Fetching the paper…
Reading the bibliography…
A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces.
“Comparing numerical methods for ordinary differential equations”
TE Hull, WH Enright, BM Fellen and AE Sedgwick · 1972
Earlier work this paper cites.
“A numerical and theoretical study of certain nonlinear wave phenomena”
Bengt Fornberg and Gerald Whitham · 1978
Earlier work this paper cites.
“The Korteweg-de Vries two-soliton solution as interacting two single solitons”
Tohru Yoneyama · 1984
Earlier work this paper cites.
“A fast algorithm for Chebyshev, Fourier, and sinc interpolation onto an irregular grid”
John Boyd · 1992
Earlier work this paper cites.
“On the Gibbs phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function”
David Gottlieb, Chi-Wang Shu, Alex Solomonoff and Hervé Vandeven · 1992
Earlier work this paper cites.
“Spectral methods in MATLAB”
Lloyd Trefethen · 2000
Earlier work this paper cites.
“Chebyshev and Fourier spectral methods”
John Boyd · 2001
Earlier work this paper cites.
“The finite element method for elliptic problems”
Philippe Ciarlet · 2002
Earlier work this paper cites.
“Chebyshev polynomials”
John Mason and David Handscomb · 2002
Earlier work this paper cites.
“Trigonometric series”
Antoni Zygmund · 2002
Earlier work this paper cites.
“Sparse grids”
Hans-Joachim Bungartz and Michael Griebel · 2004
Earlier work this paper cites.
“A spectral analysis of function composition and its implications for sampling in direct volume visualization”
Steven Bergner, Torsten Moller, Daniel Weiskopf and David Muraki · 2006
Earlier work this paper cites.
“Computing numerically with functions instead of numbers”
Lloyd Trefethen · 2007
Earlier work this paper cites.
“An algorithm for the rapid evaluation of special function transforms”
Michael O’Neil, Franco Woolfe and Vladimir Rokhlin · 2010
Cited alongside, same era.
“On polynomial multiplication in Chebyshev basis”
Pascal Giorgi · 2011
Cited alongside, same era.
“A survey on super-resolution imaging”
Jing Tian and Kai-Kuang Ma · 2011
Cited alongside, same era.
“Second-order nonlinear Schrödinger equation breather solutions in the degenerate and rogue wave limits”
David Kedziora, Adrian Ankiewicz and Nail Akhmediev · 2012
Cited alongside, same era.
“Solving transcendental equations: the Chebyshev polynomial proxy and other numerical rootfinders, perturbation series, and oracles”
John Boyd · 2014
Cited alongside, same era.
“Continuous analogues of matrix factorizations”
Alex Townsend and Lloyd Trefethen · 2015
Lu Lu, Pengzhan Jin and George Karniadakis · 2019
Later among the works it cites.
“Approximation Theory and Approximation Practice, Extended Edition”
Lloyd Trefethen · 2019
Later among the works it cites.
“Fourier neural operator for parametric partial differential equations”
Zongyi Li et al · 2020
Later among the works it cites.
“Neural operator: Graph kernel network for partial differential equations”
Zongyi Li et al · 2020
Later among the works it cites.
“Neural network approximation”
Ronald DeVore, Boris Hanin and Guergana Petrova · 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…
Cited alongside, same era.
“Chopping a Chebyshev series”
Jared Aurentz and Lloyd Trefethen · 2017
Cited alongside, same era.
Philipp Grohs, Fabian Hornung, Arnulf Jentzen and Philippe Von · 2018
Cited alongside, same era.
“Complex-valued neural networks with nonparametric activation functions”
Simone Scardapane, Steven Van, Amir Hussain and Aurelio Uncini · 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.
“The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems”
Bing Yu · 2018
Cited alongside, same era.
“Learning fast algorithms for linear transforms using butterfly factorizations”
Tri Dao et al · 2019
Cited alongside, same era.
“Neural operator: Learning maps between function spaces”
Nikola Kovachki et al · 2021
Later among the works it cites.
“Learning the solution operator of parametric partial differential equations with physics-informed DeepONets”
Sifan Wang, Hanwen Wang and Paris Perdikaris · 2021
Later among the works it cites.
“The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks”
Maarten De, Daniel Huang, Elizabeth Qian and Andrew Stuart · 2022
Closest in time.
Thomas Grady et al · 2022
Closest in time.
“A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data”
Lu Lu et al · 2022
Closest in time.
Jaideep Pathak et al · 2022
Closest in time.
“Generic Lithography Modeling with Dual-band Optics-Inspired Neural Networks”
Haoyu Yang et al · 2022
Closest in time.