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Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data.
A rapidly convergent iteration method and non-linear partial differential equations-i
J. Moser · 1966
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Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
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Gaussian error linear units (gelus)
D. Hendrycks and K. Gimpel · 2016
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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 · 2019
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Deep neural network expression of posterior expectations in Bayesian PDE inversion
L. Herrmann, C. Schwab, and J. Zech · 2020
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Model reduction and neural networks for parametric pdes
K. Bhattacharya, B. Hosseini, N. B. Kovachki, and A. M. Stuart · 2021
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On universal approximation and error bounds for fourier neural operators
N. Kovachki, S. Lanthaler, and S. Mishra · 2021
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Fourier neural operator for parametric partial differential equations
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2021
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Learning nonlinear operators via deeponet based on the universal approximation theorem of operators
L. Lu, P. Jin, G. Pang, Z. Zhang, and G. E. Karniadakis · 2021
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The random feature model for input-output maps between banach spaces
N. H. Nelsen and A. M. Stuart · 2021
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Incremental spatial and spectral learning of neural operators for solving large-scale pdes
R. J. George, J. Zhao, J. Kossaifi, Z. Li, and A. Anandkumar · 2022
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Constructive deep relu neural network approximation
L. Herrmann, J. A. Opschoor, and C. Schwab · 2022
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Error estimates for deeponets: A deep learning framework in infinite dimensions
S. Lanthaler, S. Mishra, and G. E. Karniadakis · 2022
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Fourier neural operator with learned deformations for pdes on general geometries
Z. Li, D. Z. Huang, B. Liu, and A. Anandkumar · 2023
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De rham compatible deep neural network fem
M. Longo, J. A. Opschoor, N. Disch, C. Schwab, and J. Zech · 2023
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Learning homogenization for elliptic operators
K. Bhattacharya, N. Kovachki, A. Rajan, A. M. Stuart, and M. Trautner · 2024
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Neural and spectral operator surrogates: unified construction and expression rate bounds, 2024
L. Herrmann, C. Schwab, and J. Zech · 2024
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Operator learning: Algorithms and analysis
N. B. Kovachki, S. Lanthaler, and A. M. Stuart · 2024
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Convolutional neural operators for robust and accurate learning of pdes
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Are neural operators really neural operators? frame theory meets operator learning
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Neural operator: Learning maps between function spaces with applications to pdes
N. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2023
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B. Raonic, R. Molinaro, T. De Ryck, T. Rohner, F. Bartolucci, R. Alaifari, S. Mishra, and E. de Bézenac · 2024
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Ai-aided geometric design of anti-infection catheters
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