Fetching the paper…
Reading the bibliography…
Learning the mapping between two function spaces has garnered considerable research attention.
Methods of mathematical physics. Vol. I
R. Courant and D. Hilbert · 1953
Earlier work this paper cites.
Boundary problems for pseudo-differential operators
Louis Boutet de Monvel · 1971
Earlier work this paper cites.
Fourier integral operators. I
Lars Hörmander · 1971
Earlier work this paper cites.
Fourier integral operators. II
J. J. Duistermaat and L. Hörmander · 1972
Earlier work this paper cites.
Methods of modern mathematical physics. I. Functional analysis
Michael Reed and Barry Simon · 1972
Earlier work this paper cites.
The analysis of linear partial differential operators. I
Lars Hörmander · 1990
Earlier work this paper cites.
The analysis of linear partial differential operators. III
Lars Hörmander · 1994
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
Earlier work this paper cites.
Fourier integral operators , volume 130 of Progress in Mathematics
J. J. Duistermaat · 1996
Earlier work this paper cites.
Neural operator: Graph kernel network for partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2003
Earlier work this paper cites.
Multipole graph neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2006
Earlier work this paper cites.
Spectral methods for time-dependent problems , volume 21
Jan S Hesthaven, Sigal Gottlieb, and David Gottlieb · 2007
Earlier work this paper cites.
Pseudo-differential operators and symmetries: background analysis and advanced topics , volume 2
Michael Ruzhansky and Ville Turunen · 2009
Earlier work this paper cites.
Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2010
Earlier work this paper cites.
Deep sparse rectifier neural networks
Xavier Glorot, Antoine Bordes, and Yoshua Bengio · 2011
Cited alongside, same era.
Convolutional neural networks for steady flow approximation
Xiaoxiao Guo, Wei Li, and Francesco Iorio · 2016
Cited alongside, same era.
Gaussian error linear units (gelus)
Dan Hendrycks and Kevin Gimpel · 2016
Cited alongside, same era.
Searching for activation functions
Prajit Ramachandran, Barret Zoph, and Quoc V Le · 2017
Cited alongside, same era.
Pseudodifferential Operators (PMS-34)
Michael Eugene Taylor · 2017
Cited alongside, same era.
The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems
Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach
Hyung Ju Hwang, Jin Woo Jang, Hyeontae Jo, and Jae Yong Lee · 2020
Later among the works it cites.
Adaptive fourier neural operators: Efficient token mixers for transformers
John Guibas, Morteza Mardani, Zongyi Li, Andrew Tao, Anima Anandkumar, and Bryan Catanzaro · 2021
Later among the works it cites.
Multiwavelet-based operator learning for differential equations
Gaurav Gupta, Xiongye Xiao, and Paul Bogdan · 2021
Later among the works it cites.
Solving pde-constrained control problems using operator learning
Rakhoon Hwang, Jae Yong Lee, Jin Young Shin, and Hyung Ju Hwang · 2021
Later among the works it cites.
Solving parametric PDE problems with artificial neural networks
Yuehaw Khoo, Jianfeng Lu, and Lexing Ying · 2021
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Weinan E and Bing Yu · 2018
Cited alongside, same era.
A deep neural network surrogate for high-dimensional random partial differential equations
Mohammad Amin Nabian and Hadi Meidani · 2018
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 · 2018
Cited alongside, same era.
DGM: a deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
Cited alongside, same era.
Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification
Yinhao Zhu and Nicholas Zabaras · 2018
Cited alongside, same era.
Prediction of aerodynamic flow fields using convolutional neural networks
Saakaar Bhatnagar, Yaser Afshar, Shaowu Pan, Karthik Duraisamy, and Shailendra Kaushik · 2019
Cited alongside, same era.
Lu Lu, Pengzhan Jin, and George Em Karniadakis · 2019
Cited alongside, same era.
The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via
Jae Yong Lee, Jin Woo Jang, and Hyung Ju Hwang · 2021
Later among the works it cites.
Sifan Wang, Hanwen Wang, and Paris Perdikaris · 2021
Later among the works it cites.
Learning operators with coupled attention
Georgios Kissas, Jacob Seidman, Leonardo Ferreira Guilhoto, Victor M Preciado, George J Pappas, and Paris Perdikaris · 2022
Closest in time.
A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis · 2022
Closest in time.
U-no: U-shaped neural operators
Md Ashiqur Rahman, Zachary E Ross, and Kamyar Azizzadenesheli · 2022
Closest in time.
Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems
Tapas Tripura and Souvik Chakraborty · 2022
Closest in time.
Physics-informed deep neural operator networks
Somdatta Goswami, Aniruddha Bora, Yue Yu, and George Em Karniadakis · 2023
Closest in time.
HyperdeepONet: learning operator with complex target function space using the limited resources via hypernetwork
Jae Yong Lee, SungWoong CHO, and Hyung Ju Hwang · 2023
Closest in time.