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Recent advances in the literature show promising potential of deep learning methods, particularly neural operators, in obtaining numerical solutions to partial differential equations (PDEs) beyond the reach of current numerical solvers.
Constructive approximation
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Pde-net: Learning pdes from data
Z. Long, Y. Lu, X. Ma, and B. Dong · 2018
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DGM: A deep learning algorithm for solving partial differential equations
J. A. Sirignano and K. Spiliopoulos · 2018
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L. Lu, P. Jin, and G. E. Karniadakis · 2019
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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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Model reduction and neural networks for parametric pdes
K. Bhattacharya, B. Hosseini, N. B. Kovachki, and A. M. Stuart · 2020
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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
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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
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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.
S. Wang, H. Wang, and P. Perdikaris · 2021
Cited alongside, same era.
Bayesian neural networks for weak solution of pdes with uncertainty quantification
X. Zhang and K. C. Garikipati · 2021
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GCN-FFNN: A two-stream deep model for learning solution to partial differential equations
Enhanced deeponet for modeling partial differential operators considering multiple input functions
L. Tan and L. Chen · 2022
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Mod-net: A machine learning approach via model-operator-data network for solving pdes
L. Zhang, T. Luo, Y. Zhang, W. E, Z.-Q. John Xu, and Z. Ma · 2022
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LNO: laplace neural operator for solving differential equations
Q. Cao, S. Goswami, and G. E. Karniadakis · 2023
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Neural inverse operators for solving PDE inverse problems
R. Molinaro, Y. Yang, B. Engquist, and S. Mishra · 2023
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A graph convolutional autoencoder approach to model order reduction for parametrized pdes
F. Pichi, B. Moya, and J. S. Hesthaven · 2023
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O. Bilgin, T. Vergutz, and S. Mehrkanoon · 2022
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V. Fanaskov and I. V. Oseledets · 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 · 2022
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Non-equispaced fourier neural solvers for pdes
H. Lin, L. Wu, Y. Xu, Y. Huang, S. Li, G. Zhao, and S. Z. Li · 2022
Cited alongside, same era.
U-NO: u-shaped neural operators
M. A. Rahman, Z. E. Ross, and K. Azizzadenesheli · 2022
Cited alongside, same era.
NOMAD: nonlinear manifold decoders for operator learning
J. H. Seidman, G. Kissas, P. Perdikaris, and G. J. Pappas · 2022
Cited alongside, same era.
Lordnet: Learning to solve parametric partial differential equations without simulated data
W. Shi, X. Huang, X. Gao, X. Wei, J. Zhang, J. Bian, M. Yang, and T. Liu · 2022
Cited alongside, same era.
J. Shin, J. Y. Lee, and H. J. Hwang · 2022
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A metalearning approach for physics-informed neural networks (PINNs): Application to parameterized PDEs
M. Penwarden, S. Zhe, A. Narayan, and R. M. Kirby · 2023
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Convolutional neural operators for robust and accurate learning of pdes, 2023
B. Raonić, R. Molinaro, T. D. Ryck, T. Rohner, F. Bartolucci, R. Alaifari, S. Mishra, and E. de Bézenac · 2023
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Towards foundation models for scientific machine learning: Characterizing scaling and transfer behavior
S. Subramanian, P. Harrington, K. Keutzer, W. Bhimji, D. Morozov, M. W. Mahoney, and A. Gholami · 2023
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Factorized fourier neural operators
A. Tran, A. P. Mathews, L. Xie, and C. S. Ong · 2023
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Random grid neural processes for parametric partial differential equations
A. Vadeboncoeur, I. Kazlauskaite, Y. Papandreou, F. Cirak, M. Girolami, and Ö. D. Akyildiz · 2023
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Speeding up fourier neural operators via mixed precision
C. White, R. Tu, J. Kossaifi, G. Pekhimenko, K. Azizzadenesheli, and A. Anandkumar · 2023
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Poseidon: Efficient foundation models for pdes
M. Herde, B. Raonic, T. Rohner, R. Käppeli, R. Molinaro, E. de Bézenac, and S. Mishra · 2024
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