---
references:
- id: BezginJAXFLUIDS2022
  accessed:
    - year: 2022
      month: 5
      day: 2
  author:
    - family: Bezgin
      given: Deniz A.
    - family: Buhendwa
      given: Aaron B.
    - family: Adams
      given: Nikolaus A.
  citation-key: BezginJAXFLUIDS2022
  container-title: arXiv:2203.13760 [physics]
  issued:
    - year: 2022
      month: 3
      day: 25
  title: >-
    JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics
    solver for compressible two-phase flows
  type: article-journal
  URL: http://arxiv.org/abs/2203.13760

- id: BorziComputational2012
  author:
    - family: Borzì
      given: Alfio
    - family: Schulz
      given: Volker
  call-number: QA402.5 .B655 2012
  citation-key: BorziComputational2012
  collection-title: Computational science and engineering series
  contributor:
    - family: Society for Industrial and Applied Mathematics
      given: ''
  event-place: Philadelphia
  ISBN: 978-1-61197-204-7
  issued:
    - year: 2012
  number-of-pages: '282'
  publisher: Society for Industrial and Applied Mathematics
  publisher-place: Philadelphia
  title: >-
    Computational optimization of systems governed by partial differential
    equations
  type: book

- id: CaoAdjoint2003
  accessed:
    - year: 2019
      month: 8
      day: 31
  author:
    - family: Cao
      given: Y.
    - family: Li
      given: S.
    - family: Petzold
      given: L.
    - family: Serban
      given: R.
  citation-key: CaoAdjoint2003
  container-title: SIAM Journal on Scientific Computing
  container-title-short: SIAM J. Sci. Comput.
  DOI: 10.1137/S1064827501380630
  ISSN: 1064-8275
  issue: '3'
  issued:
    - year: 2003
      month: 1
      day: 1
  page: 1076-1089
  title: >-
    Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The
    Adjoint DAE System and Its Numerical Solution
  type: article-journal
  URL: http://people.cs.vt.edu/~ycao/publication/adjdae.pdf
  volume: '24'

- id: ChuLearning2021
  accessed:
    - year: 2021
      month: 8
      day: 19
  author:
    - family: Chu
      given: Mengyu
    - family: Thuerey
      given: Nils
    - family: Seidel
      given: Hans-Peter
    - family: Theobalt
      given: Christian
    - family: Zayer
      given: Rhaleb
  citation-key: ChuLearning2021
  container-title: ACM Transactions on Graphics
  container-title-short: ACM Trans. Graph.
  DOI: 10.1145/3476576.3476661
  ISSN: 0730-0301, 1557-7368
  issue: '4'
  issued:
    - year: 2021
      month: 8
  language: en
  page: 1-13
  title: Learning meaningful controls for fluids
  type: article-journal
  URL: https://people.mpi-inf.mpg.de/~mchu/gvv-den2vel/den2vel.html
  volume: '40'

- id: ErricoWhat1997
  accessed:
    - year: 2019
      month: 8
      day: 31
  author:
    - family: Errico
      given: Ronald M.
  citation-key: ErricoWhat1997
  container-title: Bulletin of the American Meteorological Society
  container-title-short: Bull. Amer. Meteor. Soc.
  DOI: 10.1175/1520-0477(1997)078<2577:WIAAM>2.0.CO;2
  ISSN: 0003-0007
  issue: '11'
  issued:
    - year: 1997
      month: 11
      day: 1
  page: 2577-2592
  publisher: American Meteorological Society
  section: Bulletin of the American Meteorological Society
  title: What Is an Adjoint Model?
  type: article-journal
  URL: http://bio.cgrer.uiowa.edu/people/tchai/HTM/Reference/adjoint_errico.pdf
  volume: '78'

- id: freeman2021brax
  author:
    - family: Freeman
      given: C Daniel
    - family: Frey
      given: Erik
    - family: Raichuk
      given: Anton
    - family: Girgin
      given: Sertan
    - family: Mordatch
      given: Igor
    - family: Bachem
      given: Olivier
  citation-key: freeman2021brax
  container-title: arXiv preprint arXiv:2106.13281
  issued:
    - year: 2021
  title: Brax–A differentiable physics engine for large scale rigid body simulation
  type: article-journal
  URL: https://arxiv.org/abs/2106.13281

