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We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition.
Long short-term memory
Sepp Hochreiter and Juergen Schmidhuber · 1986
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There exists a neural network that does not make avoidable mistakes
Ronald Gallant and Halbert White · 1988
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Multilayer feedforward networks are universal approximators
Kurk Hornik, Maxwell Stinchcombe, and Halbert White · 1989
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1992
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Applied Probability Models with Optimization Applications
Sheldon Ross · 1992
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Universal approximation bounds for superpositions of a sigmoidal function
Andrew Barron · 1993
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
Moshe Leshno, Vladimir Lin, Allan Pinkus, and Shimon Schocken · 1993
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On least squares estimation of fourier coefficients and of the regression function
W. Popiński · 1993
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Learning internal representations by error propagation
David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams · 1997
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Yann LeCun, Patrick Haffner, Léon Bottou, and Yoshua Bengio · 1999
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Adrian Silvescu · 1999
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Fundamentals of Finite Element Analysis
David Hutton · 2004
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Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Steven L. Brunton, Joshua L. Proctor, and Nathan Kutz · 2016
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Activation functions: Comparison of trends in practice and research for deep learning
Chigozie Nwankpa, Winifred Ijomah, Anthony Gachagan, and Stephen Marshall · 2018
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Deep hidden physics models: Deep learning of nonlinear partial differential equations
Maziar Raissi · 2018
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Dgm: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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A discussion on solving partial differential equations using neural networks
Tim Dockhorn · 2019
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On weight initialization in deep neural networks
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Data-driven discovery of partial differential equations
Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and Nathan Kutz · 2017
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Neural ordinary differential equations
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Pde-net: Learning pdes from data
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Deep neural networks motivated by partial differential equations
Lars Ruthotto and Eldad Haber · 2019
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Fourier neural networks: A comparative study
Abylay Zhumekenov, Malika Uteuliyeva, Olzhas Kabdolov, Rustem Takhanov, Zhenisbek Assylbekov, and Alejandro J. Castro · 2019
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Fourier neural operator for parametric partial differential equations, 2021
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