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Transformers have empowered many milestones across various fields and have recently been applied to solve partial differential equations (PDEs).
Darcy’s law and the field equations of the flow of underground fluids
Hubbert, M. K · 1956
Earlier work this paper cites.
The proof and measurement of association between two things
Spearman, C · 1961
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Solid mechanics
Dym, C. L., Shames, I. H., et al · 1973
Earlier work this paper cites.
Numerical analysis of spectral methods: theory and applications
Gottlieb, D. and Orszag, S. A · 1977
Earlier work this paper cites.
Aerodynamics, aeronautics, and flight mechanics
McCormick, B. W · 1994
Earlier work this paper cites.
Introduction to multigrid methods
Wesseling, P · 1995
Earlier work this paper cites.
Partial differential equations : methods and applications
Wazwaz, A. M · 2002
Earlier work this paper cites.
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
Earlier work this paper cites.
Neural operator: Graph kernel network for partial differential equations
Li, Z.-Y., Kovachki, N. B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2003
Earlier work this paper cites.
Partial differential equations and the finite element method
Ŝolín, P · 2005
Earlier work this paper cites.
Fluid-structure interaction: modelling, simulation, optimisation
Bungartz, H.-J. and Schäfer, M · 2006
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Continuum fluid mechanics and the navier-stokes equations
McLean, D · 2012
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Nonlinear partial differential equations with applications
Roubíček, T · 2013
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Shapenet: An information-rich 3d model repository
Chang, A. X., Funkhouser, T., Guibas, L., Hanrahan, P., Huang, Q., Li, Z., Savarese, S., Savva, M., Song, S., Su, H., et al · 2015
Earlier work this paper cites.
Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2015
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U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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Training deep nets with sublinear memory cost
Chen, T., Xu, B., Zhang, C., and Guestrin, C · 2016
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Geometric deep learning: going beyond euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., and Vandergheynst, P · 2017
Earlier work this paper cites.
Inductive representation learning on large graphs
Hamilton, W., Ying, Z., and Leskovec, J · 2017
Earlier work this paper cites.
Pointnet: Deep learning on point sets for 3d classification and segmentation
Qi, C. R., Su, H., Mo, K., and Guibas, L. J · 2017
Earlier work this paper cites.
Attention is all you need
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L. u., and Polosukhin, I · 2017
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The deep ritz method: A deep learning-based numerical algorithm for solving variational problems
Weinan, E. and Yu, T · 2017
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Learning three-dimensional flow for interactive aerodynamic design
Umetani, N. and Bickel, B · 2018
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Bert: Pre-training of deep bidirectional transformers for language understanding
Devlin, J., Chang, M.-W., Lee, K., and Toutanova, K · 2019
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Graph u-nets
Gao, H. and Ji, S · 2019
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Decoupled weight decay regularization
Loshchilov, I. and Hutter, F · 2019
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Point transformer
Zhao, H., Jiang, L., Jia, J., Torr, P. H., and Koltun, V · 2021
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AirfRANS: High fidelity computational fluid dynamics dataset for approximating reynolds-averaged navier–stokes solutions
Bonnet, F., Mazari, J. A., Cinnella, P., and patrick gallinari · 2022
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Deep transfer operator learning for partial differential equations under conditional shift
Goswami, S., Kontolati, K., Shields, M. D., and Karniadakis, G. E · 2022
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Fourier neural operator with learned deformations for pdes on general geometries
Li, Z.-Y., Huang, D. Z., Liu, B., and Anandkumar, A · 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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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
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Language models are few-shot learners
Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., Agarwal, S., Herbert-Voss, A., Krueger, G., Henighan, T., Child, R., Ramesh, A., Ziegler, D., Wu, J., Winter, C., Hesse, C., Chen, M., Sigler, E., Litwin, M., Gray, S., Chess, B., Clark, J., Berner, C., McCandlish, S., Radford, A., Sutskever, I., and Amodei, D · 2020
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Reformer: The efficient transformer
Kitaev, N., Kaiser, L., and Levskaya, A · 2020
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Learning to simulate complex physics with graph networks
Sanchez-Gonzalez, A., Godwin, J., Pfaff, T., Ying, R., Leskovec, J., and Battaglia, P · 2020
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Choose a transformer: Fourier or galerkin
Cao, S · 2021
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An image is worth 16x16 words: Transformers for image recognition at scale
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N · 2021
Cited alongside, same era.
Trockman, A. and Kolter, J. Z · 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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Flowformer: Linearizing transformers with conservation flows
Wu, H., Wu, J., Xu, J., Wang, J., and Long, M · 2022
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Point-bert: Pre-training 3d point cloud transformers with masked point modeling
Yu, X., Tang, L., Rao, Y., Huang, T., Zhou, J., and Lu, J · 2022
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Achiam, J., Adler, S., Agarwal, S., Ahmad, L., Akkaya, I., Aleman, F. L., Almeida, D., Altenschmidt, J., Altman, S., Anadkat, S., et al · 2023
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Gnot: A general neural operator transformer for operator learning
Hao, Z., Ying, C., Wang, Z., Su, H., Dong, Y., Liu, S., Cheng, Z., Zhu, J., and Song, J · 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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U-no: U-shaped neural operators
Rahman, M. A., Ross, Z. E., and Azizzadenesheli, K · 2023
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Factorized fourier neural operators
Tran, A., Mathews, A., Xie, L., and Ong, C. S · 2023
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Scientific discovery in the age of artificial intelligence
Wang, H., Fu, T., Du, Y., Gao, W., Huang, K., Liu, Z., Chandak, P., Liu, S., Van Katwyk, P., Deac, A., et al · 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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Ulip-2: Towards scalable multimodal pre-training for 3d understanding
Xue, L., Yu, N., Zhang, S., Li, J., Martín-Martín, R., Wu, J., Xiong, C., Xu, R., Niebles, J. C., and Savarese, S · 2023
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Geometry-guided conditional adaption for surrogate models of large-scale 3d PDEs on arbitrary geometries
Deng, J., Li, X., Xiong, H., Hu, X., and Ma, J · 2024
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Improved operator learning by orthogonal attention
Xiao, Z., Hao, Z., Lin, B., Deng, Z., and Su, H · 2024
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