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  publisher: arXiv
  title: Variational Data Assimilation with a Learned Inverse Observation Operator
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  title: Provable Active Learning of Neural Networks for Parametric PDEs
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- id: GoswamiPhysicsInformed2022
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      month: 7
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- id: GrohsDeep2022
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  issued:
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      month: 11
      day: 24
  language: en
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- id: HolzschuhScore2022
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- id: JinRecent2023
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  DOI: 10.48550/arXiv.2303.07647
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  number: arXiv:2303.07647
  publisher: arXiv
  title: >-
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- id: KadriOperatorvalued2016
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- id: KarlbauerComposing2022
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    - year: 2022
      month: 5
      day: 26
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  publisher: arXiv
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- id: KidgerNeural2022
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  publisher: Oxford
  title: On Neural Differential Equations
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- id: KochkovLearning2020
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  language: en
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- id: KossaifiMultiGrid2023
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    - year: 2023
      month: 2
      day: 28
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    - family: Anandkumar
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  issued:
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      month: 2
      day: 1
  language: en
  title: Multi-Grid Tensorized Fourier Neural Operator for High Resolution PDEs
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- id: KovachkiNeural2021
  accessed:
    - year: 2021
      month: 9
      day: 16
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    - family: Li
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    - family: Liu
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    - family: Azizzadenesheli
      given: Kamyar
    - family: Bhattacharya
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    - family: Stuart
      given: Andrew
    - family: Anandkumar
      given: Anima
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  issued:
    - year: 2021
      month: 9
      day: 6
  title: 'Neural Operator: Learning Maps Between Function Spaces'
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- id: KovachkiNeural2023
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      day: 1
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      given: Nikola
    - family: Li
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    - family: Liu
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    - family: Azizzadenesheli
      given: Kamyar
    - family: Bhattacharya
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    - family: Stuart
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    - family: Anandkumar
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  citation-key: KovachkiNeural2023
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  ISSN: 1533-7928
  issue: '89'
  issued:
    - year: 2023
  page: 1-97
  title: >-
    Neural Operator: Learning Maps Between Function Spaces With Applications to
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  URL: http://jmlr.org/papers/v24/21-1524.html
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- id: KovachkiUniversal2021
  accessed:
    - year: 2021
      month: 8
      day: 28
  author:
    - family: Kovachki
      given: Nikola
    - family: Lanthaler
      given: Samuel
    - family: Mishra
      given: Siddhartha
  citation-key: KovachkiUniversal2021
  container-title: arXiv:2107.07562 [cs, math]
  issued:
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      month: 7
      day: 15
  language: en
  title: On universal approximation and error bounds for Fourier Neural Operators
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- id: LamGraphCast2023
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      day: 23
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    - family: Sanchez-Gonzalez
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    - family: Willson
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    - family: Wirnsberger
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    - family: Fortunato
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    - family: Pritzel
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    - family: Mohamed
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    - family: Battaglia
      given: Peter
  citation-key: LamGraphCast2023
  DOI: 10.48550/arXiv.2212.12794
  issued:
    - year: 2023
      month: 8
      day: 4
  title: 'GraphCast: Learning skillful medium-range global weather forecasting'
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- id: LamLearning2023
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      month: 2
      day: 23
  archive_location: world
  author:
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    - family: Sanchez-Gonzalez
      given: Alvaro
    - family: Willson
      given: Matthew
    - family: Wirnsberger
      given: Peter
    - family: Fortunato
      given: Meire
    - family: Alet
      given: Ferran
    - family: Ravuri
      given: Suman
    - family: Ewalds
      given: Timo
    - family: Eaton-Rosen
      given: Zach
    - family: Hu
      given: Weihua
    - family: Merose
      given: Alexander
    - family: Hoyer
      given: Stephan
    - family: Holland
      given: George
    - family: Vinyals
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    - family: Stott
      given: Jacklynn
    - family: Pritzel
      given: Alexander
    - family: Mohamed
      given: Shakir
    - family: Battaglia
      given: Peter
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  container-title: Science
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  issued:
    - year: 2023
      month: 12
      day: 22
  language: EN
  publisher: American Association for the Advancement of Science
  title: Learning skillful medium-range global weather forecasting
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- id: LanthalerCurse2023
  accessed:
    - year: 2023
      month: 8
      day: 6
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    - family: Stuart
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  DOI: 10.48550/arXiv.2306.15924
  issued:
    - year: 2023
      month: 6
      day: 28
  number: arXiv:2306.15924
  publisher: arXiv
  title: The curse of dimensionality in operator learning
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- id: LiFourier2020
  accessed:
    - year: 2020
      month: 11
      day: 17
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    - family: Kovachki
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    - family: Azizzadenesheli
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    - family: Liu
      given: Burigede
    - family: Bhattacharya
      given: Kaushik
    - family: Stuart
      given: Andrew
    - family: Anandkumar
      given: Anima
  citation-key: LiFourier2020
  container-title: arXiv:2010.08895 [cs, math]
  issued:
    - year: 2020
      month: 10
      day: 17
  title: Fourier Neural Operator for Parametric Partial Differential Equations
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  URL: http://arxiv.org/abs/2010.08895

