Fetching the paper…
Reading the bibliography…
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets.
Über die praktische auflösung von integralgleichungen mit anwendungen auf randwertaufgaben
Evert J Nyström · 1930
Earlier work this paper cites.
Functions differentiable on the boundaries of regions
Hassler Whitney · 1934
Earlier work this paper cites.
An extension of tietze’s theorem
J. Dugundji · 1951
Earlier work this paper cites.
Produits tensoriels topologiques et espaces nucléaires , volume 16
A Grothendieck · 1955
Earlier work this paper cites.
Inertial ranges in two‐dimensional turbulence
Robert H. Kraichnan · 1967
Earlier work this paper cites.
Singular Integrals and Differentiability Properties of Functions
Elias M. Stein · 1970
Earlier work this paper cites.
Construction of an orthonormal basis in cm(id) and wmp(id)
Z. Ciesielski and J. Domsta · 1972
Earlier work this paper cites.
Science and statistics
George EP Box · 1976
Earlier work this paper cites.
An introduction to continuum mechanics
Morton E Gurtin · 1982
Earlier work this paper cites.
N-Widths in Approximation Theory
A. Pinkus · 1985
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, Halbert White, et al · 1989
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.
Bayesian Learning for Neural Networks
Radford M. Neal · 1996
Earlier work this paper cites.
Computing with infinite networks
Christopher K. I. Williams · 1996
Earlier work this paper cites.
An Introduction to Infinite Ergodic Theory
J. Aaronson · 1997
Earlier work this paper cites.
A new version of the fast multipole method for the laplace equation in three dimensions
Leslie Greengard and Vladimir Rokhlin · 1997
Earlier work this paper cites.
Nonlinear approximation
Ronald A. DeVore · 1998
Earlier work this paper cites.
Statistical Learning Theory
Vladimir N. Vapnik · 1998
Earlier work this paper cites.
Approximation theory of the mlp model in neural networks
Allan Pinkus · 1999
Earlier work this paper cites.
Spectral methods in MATLAB , volume 10
Lloyd N Trefethen · 2000
Earlier work this paper cites.
Chebyshev and Fourier spectral methods
John P Boyd · 2001
Earlier work this paper cites.
Contribution to the isomorphic classification of sobolev spaces lpk(omega)
Aleksander Pełczyński and Michał Wojciechowski · 2001
Earlier work this paper cites.
Spectral partitioning with indefinite kernels using the nyström extension
Serge Belongie, Charless Fowlkes, Fan Chung, and Jitendra Malik · 2002
Earlier work this paper cites.
Sobolev Spaces
R. A. Adams and J. J. Fournier · 2003
Earlier work this paper cites.
Hierarchical matrices
Steffen Börm, Lars Grasedyck, and Wolfgang Hackbusch · 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.
Fourier neural networks: An approach with sinusoidal activation functions
Luis Mingo, Levon Aslanyan, Juan Castellanos, Miguel Diaz, and Vladimir Riazanov · 2004
Earlier work this paper cites.
A unifying view of sparse approximate gaussian process regression
Joaquin Quiñonero Candela and Carl Edward Rasmussen · 2005
Earlier work this paper cites.
Topics in Banach space theory
Fernando Albiac and Nigel J. Kalton · 2006
Earlier work this paper cites.
Learning low-rank kernel matrices
Brian Kulis, Mátyás Sustik, and Inderjit Dhillon · 2006
Earlier work this paper cites.
Scaling learning algorithms towards ai
Yoshua Bengio, Yann LeCun, et al · 2007
Earlier work this paper cites.
Measure Theory , volume 2
V. I. Bogachev · 2007
Earlier work this paper cites.
Accurate, high-order representation of complex three-dimensional surfaces via fourier continuation analysis
Oscar P Bruno, Youngae Han, and Matthew M Pohlman · 2007
Earlier work this paper cites.
A Course in Functional Analysis
J. B. Conway · 2007
Earlier work this paper cites.
Cm extension by linear operators
Charles Fefferman · 2007
Earlier work this paper cites.
Continuous neural networks
Nicolas Le Roux and Yoshua Bengio · 2007
Earlier work this paper cites.
Solver-in-the-loop: Learning from differentiable physics to interact with iterative PDE-solvers
Kiwon Um, Philipp Holl, Robert Brand, Nils Thuerey, et al · 2007
Earlier work this paper cites.
Uniform approximation of functions with random bases
Ali Rahimi and Benjamin Recht · 2008
Earlier work this paper cites.
The graph neural network model
Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini · 2008
Earlier work this paper cites.
