Fetching the paper…
Reading the bibliography…
We present a neural network-based method for solving linear and nonlinear partial differential equations, by combining the ideas of extreme learning machines (ELM), domain decomposition and local neural networks.
The perceptron: a probabilistic model for information storage and organization in the brain
F. Rosenblatt · 1958
Earlier work this paper cites.
Beyond regression: new tools for prediction and alaysis in the behavioral sciences
P.J. Werbos · 1974
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
Earlier work this paper cites.
The stone-weierstrass theorem and its application to neural networks
N.E. Cotter · 1990
Earlier work this paper cites.
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
K. Hornik, M. Stinchcombe, and H. White · 1990
Earlier work this paper cites.
Learning and generalization characteristics of the random vector functional-link net
Y.H. Pao, G.H. Park, and D.J. Sobajic · 1994
Earlier work this paper cites.
Stochastic choice of basis functions in adaptive function approximation and the functional-link net
B. Igelnik and Y.H. Pao · 1995
Earlier work this paper cites.
Matrix Computations, 3rd Ed
G.H. Golub and C.F.V. Loan · 1996
Earlier work this paper cites.
Simultaneous approximations of mulvariate functions and their derivatives by neural networks with one hidden layer
X. Li · 1996
Earlier work this paper cites.
Domain decomposition : parallel multilevel methods for elliptic partial differential equations
Barry F. Smith, Petter E. Bjørstad, and William D. Gropp · 1996
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
I.E. Lagaris, A.C. Likas, and D.I. Fotiadis · 1998
Earlier work this paper cites.
Neural Networks: A Comprehensive Foundation
S. Haykin · 1999
Earlier work this paper cites.
Neural-network methods for boundary value problems with irregular boundaries
I.E. Lagaris, A.C. Likas, and D.G. Papageorgiou · 2000
Earlier work this paper cites.
On the computational power of recurrent circuits of spiking neurons
W. Maass and H. Markram · 2004
Earlier work this paper cites.
Spectral/hp element methods for computational fluid dynamics, 2nd edn
G.E. Karniadakis and S.J. Sherwin · 2005
Earlier work this paper cites.
Domain Decomposition Methods − - Algorithms and Theory
A. Toselli and O. Widlund · 2005
Earlier work this paper cites.
Extreme learning machine: theory and applications
G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew · 2006
Cited alongside, same era.
Numerical Optimization, Second Edition
J. Nocedal and S.J. Wright · 2006
Cited alongside, same era.
Optimization and applications of echo state networks with leaky integrator neurons
H. Jaeger, M. Lukosevicius, D. Popovici, and U. Siewert · 2007
Cited alongside, same era.
A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems
S. Dong and Z. Yosibash · 2009
Cited alongside, same era.
BDF-like methods for nonlinear dynamic analysis
S. Dong · 2010
Cited alongside, same era.
Application of error minimized extreme learning machine for simultaneous learning of a function and its derivativs
S. Balasundaram and Kapil · 2011
Multiphase flows of N immiscible incompressible fluids: a reduction-consistent and thermodynamically-consistent formulation and associated algorithm
S. Dong · 2018
Later among the works it cites.
The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems
W. E and B. Yu · 2018
Later among the works it cites.
DGM: A deep learning algorithm for solving partial differential equations
J. Sirignano and K. Spoliopoulos · 2018
Later among the works it cites.
A novel improved extreme learning machine algorithm in solving ordinary differential equations by legendre neural network methods
Y. Yang, M. Hou, and J. Luo · 2018
Later among the works it cites.
MgNet: A unified framework for multigrid and convolutional neural network
J. He and J. Xu · 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…
Cited alongside, same era.
Extreme learning machines: a survey
G.-B. Huang, D.H. Wang, and Y. Lan · 2011
Cited alongside, same era.
A time-stepping scheme involving constant coefficient matrices for phase field simulations of two-phase incompressible flows with large density ratios
S. Dong and J. Shen · 2012
Cited alongside, same era.
Alan Turing’s unorganized machines and artificial neural networks: his remarkable early work and future possibilities
C.S. Webster · 2012
Cited alongside, same era.
An eigen-based high-order expansion basis for structured spectral elements
X. Zheng and S. Dong · 2012
Cited alongside, same era.
Adam: a method for stochastic optimization
D.P. Kingma and J. Ba · 2014
Cited alongside, same era.
A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows
S. Dong and J. Shen · 2015
Cited alongside, same era.
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.
Solving partial differential equations based on bernsteirn neural network and extreme learning machine algorithm
H. Sun, M. Hou, Y. Yang, T. Zhang, F. Weng, and F. Han · 2019
Later among the works it cites.
S. Dong and N. Ni · 2020
Closest in time.
Physics informed extreme learning machine (pielm) − - a rapid method for the numerical solution of partial differential equations
V. Dwivedi and B. Srinivasan · 2020
Closest in time.
Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
A.D. Jagtap, E. Kharazmi, and G.E. Karniadakis · 2020
Closest in time.
D3M: A deep domain decomposition method for partial differential equations
K. Li, K. Tang, T. Wu, and Q. Liao · 2020
Closest in time.
Legendre neural network method for several classes of singularly perturbed differential equations based on mapping and piecewise optimization technology
H. Liu, B. Xing, Z. Wang, and L. Li · 2020
Closest in time.
Optimization free neural network approach for solving ordinary and partial differential equations
S. Panghal and M. Kumar · 2020
Closest in time.
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
E. Samanaiego, C. Anitescu, S. Goswami, V.M. Nguyen-Thanh, H. Guo, K. Hamdia, X. Zhuang, and T. Rabczuk · 2020
Closest in time.
The finite neuron method and convergence analysis
J. Xu · 2020
Closest in time.
Weak adversarial networks for high-dimensional partial differential equations
Y. Zang, G. Bao, X. Ye, and H. Zhou · 2020
Closest in time.