- id: LiFourier2022
  accessed:
    - year: 2022
      month: 8
      day: 11
  author:
    - family: Li
      given: Zongyi
    - family: Huang
      given: Daniel Zhengyu
    - family: Liu
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    - family: Anandkumar
      given: Anima
  citation-key: LiFourier2022
  DOI: 10.48550/arXiv.2207.05209
  issued:
    - year: 2022
      month: 7
      day: 11
  number: arXiv:2207.05209
  publisher: arXiv
  title: >-
    Fourier Neural Operator with Learned Deformations for PDEs on General
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  URL: http://arxiv.org/abs/2207.05209

- id: LiMultipole2020
  accessed:
    - year: 2020
      month: 11
      day: 17
  author:
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    - family: Kovachki
      given: Nikola
    - family: Azizzadenesheli
      given: Kamyar
    - family: Liu
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    - family: Stuart
      given: Andrew
    - family: Bhattacharya
      given: Kaushik
    - family: Anandkumar
      given: Anima
  citation-key: LiMultipole2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: >-
    Multipole Graph Neural Operator for Parametric Partial Differential
    Equations
  type: paper-conference
  URL: tensor
  volume: '33'

- id: LiNeural2020
  accessed:
    - year: 2022
      month: 8
      day: 12
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    - family: Kovachki
      given: Nikola
    - family: Azizzadenesheli
      given: Kamyar
    - family: Liu
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    - family: Bhattacharya
      given: Kaushik
    - family: Stuart
      given: Andrew
    - family: Anandkumar
      given: Anima
  citation-key: LiNeural2020
  DOI: 10.48550/arXiv.2003.03485
  event-title: >-
    ICLR 2020 Workshop on Integration of Deep Neural Models and Differential
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    - year: 2020
      month: 6
      day: 14
  publisher: arXiv
  title: 'Neural Operator: Graph Kernel Network for Partial Differential Equations'
  type: paper-conference
  URL: http://arxiv.org/abs/2003.03485

- id: LiPhysicsInformed2021
  accessed:
    - year: 2022
      month: 8
      day: 9
  author:
    - family: Li
      given: Zongyi
    - family: Zheng
      given: Hongkai
    - family: Kovachki
      given: Nikola Borislavov
    - family: Jin
      given: David
    - family: Chen
      given: Haoxuan
    - family: Liu
      given: Burigede
    - family: Stuart
      given: Andrew
    - family: Azizzadenesheli
      given: Kamyar
    - family: Anandkumar
      given: Anima
  citation-key: LiPhysicsInformed2021
  issued:
    - year: 2021
      month: 11
      day: 23
  language: en
  title: Physics-Informed Neural Operator for Learning Partial Differential Equations
  type: article-journal
  URL: https://openreview.net/forum?id=dtYnHcmQKeM

