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Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning.
Introduction to partial differential equations with applications
Zachmanoglou, E. C. and Thoe, D. W · 1986
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Adaptive mixtures of local experts
Jacobs, R. A., Jordan, M. I., Nowlan, S. J., and Hinton, G. E · 1991
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A survey of unstructured mesh generation technology
Owen, S. J · 1998
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Principles of multiscale modeling
Weinan, E · 2011
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U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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Decoupled weight decay regularization
Loshchilov, I. and Hutter, F · 2017
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Generating long sequences with sparse transformers
Child, R., Gray, S., Radford, A., and Sutskever, I · 2019
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Ccnet: Criss-cross attention for semantic segmentation
Huang, Z., Wang, X., Huang, L., Huang, C., Wei, Y., and Liu, W · 2019
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Lu, L., Jin, P., and Karniadakis, G. E · 2019
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Super-convergence: Very fast training of neural networks using large learning rates
Smith, L. N. and Topin, N · 2019
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Longformer: The long-document transformer
Beltagy, I., Peters, M. E., and Cohan, A · 2020
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Rethinking attention with performers
Choromanski, K., Likhosherstov, V., Dohan, D., Song, X., Gane, A., Sarlos, T., Hawkins, P., Davis, J., Mohiuddin, A., Kaiser, L., et al · 2020
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Scaling laws for neural language models
Kaplan, J., McCandlish, S., Henighan, T., Brown, T. B., Chess, B., Child, R., Gray, S., Radford, A., Wu, J., and Amodei, D · 2020
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Transformers are rnns: Fast autoregressive transformers with linear attention
Katharopoulos, A., Vyas, A., Pappas, N., and Fleuret, F · 2020
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Reformer: The efficient transformer
Kitaev, N., Kaiser, Ł., and Levskaya, A · 2020
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Gshard: Scaling giant models with conditional computation and automatic sharding
Lepikhin, D., Lee, H., Xu, Y., Chen, D., Firat, O., Huang, Y., Krikun, M., Shazeer, N., and Chen, Z · 2020
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Fourier neural operator for parametric partial differential equations
Factorized fourier neural operators
Tran, A., Mathews, A., Xie, L., and Ong, C. S · 2021
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Learning the solution operator of parametric partial differential equations with physics-informed deeponets
Wang, S., Wang, H., and Perdikaris, P · 2021
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Towards large-scale learned solvers for parametric pdes with model-parallel fourier neural operators
Grady II, 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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Physics-informed machine learning: A survey on problems, methods and applications
Hao, Z., Liu, S., Zhang, Y., Ying, C., Feng, Y., Su, H., and Zhu, J · 2022
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Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2020
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Efficient transformers: A survey
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Multiwavelet-based operator learning for differential equations
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Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
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Hu, Z., Jagtap, A. D., Karniadakis, G. E., and Kawaguchi, K · 2022
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Mionet: Learning multiple-input operators via tensor product
Jin, P., Meng, S., and Lu, L · 2022
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Mesh-independent operator learning for partial differential equations
Lee, S · 2022
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Ht-net: Hierarchical transformer based operator learning model for multiscale pdes
Liu, X., Xu, B., and Zhang, L · 2022
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Variable-input deep operator networks
Prasthofer, M., De Ryck, T., and Mishra, S · 2022
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Improved architectures and training algorithms for deep operator networks
Wang, S., Wang, H., and Perdikaris, P · 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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Nuno: A general framework for learning parametric pdes with non-uniform data
Liu, S., Hao, Z., Ying, C., Su, H., Cheng, Z., and Zhu, J · 2023
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