Fetching the paper…
Reading the bibliography…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions.
A counterexample to the approximation problem in Banach spaces
P. Enflo · 1973
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
Earlier work this paper cites.
Optimal nonlinear approximation
R. A. DeVore, R. Howard, and C. Micchelli · 1989
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
Earlier work this paper cites.
Design and analysis of computer experiments
J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn · 1989
Earlier work this paper cites.
Some tools for functional data analysis
J. O. Ramsay and C. Dalzell · 1991
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
Earlier work this paper cites.
Constructive approximation
R. A. DeVore and G. G. Lorentz · 1993
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
T. Chen and H. Chen · 1995
Earlier work this paper cites.
Neural networks for functional approximation and system identification
H. N. Mhaskar and N. Hahm · 1997
Earlier work this paper cites.
Nonlinear approximation
R. A. DeVore · 1998
Earlier work this paper cites.
Approximation theory of the mlp model in neural networks
A. Pinkus · 1999
Earlier work this paper cites.
Statistical and Computational Inverse Problems
J. Kaipio and E. Somersalo · 2006
Earlier work this paper cites.
Random features for large-scale kernel machines
A. Rahimi and B. Recht · 2007
Earlier work this paper cites.
Optimization with PDE constraints
M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich · 2008
Earlier work this paper cites.
A new approach to collaborative filtering: Operator estimation with spectral regularization
J. Abernethy, F. Bach, T. Evgeniou, and J.-P. Vert · 2009
Earlier work this paper cites.
Convergence rates of best n-term galerkin approximations for a class of elliptic SPDEs
A. Cohen, R. DeVore, and C. Schwab · 2010
Earlier work this paper cites.
Partial differential equations
L. C. Evans · 2010
Earlier work this paper cites.
On learning with integral operators
L. Rosasco, M. Belkin, and E. D. Vito · 2010
Earlier work this paper cites.
Inverse problems: A Bayesian perspective
A. M. Stuart · 2010
Earlier work this paper cites.
Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs
A. Cohen, R. Devore, and C. Schwab · 2011
Earlier work this paper cites.
MCMC methods for functions: Modifying old algorithms to make them faster
S. Cotter, G. Roberts, A. Stuart, and D. White · 2012
Earlier work this paper cites.
Functional maps: A flexible representation of maps between shapes
M. Ovsjanikov, M. Ben-Chen, J. Solomon, A. Butscher, and L. Guibas · 2012
Earlier work this paper cites.
Sparse adaptive taylor approximation algorithms for parametric and stochastic elliptic PDEs
A. Chkifa, A. Cohen, R. DeVore, and C. Schwab · 2013
Earlier work this paper cites.
Asymptotics of prediction in functional linear regression with functional outputs
C. Crambes and A. Mas · 2013
Earlier work this paper cites.
Classical Banach Spaces I: Sequence Spaces
J. Lindenstrauss and L. Tzafriri · 2013
Earlier work this paper cites.
Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions
M. Hairer, A. M. Stuart, and S. J. Vollmer · 2014
Earlier work this paper cites.
Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
A. Chkifa, A. Cohen, and C. Schwab · 2015
Earlier work this paper cites.
Approximation of high-dimensional parametric PDEs
A. Cohen and R. DeVore · 2015
Earlier work this paper cites.
Deep Learning
I. Goodfellow, Y. Bengio, and A. Courville · 2016
Earlier work this paper cites.
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
J. Ling, A. Kurzawski, and J. Templeton · 2016
Earlier work this paper cites.
Data-driven operator inference for nonintrusive projection-based model reduction
B. Peherstorfer and K. Willcox · 2016
Earlier work this paper cites.
Breaking the curse of dimensionality with convex neural networks
F. Bach · 2017
Earlier work this paper cites.
Kolmogorov widths and low-rank approximations of parametric elliptic PDEs
M. Bachmayr and A. Cohen · 2017
Earlier work this paper cites.
Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
Q. Li, F. Dietrich, E. M. Bollt, and I. G. Kevrekidis · 2017
Earlier work this paper cites.
Deep functional maps: Structured prediction for dense shape correspondence
O. Litany, T. Remez, E. Rodola, A. Bronstein, and M. Bronstein · 2017
Earlier work this paper cites.
Attention is all you need
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin · 2017
Earlier work this paper cites.
Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data
J.-X. Wang, J.-L. Wu, and H. Xiao · 2017
Earlier work this paper cites.
Error bounds for approximations with deep ReLU networks
D. Yarotsky · 2017
Earlier work this paper cites.
Syncspeccnn: Synchronized spectral CNN for 3D shape segmentation
L. Yi, H. Su, X. Guo, and L. J. Guibas · 2017
Earlier work this paper cites.
Non-intrusive reduced order modeling of nonlinear problems using neural networks
J. S. Hesthaven and S. Ubbiali · 2018
Earlier work this paper cites.
Deep dynamical modeling and control of unsteady fluid flows
J. Morton, F. D. Witherden, A. Jameson, and M. J. Kochenderfer · 2018
Earlier work this paper cites.
Nonlinear integro-differential operator regression with neural networks
R. G. Patel and O. Desjardins · 2018
Earlier work this paper cites.
Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework
J.-L. Wu, H. Xiao, and E. Paterson · 2018
Earlier work this paper cites.
Optimal approximation with sparsely connected deep neural networks
H. Bolcskei, P. Grohs, G. Kutyniok, and P. Petersen · 2019
Earlier work this paper cites.
Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ
C. Schwab and J. Zech · 2019
Earlier work this paper cites.
Nonlinear approximation via compositions
Z. Shen, H. Yang, and S. Zhang · 2019
Earlier work this paper cites.
Projection-based model reduction: Formulations for physics-based machine learning
R. Swischuk, L. Mainini, B. Peherstorfer, and K. Willcox · 2019
Earlier work this paper cites.
Learning deep neural network representations for Koopman operators of nonlinear dynamical systems
E. Yeung, S. Kundu, and N. Hodas · 2019
Earlier work this paper cites.
Deepgreen: Deep learning of Green’s functions for nonlinear boundary value problems
C. R. Gin, D. E. Shea, S. L. Brunton, and J. N. Kutz · 2020
Earlier work this paper cites.
Learning constitutive relations from indirect observations using deep neural networks
D. Z. Huang, K. Xu, C. Farhat, and E. Darve · 2020
Cited alongside, same era.
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
K. Lee and K. T. Carlberg · 2020
Cited alongside, same era.
Neural operator: Graph kernel network for partial differential equations
Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. M. Stuart, and A. Anandkumar · 2020
Cited alongside, same era.
Multipole graph neural operator for parametric partial differential equations
Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. Liu, A. M. Stuart, K. Bhattacharya, and A. Anandkumar · 2020
Cited alongside, same era.
Function approximation by deep networks
H. Mhaskar and T. Poggio · 2020
Cited alongside, same era.
Generic bounds on the approximation error for physics-informed (and) operator learning
T. D. Ryck and S. Mishra · 2022
Later among the works it cites.
NOMAD: Nonlinear manifold decoders for operator learning
J. Seidman, G. Kissas, P. Perdikaris, and G. J. Pappas · 2022
Later among the works it cites.
Diffusionnet: Discretization agnostic learning on surfaces
N. Sharp, S. Attaiki, K. Crane, and M. Ovsjanikov · 2022
Later among the works it cites.
Functional linear regression with mixed predictors
D. Wang, Z. Zhao, Y. Yu, and R. Willett · 2022
Later among the works it cites.
Neural network architecture beyond width and depth
S. Zhang, Z. Shen, and H. Yang · 2022
Later among the works it cites.
Optimal approximation of infinite-dimensional holomorphic functions
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
E. Qian, B. Kramer, B. Peherstorfer, and K. Willcox · 2020
Cited alongside, same era.