- id: LiuStatistical2020
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    - year: 2021
      month: 2
      day: 21
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    - family: Yeo
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    - family: Lu
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  citation-key: LiuStatistical2020
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- id: LongPDENet2018
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      day: 4
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    - family: Long
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    - family: Lu
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    - family: Ma
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    - family: Dong
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    - year: 2018
      month: 7
      day: 3
  language: en
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  publisher: PMLR
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- id: LuComprehensive2022
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      day: 21
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  language: en
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  title: >-
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- id: LuDeepONet2020
  accessed:
    - year: 2020
      month: 9
      day: 15
  author:
    - family: Lu
      given: Lu
    - family: Jin
      given: Pengzhan
    - family: Karniadakis
      given: George Em
  citation-key: LuDeepONet2020
  container-title: arXiv:1910.03193 [cs, stat]
  issued:
    - year: 2020
      month: 4
      day: 14
  title: >-
    DeepONet: Learning nonlinear operators for identifying differential
    equations based on the universal approximation theorem of operators
  type: article-journal
  URL: http://arxiv.org/abs/1910.03193

- id: LuDeepXDE2021
  accessed:
    - year: 2021
      month: 11
      day: 15
  author:
    - family: Lu
      given: Lu
    - family: Meng
      given: Xuhui
    - family: Mao
      given: Zhiping
    - family: Karniadakis
      given: George Em
  citation-key: LuDeepXDE2021
  container-title: SIAM Review
  container-title-short: SIAM Rev.
  DOI: 10.1137/19M1274067
  ISSN: 0036-1445
  issue: '1'
  issued:
    - year: 2021
      month: 1
      day: 1
  page: 208-228
  publisher: Society for Industrial and Applied Mathematics
  title: 'DeepXDE: A Deep Learning Library for Solving Differential Equations'
  type: article-journal
  volume: '63'

- id: LuoEfficient2023
  accessed:
    - year: 2023
      month: 9
      day: 25
  author:
    - family: Luo
      given: Dingcheng
    - family: O'Leary-Roseberry
      given: Thomas
    - family: Chen
      given: Peng
    - family: Ghattas
      given: Omar
  citation-key: LuoEfficient2023
  DOI: 10.48550/arXiv.2305.20053
  issued:
    - year: 2023
      month: 5
      day: 31
  number: arXiv:2305.20053
  publisher: arXiv
  title: >-
    Efficient PDE-Constrained optimization under high-dimensional uncertainty
    using derivative-informed neural operators
  type: article
  URL: http://arxiv.org/abs/2305.20053

- id: LuTheory
  author:
    - family: Lu
      given: Lu
  citation-key: LuTheory
  issued:
    - year: 2020
  language: en
  title: Theory, Algorithms, and Software for Physics-Informed Deep Learning
  type: thesis

- id: MacKinlayModel2021
  author:
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      given: Dan
    - family: Pagendam
      given: Dan
    - family: Kuhnert
      given: Petra M
    - family: Cui
      given: Tao
    - family: Robertson
      given: David
    - family: Janardhanan
      given: Sreekanth
  citation-key: MacKinlayModel2021
  event-title: Neurips Workshop on Machine learning for the Physical Sciences
  issued:
    - year: 2021
  language: en
  page: '7'
  title: >-
    Model Inversion for Spatio-temporal Processes using the Fourier Neural
    Operator
  type: paper-conference
  URL: https://ml4physicalsciences.github.io/2021/files/NeurIPS_ML4PS_2021_8.pdf

- id: MagnaniApproximate2022
  accessed:
    - year: 2022
      month: 8
      day: 11
  author:
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      given: Emilia
    - family: Krämer
      given: Nicholas
    - family: Eschenhagen
      given: Runa
    - family: Rosasco
      given: Lorenzo
    - family: Hennig
      given: Philipp
  citation-key: MagnaniApproximate2022
  issued:
    - year: 2022
      month: 8
      day: 2
  language: en
  number: arXiv:2208.01565
  publisher: arXiv
  title: >-
    Approximate Bayesian Neural Operators: Uncertainty Quantification for
    Parametric PDEs
  type: article
  URL: http://arxiv.org/abs/2208.01565