Consistency of spectral clustering
Ulrike Von Luxburg, Mikhail Belkin, and Olivier Bousquet · 2008
Earlier work this paper cites.
Bayesian inverse problems for functions and applications to fluid mechanics
Simon L Cotter, Massoumeh Dashti, James Cooper Robinson, and Andrew M Stuart · 2009
Earlier work this paper cites.
A First Course in Sobolev Spaces
G. Leoni · 2009
Earlier work this paper cites.
Concrete Functional Calculus
R.M. Dudley and R. Norvaiša · 2010
Cited alongside, same era.
Inverse problems: A bayesian perspective
A. M. Stuart · 2010
Cited alongside, same era.
Concrete Functional Calculus , volume 149
R. Dudley and Rimas Norvaisa · 2011
Cited alongside, same era.
Principles of Multiscale Modeling
Weinan E · 2011
Cited alongside, same era.
Methods of Geometric Analysis in Extension and Trace Problems , volume 1
Alexander Brudnyi and Yuri Brudnyi · 2012
Cited alongside, same era.
Numerical solution of partial differential equations by the finite element method
Claes Johnson · 2012
Cited alongside, same era.
Sharp analysis of low-rank kernel matrix approximations
Unsupervised deep learning algorithm for PDE-based forward and inverse problems
Leah Bar and Nir Sochen · 2019
Later among the works it cites.
Prediction of aerodynamic flow fields using convolutional neural networks
Saakaar Bhatnagar, Yaser Afshar, Shaowu Pan, Karthik Duraisamy, and Shailendra Kaushik · 2019
Later among the works it cites.
Graph networks as a universal machine learning framework for molecules and crystals
Chi Chen, Weike Ye, Yunxing Zuo, Chen Zheng, and Shyue Ping Ong · 2019
Later among the works it cites.
Learning to optimize multigrid PDE solvers
Daniel Greenfeld, Meirav Galun, Ronen Basri, Irad Yavneh, and Ron Kimmel · 2019
Later among the works it cites.
Mgnet: A unified framework of multigrid and convolutional neural network
Juncai He and Jinchao 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…
Francis Bach · 2013
Cited alongside, same era.
Invariant recurrent solutions embedded in a turbulent two-dimensional kolmogorov flow
Gary J. Chandler and Rich R. Kerswell · 2013
Cited alongside, same era.
Mcmc methods for functions: Modifying old algorithms to make them faster
S. L. Cotter, G. O. Roberts, A. M. Stuart, and D. White · 2013
Cited alongside, same era.
Deep gaussian processes
Andreas Damianou and Neil Lawrence · 2013
Cited alongside, same era.
Fast training of convolutional networks through ffts, 2013
Michael Mathieu, Mikael Henaff, and Yann LeCun · 2013
Cited alongside, same era.
Chapter 3: The Theoretical Foundation of Reduced Basis Methods
Ronald A. DeVore · 2014
Cited alongside, same era.
Yuehaw Khoo and Lexing Ying · 2019
Later among the works it cites.
Lu Lu, Pengzhan Jin, and George Em Karniadakis · 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
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
Later among the works it cites.
Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
Christoph Schwab and Jakob Zech · 2019
Later among the works it cites.
Model reduction and neural networks for parametric PDEs
Kaushik Bhattacharya, Bamdad Hosseini, Nikola B Kovachki, and Andrew M Stuart · 2020
Later among the works it cites.
Nonlinear methods for model reduction
Andrea Bonito, Albert Cohen, Ronald DeVore, Diane Guignard, Peter Jantsch, and Guergana Petrova · 2020
Later among the works it cites.
Language models are few-shot learners
Tom B Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al · 2020
Later among the works it cites.
Rethinking attention with performers
Krzysztof Choromanski, Valerii Likhosherstov, David Dohan, Xingyou Song, Andreea Gane, Tamas Sarlos, Peter Hawkins, Jared Davis, Afroz Mohiuddin, Lukasz Kaiser, et al · 2020
Later among the works it cites.
Optimal stable nonlinear approximation
Albert Cohen, Ronald Devore, Guergana Petrova, and Przemyslaw Wojtaszczyk · 2020
Later among the works it cites.
An image is worth 16x16 words: Transformers for image recognition at scale
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al · 2020
Later among the works it cites.
Deep relu neural network expression rates for data-to-qoi maps in bayesian PDE inversion
L Herrmann, Ch Schwab, and J Zech · 2020
Later among the works it cites.
Meshfreeflownet: A physics-constrained deep continuous space-time super-resolution framework
Chiyu Max Jiang, Soheil Esmaeilzadeh, Kamyar Azizzadenesheli, Karthik Kashinath, Mustafa Mustafa, Hamdi A Tchelepi, Philip Marcus, Anima Anandkumar, et al · 2020
Later among the works it cites.