- id: gan2020threedworld
  author:
    - family: Gan
      given: Chuang
    - family: Schwartz
      given: Jeremy
    - family: Alter
      given: Seth
    - family: Schrimpf
      given: Martin
    - family: Traer
      given: James
    - family: De Freitas
      given: Julian
    - family: Kubilius
      given: Jonas
    - family: Bhandwaldar
      given: Abhishek
    - family: Haber
      given: Nick
    - family: Sano
      given: Megumi
    - literal: others
  citation-key: gan2020threedworld
  container-title: arXiv preprint arXiv:2007.04954
  issued:
    - year: 2020
  title: 'Threedworld: A platform for interactive multi-modal physical simulation'
  type: article-journal
  URL: https://arxiv.org/abs/2007.04954

- id: GiannakoglouAdjointOptimisationFoam2020
  author:
    - family: Giannakoglou
      given: K C
    - family: Papoutsis-Kiachagias
      given: Dr E M
    - family: Gkaragkounis
      given: K T
  citation-key: GiannakoglouAdjointOptimisationFoam2020
  issued:
    - year: 2020
  language: en
  title: adjointOptimisationFoam, an OpenFOAM-based optimisation tool
  type: report

- id: GranasFixed2003
  accessed:
    - year: 2021
      month: 9
      day: 7
  author:
    - family: Granas
      given: Andrzej
    - family: Dugundji
      given: James
  citation-key: GranasFixed2003
  collection-title: Springer Monographs in Mathematics
  DOI: 10.1007/978-0-387-21593-8
  event-place: New York, NY
  ISBN: 978-1-4419-1805-5 978-0-387-21593-8
  issued:
    - year: 2003
  publisher: Springer New York
  publisher-place: New York, NY
  title: Fixed Point Theory
  type: book
  URL: http://link.springer.com/10.1007/978-0-387-21593-8

- id: HennighNVIDIA2020
  accessed:
    - year: 2022
      month: 2
      day: 20
  author:
    - family: Hennigh
      given: Oliver
    - family: Narasimhan
      given: Susheela
    - family: Nabian
      given: Mohammad Amin
    - family: Subramaniam
      given: Akshay
    - family: Tangsali
      given: Kaustubh
    - family: Rietmann
      given: Max
    - family: Ferrandis
      given: Jose del Aguila
    - family: Byeon
      given: Wonmin
    - family: Fang
      given: Zhiwei
    - family: Choudhry
      given: Sanjay
  citation-key: HennighNVIDIA2020
  container-title: arXiv:2012.07938 [physics]
  issued:
    - year: 2020
      month: 12
      day: 14
  title: 'NVIDIA SimNet™️: an AI-accelerated multi-physics simulation framework'
  type: article-journal
  URL: http://arxiv.org/abs/2012.07938

- id: HollLearning2020
  author:
    - family: Holl
      given: Philipp
    - family: Thuerey
      given: Nils
    - family: Koltun
      given: Vladlen
  citation-key: HollLearning2020
  container-title: ICLR
  event-title: ICLR
  issued:
    - year: 2020
  language: en
  page: '5'
  title: Learning to Control PDEs with Differentiable Physics
  type: paper-conference
  URL: http://arxiv.org/abs/2001.07457

- id: HollPhiflow2020
  author:
    - family: Holl
      given: Philipp
    - family: Koltun
      given: Vladlen
    - family: Um
      given: Kiwon
    - family: Thuerey
      given: Nils
  citation-key: HollPhiflow2020
  container-title: NeurIPS Workshop
  issued:
    - year: 2020
  title: >-
    Phiflow: A Differentiable PDE Solving Framework for Deep Learning via
    Physical Simulations
  type: paper-conference
  URL: http://montrealrobotics.ca/diffcvgp/assets/papers/3.pdf

- id: HolzschuhScore2022
  author:
    - family: Holzschuh
      given: Benjamin
    - family: Vegetti
      given: Simona
    - family: Thuerey
      given: Nils
  citation-key: HolzschuhScore2022
  issued:
    - year: 2022
  language: en
  page: '7'
  title: Score Matching via Differentiable Physics
  type: article-journal

- id: HuDiffTaichi2020
  accessed:
    - year: 2020
      month: 4
      day: 25
  author:
    - family: Hu
      given: Yuanming
    - family: Anderson
      given: Luke
    - family: Li
      given: Tzu-Mao
    - family: Sun
      given: Qi
    - family: Carr
      given: Nathan
    - family: Ragan-Kelley
      given: Jonathan
    - family: Durand
      given: Frédo
  citation-key: HuDiffTaichi2020
  container-title: ICLR
  event-title: ICLR
  issued:
    - year: 2020
      month: 2
      day: 14
  title: 'DiffTaichi: Differentiable Programming for Physical Simulation'
  type: paper-conference
  URL: http://arxiv.org/abs/1910.00935

