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Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications.
Quantum mechanics; 1st ed
Cohen-Tannoudji, C., Diu, B., and Laloë, F · 1973
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Numerical Methods for Conservation Laws
LeVeque, R. J · 1992
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Computing fourier transforms and convolutions on the 2-sphere
Driscoll, J. and Healy, D · 1994
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Neural operator: Graph kernel network for partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2003
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Fourier neural operator for parametric partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2010
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Numerical partial differential equations: finite difference methods , volume 22
Thomas, J. W · 2013
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Scale-invariant convolutional neural networks
Xu, Y., Xiao, T., Zhang, J., Yang, K., and Zhang, Z · 2014
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U-Net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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Group equivariant convolutional networks
Cohen, T. and Welling, M · 2016
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Scale equivariance in cnns with vector fields
Marcos, D., Kellenberger, B., Lobry, S., and Tuia, D · 2018
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Deep parametric continuous convolutional neural networks
Wang, S., Suo, S., Ma, W.-C., Pokrovsky, A., and Urtasun, R · 2018
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Bekkers, E. J · 2019
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Scale steerable filters for locally scale-invariant convolutional neural networks
Ghosh, R. and Gupta, A. K · 2019
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Scale-equivariant steerable networks
Sosnovik, I., Szmaja, M., and Smeulders, A · 2019
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Deep scale-spaces: Equivariance over scale
Worrall, D. and Welling, M · 2019
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From discrete to continuous convolution layers
Shocher, A., Feinstein, B., Haim, N., and Irani, M · 2020
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Alias-free generative adversarial networks
Karras, T., Aittala, M., Laine, S., Härkönen, E., Hellsten, J., Lehtinen, J., and Aila, T · 2021
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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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Physics-informed neural operator for learning partial differential equations
Li, Z., Zheng, H., Kovachki, N., Jin, D., Chen, H., Liu, B., Azizzadenesheli, K., and Anandkumar, A · 2021
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Spherical Fourier neural operators: Learning stable dynamics on the sphere
Bonev, B., Kurth, T., Hundt, C., Pathak, J., Baust, M., Kashinath, K., and Anandkumar, A · 2023
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Learning skillful medium-range global weather forecasting
Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., et al · 2023
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Geometry-informed neural operator for large-scale 3d pdes
Li, Z., Kovachki, N. B., Choy, C., Li, B., Kossaifi, J., Otta, S. P., Nabian, M. A., Stadler, M., Hundt, C., Azizzadenesheli, K., et al · 2023
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Truly scale-equivariant deep nets with Fourier layers
Rahman, M. A. and Yeh, R. A · 2023
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Disco: accurate discrete scale convolutions
Sosnovik, I., Moskalev, A., and Smeulders, A · 2021
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Scientific machine learning through physics–informed neural networks: Where we are and what’s next
Cuomo, S., Di Cola, V. S., Giampaolo, F., Rozza, G., Raissi, M., and Piccialli, F · 2022
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Towards multi-spatiotemporal-scale generalized pde modeling
Gupta, J. K. and Brandstetter, J · 2022
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Scalable and equivariant spherical CNNs by discrete-continuous (DISCO) convolutions
Ocampo, J., Price, M. A., and McEwen, J. D · 2022
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Pathak, J., Subramanian, S., Harrington, P., Raja, S., Chattopadhyay, A., Mardani, M., Kurth, T., Hall, D., Li, Z., Azizzadenesheli, K., Hassanzadeh, P., Kashinath, K., and Anandkumar, A · 2022
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PDEBench: An extensive benchmark for scientific machine learning
Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D., and Niepert, M · 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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Raonić, B., Molinaro, R., Rohner, T., Mishra, S., and de Bezenac, E · 2023
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Shi, Y., Lavrentiadis, G., Asimaki, D., Ross, Z. E., and Azizzadenesheli, K · 2023
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Phase neural operator for multi-station picking of seismic arrivals
Sun, H., Ross, Z. E., Zhu, W., and Azizzadenesheli, K · 2023
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Real-time high-resolution CO 2 geological storage prediction using nested Fourier neural operators
Wen, G., Li, Z., Long, Q., Azizzadenesheli, K., Anandkumar, A., and Benson, S. M · 2023
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On the locality of local neural operator in learning fluid dynamics
Ye, X., Li, H., Huang, J., and Qin, G · 2023
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Artificial intelligence for science in quantum, atomistic, and continuum systems
Zhang, X., Wang, L., Helwig, J., Luo, Y., Fu, C., Xie, Y., Liu, M., Lin, Y., Xu, Z., Yan, K., et al · 2023
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Neural operators for accelerating scientific simulations and design
Azizzadenesheli, K., Kovachki, N., Li, Z., Liu-Schiaffini, M., Kossaifi, J., and Anandkumar, A · 2024
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Generating synthetic data for neural operators
Hasani, E. and Ward, R. A · 2024
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Pretraining codomain attention neural operators for solving multiphysics PDEs
Rahman, M. A., George, R. J., Elleithy, M., Leibovici, D., Li, Z., Bonev, B., White, C., Berner, J., Yeh, R. A., Kossaifi, J., et al · 2024
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