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Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data.
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Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
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Neural operator: Graph kernel network for partial differential equations
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Multipole graph neural operator for parametric partial differential equations
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On universal approximation and error bounds for Fourier neural operators
Continuous generative neural networks
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Learning operators with coupled attention
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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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Variable input deep operator networks
M. Prasthofer, T. De Ryck, and S. Mishra · 2022
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N. Kovachki, S. Lanthaler, and S. Mishra · 2021
Cited alongside, same era.
Neural operator: Learning maps between function spaces
N. B. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. M. Stuart, and A. Anandkumar · 2021
Cited alongside, same era.
Fourier neural operator for parametric partial differential equations
Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2021
Cited alongside, same era.
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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J. H. Seidman, G. Kissas, P. Perdikaris, and G. J. Pappas · 2022
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The lie derivative for measuring learned equivariance
N. Gruver, M. A. Finzi, M. Goldblum, and A. G. Wilson · 2023
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Convolutional neural operators for robust and accurate learning of PDEs
B. Raonić, R. Molinaro, T. De Ryck, T. Rohner, F. Bartolucci, R. Alaifari, S. Mishra, and E. de Bézenac · 2023
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