- id: HuTaichi2019
  accessed:
    - year: 2020
      month: 4
      day: 25
  author:
    - family: Hu
      given: Yuanming
    - family: Li
      given: Tzu-Mao
    - family: Anderson
      given: Luke
    - family: Ragan-Kelley
      given: Jonathan
    - family: Durand
      given: Frédo
  citation-key: HuTaichi2019
  container-title: ACM Transactions on Graphics
  container-title-short: ACM Trans. Graph.
  DOI: 10.1145/3355089.3356506
  ISSN: 0730-0301, 1557-7368
  issue: '6'
  issued:
    - year: 2019
      month: 11
      day: 8
  language: en
  page: 1-16
  title: >-
    Taichi: a language for high-performance computation on spatially sparse data
    structures
  type: article-journal
  volume: '38'

- id: JohnsonNotes2012
  author:
    - family: Johnson
      given: Steven G
  citation-key: JohnsonNotes2012
  issued:
    - year: 2012
  language: en
  page: '6'
  title: Notes on Adjoint Methods for 18.335
  type: article-journal
  URL: https://math.mit.edu/~stevenj/18.336/adjoint.pdf

- id: KadriOperatorvalued2016
  author:
    - family: Kadri
      given: Hachem
    - family: Duflos
      given: Emmanuel
    - family: Preux
      given: Philippe
    - family: Canu
      given: Stéphane
    - family: Rakotomamonjy
      given: Alain
    - family: Audiffren
      given: Julien
  citation-key: KadriOperatorvalued2016
  container-title: The Journal of Machine Learning Research
  container-title-short: J. Mach. Learn. Res.
  ISSN: 1532-4435
  issue: '1'
  issued:
    - year: 2016
      month: 1
      day: 1
  page: 613–666
  title: Operator-valued kernels for learning from functional response data
  type: article-journal
  URL: http://arxiv.org/abs/1510.08231
  volume: '17'

- id: KavvadiasProper2015
  accessed:
    - year: 2023
      month: 5
      day: 14
  author:
    - family: Kavvadias
      given: I. S.
    - family: Papoutsis-Kiachagias
      given: E. M.
    - family: Giannakoglou
      given: K. C.
  citation-key: KavvadiasProper2015
  container-title: Journal of Computational Physics
  container-title-short: Journal of Computational Physics
  DOI: 10.1016/j.jcp.2015.08.012
  ISSN: 0021-9991
  issued:
    - year: 2015
      month: 11
      day: 15
  language: en
  page: 1-18
  title: >-
    On the proper treatment of grid sensitivities in continuous adjoint methods
    for shape optimization
  type: article-journal
  volume: '301'

- id: KochkovMachine2021
  accessed:
    - year: 2021
      month: 10
      day: 28
  author:
    - family: Kochkov
      given: Dmitrii
    - family: Smith
      given: Jamie A.
    - family: Alieva
      given: Ayya
    - family: Wang
      given: Qing
    - family: Brenner
      given: Michael P.
    - family: Hoyer
      given: Stephan
  citation-key: KochkovMachine2021
  container-title: Proceedings of the National Academy of Sciences
  container-title-short: PNAS
  DOI: 10.1073/pnas.2101784118
  ISSN: 0027-8424, 1091-6490
  issue: '21'
  issued:
    - year: 2021
      month: 5
      day: 25
  language: en
  PMID: '34006645'
  publisher: National Academy of Sciences
  section: Physical Sciences
  title: Machine learning–accelerated computational fluid dynamics
  type: article-journal
  volume: '118'

- id: KramerProbabilistic2021
  accessed:
    - year: 2022
      month: 7
      day: 19
  author:
    - family: Krämer
      given: Nicholas
    - family: Bosch
      given: Nathanael
    - family: Schmidt
      given: Jonathan
    - family: Hennig
      given: Philipp
  citation-key: KramerProbabilistic2021
  DOI: 10.48550/arXiv.2110.11812
  issued:
    - year: 2021
      month: 10
      day: 22
  number: arXiv:2110.11812
  publisher: arXiv
  title: Probabilistic ODE Solutions in Millions of Dimensions
  type: article
  URL: http://arxiv.org/abs/2110.11812