A survey of deep learning for scientific discovery
M. Raghu and E. Schmidt · 2020
Cited alongside, same era.
Nonparametric regression using deep neural networks with ReLU activation function
J. Schmidt-Hieber · 2020
Cited alongside, same era.
The phase diagram of approximation rates for deep neural networks
D. Yarotsky and A. Zhevnerchuk · 2020
Cited alongside, same era.
Gradient-based dimension reduction of multivariate vector-valued functions
O. Zahm, P. G. Constantine, C. Prieur, and Y. M. Marzouk · 2020
Cited alongside, same era.
Model reduction and neural networks for parametric PDEs
K. Bhattacharya, B. Hosseini, N. B. Kovachki, and A. M. Stuart · 2021
Cited alongside, same era.
Convergence rate of DeepONets for learning operators arising from advection-diffusion equations
B. Deng, Y. Shin, L. Lu, Z. Zhang, and G. E. Karniadakis · 2021
Cited alongside, same era.
B. Adcock, N. Dexter, and S. Moraga · 2023
Later among the works it cites.
B. Adcock, N. Dexter, and S. Moraga · 2023
Later among the works it cites.
Are neural operators really neural operators? Frame theory meets operator learning
F. Bartolucci, E. de Bézenac, B. Raonić, R. Molinaro, S. Mishra, and R. Alaifari · 2023
Later among the works it cites.
Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation
J. A. L. Benitez, T. Furuya, F. Faucher, A. Kratsios, X. Tricoche, and M. V. de Hoop · 2023
Later among the works it cites.
Spherical fourier neural operators: learning stable dynamics on the sphere
B. Bonev, T. Kurth, C. Hundt, J. Pathak, M. Baust, K. Kashinath, and A. Anandkumar · 2023
Later among the works it cites.
Learning elliptic partial differential equations with randomized linear algebra
N. Boullé and A. Townsend · 2023
Later among the works it cites.
Machine learning for partial differential equations
S. L. Brunton and J. N. Kutz · 2023
Later among the works it cites.
The Kolmogorov infinite dimensional equation in a Hilbert space via deep learning methods
J. Castro · 2023
Later among the works it cites.
Deep operator learning lessens the curse of dimensionality for pdes
K. Chen, C. Wang, and H. Yang · 2023
Later among the works it cites.
Convergence rates for learning linear operators from noisy data
M. V. de Hoop, N. B. Kovachki, N. H. Nelsen, and A. M. Stuart · 2023
Later among the works it cites.
Approximation bounds for convolutional neural networks in operator learning
N. R. Franco, S. Fresca, A. Manzoni, and P. Zunino · 2023
Later among the works it cites.
Basis operator network: A neural network-based model for learning nonlinear operators via neural basis
N. Hua and W. Lu · 2023
Later among the works it cites.
Aperiodic table of modes and maximum a posteriori estimators
I. Klebanov and T. Sullivan · 2023
Later among the works it cites.
Neural operator: Learning maps between function spaces with applications to PDEs
N. B. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2023
Later among the works it cites.
Learning skillful medium-range global weather forecasting
R. Lam, A. Sanchez-Gonzalez, M. Willson, P. Wirnsberger, M. Fortunato, F. Alet, S. Ravuri, T. Ewalds, Z. Eaton-Rosen, W. Hu, A. Merose, S. Hoyer, G. Holland, O. Vinyals, J. Stott, A. Pritzel, S. Mohamed, and P. Battaglia · 2023
Later among the works it cites.
Operator learning with PCA-Net: Upper and lower complexity bounds
S. Lanthaler · 2023
Later among the works it cites.
The nonlocal neural operator: Universal approximation
S. Lanthaler, Z. Li, and A. M. Stuart · 2023
Later among the works it cites.
Nonlinear reconstruction for operator learning of PDEs with discontinuities
S. Lanthaler, R. Molinaro, P. Hadorn, and S. Mishra · 2023
Later among the works it cites.
