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Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data.
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Scientific machine learning through physics–informed neural networks: Where we are and what’s next
S. Cuomo, V. S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli · 2022
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The cost-accuracy trade-off in operator learning with neural networks
M. V. de Hoop, D. Z. Huang, E. Qian, and A. M. Stuart · 2022
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Generic bounds on the approximation error for physics-informed (and) operator learning
T. De Ryck and S. Mishra · 2022
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Approximation rates of DeepONets for learning operators arising from advection–diffusion equations
B. Deng, Y. Shin, L. Lu, Z. Zhang, and G. E. Karniadakis · 2022
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V. Fanaskov and I. Oseledets · 2022
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2016
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Firedrake: automating the finite element method by composing abstractions
F. Rathgeber, D. A. Ham, L. Mitchell, M. Lange, F. Luporini, A. T. McRae, G.-T. Bercea, G. R. Markall, and P. H. Kelly · 2016
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Neural message passing for quantum chemistry
J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl · 2017
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Attention is all you need
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin · 2017
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Error bounds for approximations with deep ReLU networks
D. Yarotsky · 2017
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The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems
W. E and B. Yu · 2018
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A physics-informed variational deeponet for predicting crack path in quasi-brittle materials
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Learning operators with coupled attention
G. Kissas, J. H. Seidman, L. F. Guilhoto, V. M. Preciado, G. J. Pappas, and P. Perdikaris · 2022
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Error estimates for DeepONets: A deep learning framework in infinite dimensions
S. Lanthaler, S. Mishra, and G. E. Karniadakis · 2022
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Fourier neural operator with learned deformations for PDEs on general geometries
Z. Li, D. Z. Huang, B. Liu, and A. Anandkumar · 2022
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A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
L. Lu, X. Meng, S. Cai, Z. Mao, S. Goswami, Z. Zhang, and G. E. Karniadakis · 2022
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Training language models to follow instructions with human feedback
L. Ouyang, J. Wu, X. Jiang, D. Almeida, C. Wainwright, P. Mishkin, C. Zhang, S. Agarwal, K. Slama, A. Ray, et al · 2022
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Attention-enhanced neural network models for turbulence simulation
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Neural conservation laws: A divergence-free perspective
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Wavelet neural operator: a neural operator for parametric partial differential equations
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Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling
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Augmenting Deep Residual Surrogates with Fourier Neural Operators for Rapid Two-Phase Flow and Transport Simulations
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