- id: MeurisMachinelearningbased2023
  accessed:
    - year: 2023
      month: 3
      day: 23
  author:
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      given: Brek
    - family: Qadeer
      given: Saad
    - family: Stinis
      given: Panos
  citation-key: MeurisMachinelearningbased2023
  container-title: Scientific Reports
  container-title-short: Sci Rep
  DOI: 10.1038/s41598-022-26602-3
  ISSN: 2045-2322
  issue: '1'
  issued:
    - year: 2023
      month: 1
      day: 31
  language: en
  number: '1'
  page: '1739'
  publisher: Nature Publishing Group
  title: Machine-learning-based spectral methods for partial differential equations
  type: article-journal
  URL: https://arxiv.org/abs/2111.05307v1
  volume: '13'

- id: NuskenSolving2021
  accessed:
    - year: 2023
      month: 3
      day: 3
  author:
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      given: Nikolas
    - family: Richter
      given: Lorenz
  citation-key: NuskenSolving2021
  container-title: Partial Differential Equations and Applications
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  DOI: 10.1007/s42985-021-00102-x
  ISSN: 2662-2971
  issue: '4'
  issued:
    - year: 2021
      month: 6
      day: 21
  language: en
  page: '48'
  title: >-
    Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks:
    perspectives from the theory of controlled diffusions and measures on path
    space
  type: article-journal
  URL: http://arxiv.org/abs/2005.05409
  volume: '2'

- id: OpschoorDeep2020
  accessed:
    - year: 2023
      month: 9
      day: 6
  author:
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      given: Joost A. A.
    - family: Petersen
      given: Philipp C.
    - family: Schwab
      given: Christoph
  citation-key: OpschoorDeep2020
  container-title: Analysis and Applications
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  DOI: 10.1142/S0219530519410136
  ISSN: 0219-5305
  issue: '05'
  issued:
    - year: 2020
      month: 9
  page: 715-770
  publisher: World Scientific Publishing Co.
  title: Deep ReLU networks and high-order finite element methods
  type: article-journal
  URL: https://www.worldscientific.com/doi/abs/10.1142/S0219530519410136
  volume: '18'

- id: PathakFourcastnet2022
  author:
    - family: Pathak
      given: Jaideep
    - family: Subramanian
      given: Shashank
    - family: Harrington
      given: Peter
    - family: Raja
      given: Sanjeev
    - family: Chattopadhyay
      given: Ashesh
    - family: Mardani
      given: Morteza
    - family: Kurth
      given: Thorsten
    - family: Hall
      given: David
    - family: Li
      given: Zongyi
    - family: Azizzadenesheli
      given: Kamyar
    - family: Hassanzadeh
      given: Pedram
    - family: Kashinath
      given: Karthik
    - family: Anandkumar
      given: Animashree
  citation-key: PathakFourcastnet2022
  DOI: 10.48550/arXiv.2202.11214
  issued:
    - year: 2022
      month: 2
      day: 22
  language: en
  page: '28'
  title: >-
    Fourcastnet: A Global Data-Driven High-Resolution Weather Model Using
    Adaptive Fourier Neural Operators
  type: article-journal
  URL: https://arxiv.org/abs/2202.11214v1

- id: PestouriePhysicsenhanced2022
  accessed:
    - year: 2022
      month: 12
      day: 20
  author:
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      given: Raphaël
    - family: Mroueh
      given: Youssef
    - family: Rackauckas
      given: Chris
    - family: Das
      given: Payel
    - family: Johnson
      given: Steven G.
  citation-key: PestouriePhysicsenhanced2022
  DOI: 10.48550/arXiv.2111.05841
  issued:
    - year: 2022
      month: 11
      day: 3
  number: arXiv:2111.05841
  publisher: arXiv
  title: Physics-enhanced deep surrogates for PDEs
  type: article
  URL: http://arxiv.org/abs/2111.05841

