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  citation-key: AlexanderianFast2016
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  accessed:
    - year: 2022
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      day: 6
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- id: AtkinsonDatadriven2019
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  event-title: NeurIPS
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      day: 17
  language: en
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  publisher: PMLR
  title: >-
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- id: BarSinaiLearning2019
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- id: BasirCritical
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    - year: 2022
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  publisher: American Institute of Aeronautics and Astronautics
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- id: BeckMachine2019
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      month: 9
      day: 16
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  citation-key: BeckMachine2019
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  language: en
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- id: BezginJAXFLUIDS2022
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      day: 25
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- id: BhattacharyaModel2020
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    - year: 2020
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- id: BieglerNonlinear2010
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      day: 1
  language: en
  number-of-pages: '411'
  publisher: SIAM
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- id: BlechschmidtThree2021
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      day: 15
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- id: BotteroPhysicsInformed2020
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      month: 8
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      month: 12
      day: 12
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- id: BrandstetterClifford2022
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  event-title: The Eleventh International Conference on Learning Representations
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      month: 9
      day: 29
  language: en
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  event-title: ICLR
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      day: 26
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- id: BrehmerMining2019
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  citation-key: BrehmerMining2019
  event-title: NeurIPS
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  language: en
  page: '7'
  title: 'Mining gold: Improving simulation-based inference with latent information'
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- id: BrennerPerspective2019
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    - year: 2023
      month: 11
      day: 29
  author:
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      month: 10
      day: 16
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  title: Perspective on machine learning for advancing fluid mechanics
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- id: BruntonDatadriven2019
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    - family: Kutz
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  call-number: TA330 .B78 2019
  citation-key: BruntonDatadriven2019
  event-place: Cambridge
  ISBN: 978-1-108-42209-3
  issued:
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  publisher: Cambridge University Press
  publisher-place: Cambridge
  title: >-
    Data-driven science and engineering: machine learning, dynamical systems,
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- id: BruntonMachine2020
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      month: 11
      day: 29
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    - family: Noack
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  issue: '1'
  issued:
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  page: 477-508
  title: Machine Learning for Fluid Mechanics
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  URL: http://arxiv.org/abs/1905.11075
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- id: ChuLearning2021
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      month: 8
      day: 19
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    - family: Thuerey
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    - family: Seidel
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    - family: Theobalt
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    - family: Zayer
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  container-title: ACM Transactions on Graphics
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  ISSN: 0730-0301, 1557-7368
  issue: '4'
  issued:
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      month: 8
  language: en
  page: 1-13
  title: Learning meaningful controls for fluids
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- id: CockayneProbabilistic2020
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      month: 3
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    - family: Duncan
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  citation-key: CockayneProbabilistic2020
  issued:
    - year: 2020
      month: 9
      day: 3
  language: en
  title: Probabilistic Gradients for Fast Calibration of Differential Equation Models
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- id: CranmerLearning2019
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    - family: Xu
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    Machine Learning and the Physical Sciences  Workshop at the 33rd Conference
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  language: en
  page: '6'
  title: Learning Symbolic Physics with Graph Networks
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- id: DandekarBayesian2021
  accessed:
    - year: 2021
      month: 7
      day: 12
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    - family: Dixit
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    - family: Tarek
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    - family: Garcia-Valadez
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    - family: Vemula
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      month: 3
      day: 3
  title: Bayesian Neural Ordinary Differential Equations
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- id: DawRethinking2022
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      month: 7
      day: 12
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    - family: Bu
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    - family: Wang
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    - family: Perdikaris
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  DOI: 10.48550/arXiv.2207.02338
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      month: 7
      day: 5
  number: arXiv:2207.02338
  publisher: arXiv
  title: Rethinking the Importance of Sampling in Physics-informed Neural Networks
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- id: DiGiovanniGraph2022
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  DOI: 10.48550/arXiv.2206.10991
  issued:
    - year: 2022
      month: 8
      day: 15
  number: arXiv:2206.10991
  publisher: arXiv
  title: Graph Neural Networks as Gradient Flows
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- id: DuffinStatistical2021
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      day: 13
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    - family: Stemler
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    - family: Girolami
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  container-title: Proceedings of the National Academy of Sciences
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  issue: '2'
  issued:
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      month: 1
      day: 12
  language: en
  PMID: '33372139'
  publisher: National Academy of Sciences
  section: Physical Sciences
  title: Statistical finite elements for misspecified models
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- id: DuraisamyTurbulence2019
  accessed:
    - year: 2023
      month: 11
      day: 29
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    - family: Xiao
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  citation-key: DuraisamyTurbulence2019
  container-title: Annual Review of Fluid Mechanics
  container-title-short: Annu. Rev. Fluid Mech.