Enforcing physical constraints in cnns through differentiable PDE layer
Karthik Kashinath, Philip Marcus, et al · 2020
Later among the works it cites.
Derivative-informed projected neural networks for high-dimensional parametric maps governed by pdes
Thomas O’Leary-Roseberry, Umberto Villa, Peng Chen, and Omar Ghattas · 2020
Later among the works it cites.
Deep learning in high dimension: Relu network expression rates for bayesian PDE inversion
Joost A.A. Opschoor, Christoph Schwab, and Jakob Zech · 2020
Later among the works it cites.
Physics-informed probabilistic learning of linear embeddings of nonlinear dynamics with guaranteed stability
Shaowu Pan and Karthik Duraisamy · 2020
Later among the works it cites.
Using machine learning to augment coarse-grid computational fluid dynamics simulations, 2020
Jaideep Pathak, Mustafa Mustafa, Karthik Kashinath, Emmanuel Motheau, Thorsten Kurth, and Marcus Day · 2020
Later among the works it cites.
Learning mesh-based simulation with graph networks, 2020
Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W. Battaglia · 2020
Later among the works it cites.
Implicit neural representations with periodic activation functions
Vincent Sitzmann, Julien NP Martel, Alexander W Bergman, David B Lindell, and Gordon Wetzstein · 2020
Later among the works it cites.
Eikonet: Solving the eikonal equation with deep neural networks
Jonathan D Smith, Kamyar Azizzadenesheli, and Zachary E Ross · 2020
Later among the works it cites.
Error estimates for spectral convergence of the graph laplacian on random geometric graphs toward the laplace–beltrami operator
Nicolás García Trillos, Moritz Gerlach, Matthias Hein, and Dejan Slepčev · 2020
Later among the works it cites.
Lagrangian fluid simulation with continuous convolutions
Benjamin Ummenhofer, Lukas Prantl, Nils Thürey, and Vladlen Koltun · 2020
Later among the works it cites.
Towards physics-informed deep learning for turbulent flow prediction
Rui Wang, Karthik Kashinath, Mustafa Mustafa, Adrian Albert, and Rose Yu · 2020
Later among the works it cites.
Solving the kolmogorov pde by means of deep learning
Christian Beck, Sebastian Becker, Philipp Grohs, Nor Jaafari, and Arnulf Jentzen · 2021
Closest in time.
Adaptive fourier neural operators: Efficient token mixers for transformers
John Guibas, Morteza Mardani, Zongyi Li, Andrew Tao, Anima Anandkumar, and Bryan Catanzaro · 2021
Closest in time.
Solving parametric PDE problems with artificial neural networks
Yuehaw Khoo, Jianfeng Lu, and Lexing Ying · 2021
Closest in time.
On universal approximation and error bounds for Fourier Neural Operators
Nikola Kovachki, Samuel Lanthaler, and Siddhartha Mishra · 2021
Closest in time.
Error estimates for deeponets: A deep learning framework in infinite dimensions
Samuel Lanthaler, Siddhartha Mishra, and George Em Karniadakis · 2021
Closest in time.
Physics-informed neural operator for learning partial differential equations
Zongyi Li, Hongkai Zheng, Nikola Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, and Anima Anandkumar · 2021
Closest in time.
The random feature model for input-output maps between banach spaces
Nicholas H Nelsen and Andrew M Stuart · 2021
Closest in time.
Sifan Wang, Hanwen Wang, and Paris Perdikaris · 2021
Closest in time.
U-fno–an enhanced fourier neural operator based-deep learning model for multiphase flow
Gege Wen, Zongyi Li, Kamyar Azizzadenesheli, Anima Anandkumar, and Sally M Benson · 2021
Closest in time.
Long-short transformer: Efficient transformers for language and vision
Chen Zhu, Wei Ping, Chaowei Xiao, Mohammad Shoeybi, Tom Goldstein, Anima Anandkumar, and Bryan Catanzaro · 2021
Closest in time.
The cost-accuracy trade-off in operator learning with neural networks
Maarten De Hoop, Daniel Zhengyu Huang, Elizabeth Qian, and Andrew M Stuart · 2022
Closest in time.
Pod-dl-rom: Enhancing deep learning-based reduced order models for nonlinear parametrized pdes by proper orthogonal decomposition
Stefania Fresca and Andrea Manzoni · 2022
Closest in time.
A theoretical analysis of deep neural networks and parametric pdes
Gitta Kutyniok, Philipp Petersen, Mones Raslan, and Reinhold Schneider · 2022
Closest in time.