Fetching the paper…
Reading the bibliography…
Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces.
The fast Fourier transform and its applications
E Oran Brigham · 1988
Earlier work this paper cites.
Partial differential equations with numerical methods , volume 45
Stig Larsson and Vidar Thomée · 2003
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.
Spectral methods: fundamentals in single domains
Claudio Canuto, M Yousuff Hussaini, Alfio Quarteroni, and Thomas A Zang · 2007
Earlier work this paper cites.
Partial differential equations , volume 19
Lawrence C Evans · 2010
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.
Invariant recurrent solutions embedded in a turbulent two-dimensional kolmogorov flow
Gary J Chandler and Rich R Kerswell · 2013
Earlier work this paper cites.
Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
Earlier work this paper cites.
Very deep convolutional networks for large-scale image recognition
Karen Simonyan and Andrew Zisserman · 2014
Earlier work this paper cites.
Fully convolutional networks for semantic segmentation
Jonathan Long, Evan Shelhamer, and Trevor Darrell · 2015
Earlier work this paper cites.
U-net: Convolutional networks for biomedical image segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
Earlier work this paper cites.
Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
Cited alongside, same era.
Gaussian error linear units (gelus)
Dan Hendrycks and Kevin Gimpel · 2016
Cited alongside, same era.
End-to-end training of deep visuomotor policies
Sergey Levine, Chelsea Finn, Trevor Darrell, and Pieter Abbeel · 2016
Cited alongside, same era.
Exploring generalization in deep learning
Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nati Srebro · 2017
Cited alongside, same era.
Hidden physics models: Machine learning of nonlinear partial differential equations
Maziar Raissi and George Em Karniadakis · 2018
Cited alongside, same era.
Reconciling modern machine-learning practice and the classical bias–variance trade-off
Beyond ℋ \mathcal{H} -divergence: Domain adaptation theory with jensen-shannon divergence
Changjian Shui, Qi Chen, Jun Wen, Fan Zhou, Christian Gagné, and Boyu Wang · 2020
Later among the works it cites.
Yehuda Dar, Vidya Muthukumar, and Richard G Baraniuk · 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.
Factorized fourier neural operators
Alasdair Tran, Alexander Mathews, Lexing Xie, and Cheng Soon Ong · 2021
Later among the works it cites.
U-fno–an enhanced fourier neural operator based-deep learning model for multiphase flow
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Mikhail Belkin, Daniel Hsu, Siyuan Ma, and Soumik Mandal · 2019
Cited alongside, same era.
Symplectic recurrent neural networks
Zhengdao Chen, Jianyu Zhang, Martin Arjovsky, and Léon Bottou · 2019
Cited alongside, same era.
Gradient descent finds global minima of deep neural networks
Simon Du, Jason Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai · 2019
Cited alongside, same era.
Language models are few-shot learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al · 2020
Cited alongside, same era.
Siddhartha Mishra and Roberto Molinaro · 2020
Cited alongside, same era.
On universal approximation and error bounds for fourier neural operators
Nikola Kovachki, Samuel Lanthaler, and Siddhartha Mishra
Cited in the paper.
Neural operator: Learning maps between function spaces
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar
Cited in the paper.
Gege Wen, Zongyi Li, Kamyar Azizzadenesheli, Anima Anandkumar, and Sally M Benson · 2021
Later among the works it cites.
Seismic wave propagation and inversion with neural operators
Yan Yang, Angela F Gao, Jorge C Castellanos, Zachary E Ross, Kamyar Azizzadenesheli, and Robert W Clayton · 2021
Later among the works it cites.
Understanding deep learning (still) requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2021
Later among the works it cites.
Solving seismic wave equations on variable velocity models with fourier neural operator
Bian Li, Hanchen Wang, Xiu Yang, and Youzuo Lin · 2022
Closest in time.
Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, et al · 2022
Closest in time.
Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems
Tapas Tripura and Souvik Chakraborty · 2023
Closest in time.