- id: PoliTransform2022
  accessed:
    - year: 2023
      month: 6
      day: 15
  author:
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      given: Michael
    - family: Massaroli
      given: Stefano
    - family: Berto
      given: Federico
    - family: Park
      given: Jinkyoo
    - family: Dao
      given: Tri
    - family: Ré
      given: Christopher
    - family: Ermon
      given: Stefano
  citation-key: PoliTransform2022
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2022
      month: 12
      day: 6
  language: en
  page: 7947-7959
  title: 'Transform Once: Efficient Operator Learning in Frequency Domain'
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc/paper_files/paper/2022/hash/342339109d7d756ef7bb30cf672aec02-Abstract-Conference.html
  volume: '35'

- id: PsarosUncertainty2023
  accessed:
    - year: 2023
      month: 9
      day: 3
  author:
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      given: Apostolos F.
    - family: Meng
      given: Xuhui
    - family: Zou
      given: Zongren
    - family: Guo
      given: Ling
    - family: Karniadakis
      given: George Em
  citation-key: PsarosUncertainty2023
  container-title: Journal of Computational Physics
  container-title-short: Journal of Computational Physics
  DOI: 10.1016/j.jcp.2022.111902
  ISSN: 0021-9991
  issued:
    - year: 2023
      month: 3
      day: 15
  page: '111902'
  title: >-
    Uncertainty quantification in scientific machine learning: Methods, metrics,
    and comparisons
  type: article-journal
  volume: '477'

- id: RonnebergerUNet2015
  author:
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      given: Olaf
    - family: Fischer
      given: Philipp
    - family: Brox
      given: Thomas
  citation-key: RonnebergerUNet2015
  collection-title: Lecture Notes in Computer Science
  container-title: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015
  DOI: 10.48550/arXiv.1505.04597
  editor:
    - family: Navab
      given: Nassir
    - family: Hornegger
      given: Joachim
    - family: Wells
      given: William M.
    - family: Frangi
      given: Alejandro F.
  event-place: Cham
  ISBN: 978-3-319-24574-4
  issued:
    - year: 2015
  language: en
  page: 234-241
  publisher: Springer International Publishing
  publisher-place: Cham
  title: 'U-Net: Convolutional Networks for Biomedical Image Segmentation'
  type: article
  URL: http://arxiv.org/abs/1505.04597

- id: RuheGeometric2023
  author:
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      given: David
    - family: Gupta
      given: Jayesh K
    - family: Keninck
      given: Steven
      non-dropping-particle: de
    - family: Welling
      given: Max
    - family: Brandstetter
      given: Johannes
  citation-key: RuheGeometric2023
  container-title: arXiv preprint arXiv:2302.06594
  issued:
    - year: 2023
  title: Geometric clifford algebra networks
  type: paper-conference
  URL: http://arxiv.org/abs/2302.06594

- id: SahaLearning2020
  accessed:
    - year: 2020
      month: 12
      day: 10
  author:
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      given: Akash
    - family: Balamurugan
      given: Palaniappan
  citation-key: SahaLearning2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: Learning with Operator-valued Kernels in Reproducing Kernel Krein Spaces
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper_files/paper/2020/hash/9f319422ca17b1082ea49820353f14ab-Abstract.html
  volume: '33'

- id: TakamotoPDEBench2022
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      month: 8
      day: 4
  author:
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      given: Makoto
    - family: Praditia
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    - family: Leiteritz
      given: Raphael
    - family: MacKinlay
      given: Dan
    - family: Alesiani
      given: Francesco
    - family: Pflüger
      given: Dirk
    - family: Niepert
      given: Mathias
  citation-key: TakamotoPDEBench2022
  issued:
    - year: 2022
      month: 6
      day: 16
  language: en
  title: 'PDEBench: An Extensive Benchmark for Scientific Machine Learning'
  type: paper-conference
  URL: https://openreview.net/forum?id=dh_MkX0QfrK

- id: TranFactorized2022
  accessed:
    - year: 2023
      month: 1
      day: 19
  author:
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      given: Alasdair
    - family: Mathews
      given: Alexander
    - family: Xie
      given: Lexing
    - family: Ong
      given: Cheng Soon
  citation-key: TranFactorized2022
  DOI: 10.48550/arXiv.2111.13802
  issued:
    - year: 2022
      month: 12
      day: 15
  number: arXiv:2111.13802
  publisher: arXiv
  title: Factorized Fourier Neural Operators
  type: article
  URL: http://arxiv.org/abs/2111.13802