- id: LianNonlinear2007
  accessed:
    - year: 2020
      month: 12
      day: 7
  author:
    - family: Lian
      given: Heng
  citation-key: LianNonlinear2007
  container-title: Canadian Journal of Statistics
  DOI: 10.1002/cjs.5550350410
  ISSN: 1708-945X
  issue: '4'
  issued:
    - year: 2007
  language: en
  page: 597-606
  title: >-
    Nonlinear functional models for functional responses in reproducing kernel
    hilbert spaces
  type: article-journal
  URL: http://arxiv.org/abs/math/0702120
  volume: '35'

- 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: MituschDolfinadjoint2019
  accessed:
    - year: 2021
      month: 7
      day: 9
  author:
    - family: Mitusch
      given: Sebastian K.
    - family: Funke
      given: Simon W.
    - family: Dokken
      given: Jørgen S.
  citation-key: MituschDolfinadjoint2019
  container-title: Journal of Open Source Software
  DOI: 10.21105/joss.01292
  ISSN: 2475-9066
  issue: '38'
  issued:
    - year: 2019
      month: 6
      day: 18
  language: en
  page: '1292'
  title: 'dolfin-adjoint 2018.1: automated adjoints for FEniCS and Firedrake'
  type: article-journal
  volume: '4'

- id: NaumannArt2011
  accessed:
    - year: 2021
      month: 10
      day: 28
  author:
    - family: Naumann
      given: Uwe
  citation-key: NaumannArt2011
  DOI: 10.1137/1.9781611972078
  ISBN: 978-1-61197-206-1 978-1-61197-207-8
  issued:
    - year: 2011
      month: 1
  language: en
  publisher: Society for Industrial and Applied Mathematics
  title: >-
    The Art of Differentiating Computer Programs: An Introduction to Algorithmic
    Differentiation
  type: book
  URL: http://epubs.siam.org/doi/book/10.1137/1.9781611972078

- id: OtnessExtensible2021
  accessed:
    - year: 2022
      month: 5
      day: 16
  author:
    - family: Otness
      given: Karl
    - family: Gjoka
      given: Arvi
    - family: Bruna
      given: Joan
    - family: Panozzo
      given: Daniele
    - family: Peherstorfer
      given: Benjamin
    - family: Schneider
      given: Teseo
    - family: Zorin
      given: Denis
  citation-key: OtnessExtensible2021
  event-title: >-
    Thirty-fifth Conference on Neural Information Processing Systems Datasets
    and Benchmarks Track (Round 1)
  issued:
    - year: 2021
  language: en
  title: An Extensible Benchmark Suite for Learning to Simulate Physical Systems
  type: paper-conference
  URL: https://openreview.net/forum?id=pY9MHwmrymR

- id: PachalievaPhysicsinformed2022
  accessed:
    - year: 2022
      month: 6
      day: 24
  author:
    - family: Pachalieva
      given: Aleksandra
    - family: O’Malley
      given: Daniel
    - family: Harp
      given: Dylan Robert
    - family: Viswanathan
      given: Hari
  citation-key: PachalievaPhysicsinformed2022
  DOI: 10.48550/arXiv.2206.10718
  issued:
    - year: 2022
      month: 6
      day: 21
  number: arXiv:2206.10718
  publisher: arXiv
  title: >-
    Physics-informed machine learning with differentiable programming for
    heterogeneous underground reservoir pressure management
  type: article
  URL: http://arxiv.org/abs/2206.10718

- id: PapoutsisKiachagiasAdjoint2013
  author:
    - family: Papoutsis-Kiachagias
      given: Evangelos
  citation-key: PapoutsisKiachagiasAdjoint2013
  issued:
    - year: 2013
  language: en
  title: >-
    Adjoint Methods for Turbulent Flows, Applied to Shape or Topology
    Optimization and Robust Design
  type: thesis

