
Cited alongside, same era.
Dmitry Yarotsky and Anton Zhevnerchuk · 2019
Later among the works it cites.
A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics
Weinan E, Chao Ma, and Lei Wu · 2020
Closest in time.
Structure probling neural network deflation
Yiqi Gu, Chunmei Wang, and Haizhao Yang · 2020
Closest in time.
Selectnet: Self-paced learning for high-dimensional partial differential equations
Yiqi Gu, Haizhao Yang, and Chao Zhou · 2020
Closest in time.
Int-deep: A deep learning initialized iterative method for nonlinear problems
Jianguo Huang, Haoqin Wang, and Haizhao Yang · 2020
Closest in time.
Deep Network Approximation for Smooth Functions
Jianfeng Lu, Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2020
Closest in time.
Yiping Lu, Chao Ma, Yulong Lu, Jianfeng Lu, and Lexing Ying · 2020
Closest in time.
Error bounds for deep relu networks using the kolmogorov–arnold superposition theorem
Hadrien Montanelli and Haizhao Yang · 2020
Closest in time.
Deep network approximation characterized by number of neurons
Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2020
Closest in time.
Neural network approximation: Three hidden layers are enough
Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2020
Closest in time.
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type pdes, 2020
Yeonjong Shin, Jerome Darbon, and George Em Karniadakis · 2020
Closest in time.
Approximation in shift-invariant spaces with deep ReLU neural networks
Yunfei Yang and Yang Wang · 2020
Closest in time.