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Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning.
Pytorch: An imperative style, high-performance deep learning library
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Köpf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S · 1912
Earlier work this paper cites.
The Eightfold Way: A Theory of strong interaction symmetry
Gell-Mann, M · 1961
Earlier work this paper cites.
Handbook of mathematical functions , volume 55
Abramowitz, M., Stegun, I. A., et al · 1964
Earlier work this paper cites.
Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position
Fukushima, K · 1980
Earlier work this paper cites.
Multigrid methods
McCormick, S. F · 1987
Earlier work this paper cites.
Computing fourier transforms and convolutions on the 2-sphere
Driscoll, J. and Healy, D · 1994
Earlier work this paper cites.
Convolutional Networks for Images, Speech and Time Series , pp. 255–258
Lecun, Y. and Bengio, Y · 1995
Earlier work this paper cites.
A spectral element shallow water model on spherical geodesic grids
Giraldo, F. X · 2001
Earlier work this paper cites.
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Kalnay, E · 2003
Earlier work this paper cites.
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Nair, R. D., Thomas, S. J., and Loft, R. D · 2005
Earlier work this paper cites.
A novel sampling theorem on the sphere
McEwen, J. D. and Wiaux, Y · 2011
Earlier work this paper cites.
The universal approximation theorem for complex-valued neural networks
Voigtlaender, F · 2012
Earlier work this paper cites.
Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations
Schaeffer, N · 2013
Earlier work this paper cites.
Group equivariant convolutional networks
Cohen, T. S. and Welling, M · 2016
Earlier work this paper cites.
Sphere Packings, Lattices and Groups , volume 290
Conway, J. and Sloane, N · 2016
Earlier work this paper cites.
Gaussian Error Linear Units (GELUs)
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Earlier work this paper cites.
Instance normalization: The missing ingredient for fast stylization
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Earlier work this paper cites.
Discontinuous galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction
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Cited alongside, same era.
Data assimilation in the geosciences: An overview of methods, issues, and perspectives
Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G · 2018
Cited alongside, same era.
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Cited alongside, same era.
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Cited alongside, same era.
Weather and climate forecasting with neural networks: using general circulation models (gcms) with different complexity as a study ground
Scher, S. and Messori, G · 2019
Cited alongside, same era.
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Guibas, J., Mardani, M., Li, Z., Tao, A., Anandkumar, A., and Catanzaro, B · 2021
Later among the works it cites.
Alias-free generative adversarial networks
Karras, T., Aittala, M., Laine, S., Härkönen, E., Hellsten, J., Lehtinen, J., and Aila, T · 2021
Later among the works it cites.
Neural operator: Learning maps between function spaces
Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2021
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A functional approach to rotation equivariant non-linearities for tensor field networks
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Arcomano, T., Szunyogh, I., Pathak, J., Wikner, A., Hunt, B. R., and Ott, E · 2020
Cited alongside, same era.
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Bauer, P., Quintino, T., Wedi, N., Bonanni, A., Chrust, M., Deconinck, W., Diamantakis, M., Düben, P., English, S., Flemming, J., Gillies, P., Hadade, I., Hawkes, J., Hawkins, M., Iffrig, O., Kühnlein, C., Lange, M., Lean, P., Marsden, O., Müller, A., Saarinen, S., Sarmany, D., Sleigh, M., Smart, S., Smolarkiewicz, P., Thiemert, D., Tumolo, G., Weihrauch, C., Zanna, C., and Maciel, P · 2020
Cited alongside, same era.
An image is worth 16x16 words: Transformers for image recognition at scale
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Cited alongside, same era.
The ERA5 global reanalysis
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., Chiara, G. D., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer, A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., de Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J.-N · 2020
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Cited alongside, same era.
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Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Pritzel, A., Ravuri, S., Ewalds, T., Alet, F., Eaton-Rosen, Z., Hu, W., Merose, A., Hoyer, S., Holland, G., Stott, J., Vinyals, O., Mohamed, S., and Battaglia, P · 2022
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U-no: U-shaped neural operators
Rahman, M. A., Ross, Z. E., and Azizzadenesheli, K · 2022
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U-fno—an enhanced fourier neural operator-based deep-learning model for multiphase flow
Wen, G., Li, Z., Azizzadenesheli, K., Anandkumar, A., and Benson, S. M · 2022
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Review of Particle Physics
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Multi-grid tensorized fourier neural operator for high resolution PDEs, 2023
Kossaifi, J., Kovachki, N. B., Azizzadenesheli, K., and Anandkumar, A · 2023
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Neural operator: Learning maps between function spaces with applications to pdes
Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2023
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