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Neural operators, as an efficient surrogate model for learning the solutions of PDEs, have received extensive attention in the field of scientific machine learning.
On the partial difference equations of mathematical physics
Courant, R., Friedrichs, K., and Lewy, H · 1967
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Introduction to partial differential equations with applications
Zachmanoglou, E. C. and Thoe, D. W · 1986
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Crafting papers on machine learning
Langley, P · 2000
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The finite element method for elliptic problems
Ciarlet, P. G · 2002
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The finite element method: its basis and fundamentals
Zienkiewicz, O. C., Taylor, R. L., and Zhu, J. Z · 2005
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Numerical partial differential equations: finite difference methods
Thomas, J. W · 2013
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
Ioffe, S. and Szegedy, C · 2015
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Ba, J. L., Kiros, J. R., and Hinton, G. E · 2016
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Deep residual learning for image recognition
He, K., Zhang, X., Ren, S., and Sun, J · 2016
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Attention is all you need
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., and Polosukhin, I · 2017
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The best of both worlds: Combining recent advances in neural machine translation
Chen, M. X., Firat, O., Bapna, A., Johnson, M., Macherey, W., Foster, G., Jones, L., Schuster, M., Shazeer, N., Parmar, N., et al · 2018
Earlier work this paper cites.
Decoupled weight decay regularization
Loshchilov, I. and Hutter, F · 2018
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Image transformer
Parmar, N., Vaswani, A., Uszkoreit, J., Kaiser, L., Shazeer, N., Ku, A., and Tran, D · 2018
Cited alongside, same era.
Generating long sequences with sparse transformers
Child, R., Gray, S., Radford, A., and Sutskever, I · 2019
Cited alongside, same era.
Lu, L., Jin, P., and Karniadakis, G. E · 2019
Cited alongside, same era.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi, M., Perdikaris, P., and Karniadakis, G. E · 2019
Cited alongside, same era.
Super-convergence: Very fast training of neural networks using large learning rates
Smith, L. N. and Topin, N · 2019
Cited alongside, same era.
Biological structure and function emerge from scaling unsupervised learning to 250 million protein sequences
Rives, A., Meier, J., Sercu, T., Goyal, S., Lin, Z., Liu, J., Guo, D., Ott, M., Zitnick, C. L., Ma, J., et al · 2021
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Nyströmformer: A nyström-based algorithm for approximating self-attention
Xiong, Y., Zeng, Z., Chakraborty, R., Tan, M., Fung, G., Li, Y., and Singh, V · 2021
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Towards large-scale learned solvers for parametric pdes with model-parallel fourier neural operators
Grady, T. J., Khan, R., Louboutin, M., Yin, Z., Witte, P. A., Chandra, R., Hewett, R. J., and Herrmann, F. J · 2022
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Fourier neural operator with learned deformations for pdes on general geometries
Li, Z., Huang, D. Z., Liu, B., and Anandkumar, A · 2022
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Ht-net: Hierarchical transformer based operator learning model for multiscale pdes
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Transformers are rnns: Fast autoregressive transformers with linear attention
Katharopoulos, A., Vyas, A., Pappas, N., and Fleuret, F · 2020
Cited alongside, same era.
Fourier neural operator for parametric partial differential equations
Li, Z., Kovachki, N. B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., Anandkumar, A., et al · 2020
Cited alongside, same era.
Linformer: Self-attention with linear complexity
Wang, S., Li, B. Z., Khabsa, M., Fang, H., and Ma, H · 2020
Cited alongside, same era.
Big bird: Transformers for longer sequences
Zaheer, M., Guruganesh, G., Dubey, K. A., Ainslie, J., Alberti, C., Ontanon, S., Pham, P., Ravula, A., Wang, Q., Yang, L., et al · 2020
Cited alongside, same era.
Choose a transformer: Fourier or galerkin
Cao, S · 2021
Cited alongside, same era.
Multiwavelet-based operator learning for differential equations
Gupta, G., Xiao, X., and Bogdan, P · 2021
Cited alongside, same era.
Neural operator: Learning maps between function spaces
Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2021
Cited alongside, same era.
Liu, X., Xu, B., and Zhang, L · 2022
Later among the works it cites.
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
Later among the works it cites.
Continuous spatiotemporal transformers
Fonseca, A. H. d. O., Zappala, E., Caro, J. O., and van Dijk, D · 2023
Closest in time.
Gnot: A general neural operator transformer for operator learning
Hao, Z., Wang, Z., Su, H., Ying, C., Dong, Y., Liu, S., Cheng, Z., Song, J., and Zhu, J · 2023
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Vito: Vision transformer-operator
Ovadia, O., Kahana, A., Stinis, P., Turkel, E., and Karniadakis, G. E · 2023
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Factorized fourier neural operators
Tran, A., Mathews, A., Xie, L., and Ong, C. S · 2023
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Solving high-dimensional pdes with latent spectral models
Wu, H., Hu, T., Luo, H., Wang, J., and Long, M · 2023
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Koopman neural operator as a mesh-free solver of non-linear partial differential equations
Xiong, W., Huang, X., Zhang, Z., Deng, R., Sun, P., and Tian, Y · 2023
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