  DOI: 10.1146/annurev-fluid-010518-040547
  ISSN: 0066-4189, 1545-4479
  issue: '1'
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      month: 1
      day: 5
  language: en
  page: 357-377
  title: Turbulence Modeling in the Age of Data
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- id: EAlgorithms2020
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      day: 4
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  citation-key: EAlgorithms2020
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  issued:
    - year: 2020
      month: 9
      day: 11
  title: >-
    Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to
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- id: EDawning2021
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  container-title: Notices of the American Mathematical Society
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  issue: '04'
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  page: '1'
  title: The Dawning of a New Era in Applied Mathematics
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  URL: https://www.ams.org/notices/202104/rnoti-p565.pdf
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- id: EDeep2017
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    - family: Han
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  citation-key: EDeep2017
  container-title: Communications in Mathematics and Statistics
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  ISSN: 2194-671X
  issue: '4'
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  language: en
  page: 349-380
  title: >-
    Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial
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  URL: http://arxiv.org/abs/1706.04702
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- id: EDeep2018
  accessed:
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  citation-key: EDeep2018
  container-title: Communications in Mathematics and Statistics
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  ISSN: 2194-671X
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    The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving
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- id: EigelVariational2019
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  container-title: Advances in Computational Mathematics
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- id: FanBCRNet2019
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  title: 'BCR-Net: A neural network based on the nonstandard wavelet form'
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- id: FaroughiPhysicsGuided2023
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      month: 9
      day: 6
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- id: KovachkiNeural2023
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      day: 10
  language: en
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    Learning Parameters and Constitutive Relationships with Physics Informed
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- id: ThuereyPhysicsbased2021
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  publisher: WWW
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- id: TorradoPhysicsinformed2021
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      day: 14
  language: en
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- id: UmDifferentiable
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  citation-key: UmDifferentiable
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  language: en
  page: '5'
  title: >-
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- id: UmSolverintheLoop2021
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      day: 5
  title: >-
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- id: VadyalaPhysicsinformed2022
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  language: en
  page: '100110'
  title: >-
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- id: WackerLaplace2017
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- id: WangPhysicsInformed
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  language: en
  page: '9'
  title: >-
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- id: WangPhysicsinformed2020
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- id: WangWhen2020
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  citation-key: WangWhen2020
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  language: en
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- id: WenUFNO2022
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- id: XuAdversarial2019
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  citation-key: XuAdversarial2019
  DOI: 10.48550/arXiv.1910.06936
  issued:
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- id: YangBPINNs2021
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- id: YangPhysicsInformed2020
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  publisher: Society for Industrial and Applied Mathematics
  title: >-
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  language: en
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  title: >-
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  number: arXiv:2204.11144
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  citation-key: ZhangLearning2020
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  publisher: Society for Industrial and Applied Mathematics
  title: >-
    Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using
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- id: ZhangQuantifying2019
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  citation-key: ZhangQuantifying2019
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  language: en
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  publisher: Academic Press
  title: >-
    Quantifying total uncertainty in physics-informed neural networks for
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  citation-key: ZhiLearning2022
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  publisher: PMLR
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    - family: Balakrishnan
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  citation-key: ZubovNeuralPDE2021
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      month: 7
      day: 19
  number: arXiv:2107.09443
  publisher: arXiv
  title: >-
    NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error
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...