Error bounds for learning with vector-valued random features
S. Lanthaler and N. H. Nelsen · 2023
Later among the works it cites.
Neural oscillators are universal
S. Lanthaler, T. K. Rusch, and S. Mishra · 2023
Later among the works it cites.
The curse of dimensionality in operator learning
S. Lanthaler and A. M. Stuart · 2023
Later among the works it cites.
D. Luo, T. O’Leary-Roseberry, P. Chen, and O. Ghattas · 2023
Later among the works it cites.
Exponential convergence of deep operator networks for elliptic partial differential equations
C. Marcati and C. Schwab · 2023
Later among the works it cites.
Local approximation of operators
H. Mhaskar · 2023
Later among the works it cites.
Size lowerbounds for deep operator networks
A. Mukherjee and A. Roy · 2023
Later among the works it cites.
U-NO: U-shaped neural operators
M. A. Rahman, Z. E. Ross, and K. Azizzadenesheli · 2023
Later among the works it cites.
Convolutional neural operators
B. Raonic, R. Molinaro, T. Rohner, S. Mishra, and E. de Bezenac · 2023
Later among the works it cites.
Convolutional neural operators for robust and accurate learning of PDEs
B. Raonic, R. Molinaro, T. D. Ryck, T. Rohner, F. Bartolucci, R. Alaifari, S. Mishra, and E. de Bezenac · 2023
Later among the works it cites.
Deep operator network approximation rates for Lipschitz operators
C. Schwab, A. Stein, and J. Zech · 2023
Later among the works it cites.
Deep learning in high dimension: Neural network expression rates for analytic functions in L 2 ( ℝ d , γ d ) {L}^{2}(\mathbb{R}^{d},\gamma_{d})
C. Schwab and J. Zech · 2023
Later among the works it cites.
Optimal approximation rates for deep ReLU neural networks on Sobolev and Besov spaces
J. W. Siegel · 2023
Later among the works it cites.
Learning partial differential equations in reproducing kernel hilbert spaces
G. Stepaniants · 2023
Later among the works it cites.
Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems
T. Tripura and S. Chakraborty · 2023
Later among the works it cites.
Operator learning for hyperbolic partial differential equations
C. Wang and A. Townsend · 2023
Later among the works it cites.
BelNet: Basis enhanced learning, a mesh-free neural operator
Z. Zhang, L. Tat, and H. Schaeffer · 2023
Later among the works it cites.
Kernel methods are competitive for operator learning
P. Batlle, M. Darcy, B. Hosseini, and H. Owhadi · 2024
Closest in time.
Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
M. J. Colbrook and A. Townsend · 2024
Closest in time.
Globally injective and bijective neural operators
T. Furuya, M. Puthawala, M. Lassas, and M. V. de Hoop · 2024
Closest in time.
An operator learning perspective on parameter-to-observable maps
D. Z. Huang, N. H. Nelsen, and M. Trautner · 2024
Closest in time.
Learning nonlinear reduced models from data with operator inference
B. Kramer, B. Peherstorfer, and K. E. Willcox · 2024
Closest in time.
PDE-refiner: Achieving accurate long rollouts with neural PDE solvers
P. Lippe, B. Veeling, P. Perdikaris, R. Turner, and J. Brandstetter · 2024
Closest in time.
Deep nonparametric estimation of operators between infinite dimensional spaces
H. Liu, H. Yang, M. Chen, T. Zhao, and W. Liao · 2024
Closest in time.
Derivative-informed neural operator: An efficient framework for high-dimensional parametric derivative learning
T. O’Leary-Roseberry, P. Chen, U. Villa, and O. Ghattas · 2024
Closest in time.
Variationally mimetic operator networks
D. Patel, D. Ray, M. R. Abdelmalik, T. J. Hughes, and A. A. Oberai · 2024
Closest in time.