- id: WangPhysicsinformed2020
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      month: 4
      day: 27
  author:
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    - family: Kashinath
      given: Karthik
    - family: Mustafa
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    - family: Albert
      given: Adrian
    - family: Yu
      given: Rose
  citation-key: WangPhysicsinformed2020
  collection-title: KDD '20
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    Proceedings of the 26th ACM SIGKDD International Conference on Knowledge
    Discovery & Data Mining
  DOI: 10.1145/3394486.3403198
  event-place: New York, NY, USA
  ISBN: 978-1-4503-7998-4
  issued:
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      month: 8
      day: 23
  page: 1457–1466
  publisher: Association for Computing Machinery
  publisher-place: New York, NY, USA
  title: Towards Physics-informed Deep Learning for Turbulent Flow Prediction
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- id: WenUFNO2022
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    - year: 2022
      month: 4
      day: 27
  author:
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    - family: Li
      given: Zongyi
    - family: Azizzadenesheli
      given: Kamyar
    - family: Anandkumar
      given: Anima
    - family: Benson
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  citation-key: WenUFNO2022
  container-title: Advances in Water Resources
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  ISSN: 0309-1708
  issued:
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      month: 5
      day: 1
  language: en
  page: '104180'
  title: >-
    U-FNO—An enhanced Fourier neural operator-based deep-learning model for
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  type: article-journal
  volume: '163'

- id: WitmanNeural2022
  accessed:
    - year: 2023
      month: 3
      day: 23
  author:
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      given: David
    - family: New
      given: Alexander
    - family: Alkendry
      given: Hicham
    - family: Mrema
      given: Honest
  citation-key: WitmanNeural2022
  issued:
    - year: 2022
      month: 8
      day: 2
  language: en
  title: >-
    Neural Basis Functions for Accelerating Solutions to High Mach Euler
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  type: article
  URL: https://arxiv.org/abs/2208.01687v1

- id: XuADCME2020
  accessed:
    - year: 2020
      month: 12
      day: 13
  author:
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      given: Kailai
    - family: Darve
      given: Eric
  citation-key: XuADCME2020
  container-title: arXiv:2011.11955 [cs, math]
  issued:
    - year: 2020
      month: 11
      day: 24
  title: 'ADCME: Learning Spatially-varying Physical Fields using Deep Neural Networks'
  type: paper-conference
  URL: http://arxiv.org/abs/2011.11955

- id: YinContinuous2023
  accessed:
    - year: 2023
      month: 2
      day: 20
  author:
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      given: Yuan
    - family: Kirchmeyer
      given: Matthieu
    - family: Franceschi
      given: Jean-Yves
    - family: Rakotomamonjy
      given: Alain
    - family: Gallinari
      given: Patrick
  citation-key: YinContinuous2023
  DOI: 10.48550/arXiv.2209.14855
  issued:
    - year: 2023
      month: 2
      day: 15
  number: arXiv:2209.14855
  publisher: arXiv
  title: Continuous PDE Dynamics Forecasting with Implicit Neural Representations
  type: article
  URL: http://arxiv.org/abs/2209.14855

- id: YinInterfacing2022
  accessed:
    - year: 2023
      month: 7
      day: 21
  author:
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      given: Minglang
    - family: Zhang
      given: Enrui
    - family: Yu
      given: Yue
    - family: Karniadakis
      given: George Em
  citation-key: YinInterfacing2022
  collection-title: A Special Issue in Honor of the Lifetime Achievements of J. Tinsley Oden
  container-title: Computer Methods in Applied Mechanics and Engineering
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  DOI: 10.1016/j.cma.2022.115027
  ISSN: 0045-7825
  issued:
    - year: 2022
      month: 12
      day: 1
  language: en
  page: '115027'
  title: >-
    Interfacing finite elements with deep neural operators for fast multiscale
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  type: article-journal
  volume: '402'
...