- id: PapoutsisKiachagiasAdjointOptimisationFoam2021
  accessed:
    - year: 2023
      month: 5
      day: 14
  author:
    - family: Papoutsis-Kiachagias
      given: Evangelos
    - family: Gkaragkounis
      given: Konstantinos
    - family: Margetis
      given: Andreas-Stefanos
    - family: Skamagkis
      given: Themis
    - family: Asouti
      given: Varvara
    - family: Giannakoglou
      given: Kyriakos
  citation-key: PapoutsisKiachagiasAdjointOptimisationFoam2021
  container-title: >-
    14th International Conference on Evolutionary and Deterministic Methods for
    Design, Optimization and Control
  DOI: 10.7712/140121.7960.18382
  event-place: Athens, Greece
  event-title: >-
    14th International Conference on Evolutionary and Deterministic Methods for
    Design, Optimization and Control
  ISBN: 978-618-85072-7-2
  issued:
    - year: 2021
  language: en
  page: 191-206
  publisher: >-
    Institute of Structural Analysis and Antiseismic Research National Technical
    University of Athens
  publisher-place: Athens, Greece
  title: >-
    adjointOptimisationFoam: An Openfoam-Based Framework for Adjoint-Assisted
    Optimisation
  type: paper-conference
  URL: >-
    https://www.eccomasproceedia.org/conferences/thematic-conferences/eurogen-2021/7960

- id: PapoutsisKiachagiasContinuous2016
  accessed:
    - year: 2023
      month: 5
      day: 14
  author:
    - family: Papoutsis-Kiachagias
      given: E. M.
    - family: Giannakoglou
      given: K. C.
  citation-key: PapoutsisKiachagiasContinuous2016
  container-title: Archives of Computational Methods in Engineering
  container-title-short: Arch Computat Methods Eng
  DOI: 10.1007/s11831-014-9141-9
  ISSN: 1886-1784
  issue: '2'
  issued:
    - year: 2016
      month: 6
      day: 1
  language: en
  page: 255-299
  title: >-
    Continuous Adjoint Methods for Turbulent Flows, Applied to Shape and
    Topology Optimization: Industrial Applications
  type: article-journal
  volume: '23'

- id: PapoutsisKiachagiasNoise2015
  accessed:
    - year: 2023
      month: 5
      day: 14
  author:
    - family: Papoutsis-Kiachagias
      given: E. M.
    - family: Magoulas
      given: N.
    - family: Mueller
      given: J.
    - family: Othmer
      given: C.
    - family: Giannakoglou
      given: K. C.
  citation-key: PapoutsisKiachagiasNoise2015
  container-title: Computers & Fluids
  container-title-short: Computers & Fluids
  DOI: 10.1016/j.compfluid.2015.09.002
  ISSN: 0045-7930
  issued:
    - year: 2015
      month: 11
      day: 20
  language: en
  page: 223-232
  title: >-
    Noise reduction in car aerodynamics using a surrogate objective function and
    the continuous adjoint method with wall functions
  type: article-journal
  volume: '122'

- id: QianXinvert2023
  accessed:
    - year: 2023
      month: 10
      day: 11
  author:
    - family: Qian
      given: Yu-Kun
  citation-key: QianXinvert2023
  container-title: Journal of Open Source Software
  DOI: 10.21105/joss.05510
  ISSN: 2475-9066
  issue: '89'
  issued:
    - year: 2023
      month: 9
      day: 6
  language: en
  page: '5510'
  title: >-
    xinvert: A Python package for inversion problems in geophysical fluid
    dynamics
  type: article-journal
  URL: https://joss.theoj.org/papers/10.21105/joss.05510
  volume: '8'

- id: RackauckasUniversal2020a
  accessed:
    - year: 2023
      month: 11
      day: 15
  author:
    - family: Rackauckas
      given: Christopher
    - family: Ma
      given: Yingbo
    - family: Martensen
      given: Julius
    - family: Warner
      given: Collin
    - family: Zubov
      given: Kirill
    - family: Supekar
      given: Rohit
    - family: Skinner
      given: Dominic
    - family: Ramadhan
      given: Ali
    - family: Edelman
      given: Alan
  citation-key: RackauckasUniversal2020a
  container-title: arXiv.org
  issued:
    - year: 2020
      month: 1
      day: 13
  language: en
  title: Universal Differential Equations for Scientific Machine Learning
  type: article-journal
  URL: https://arxiv.org/abs/2001.04385v4

- id: RamsundarDifferentiable2021
  accessed:
    - year: 2021
      month: 9
      day: 20
  author:
    - family: Ramsundar
      given: Bharath
    - family: Krishnamurthy
      given: Dilip
    - family: Viswanathan
      given: Venkatasubramanian
  citation-key: RamsundarDifferentiable2021
  container-title: arXiv:2109.07573 [physics]
  issued:
    - year: 2021
      month: 9
      day: 14
  title: 'Differentiable Physics: A Position Piece'
  type: article-journal
  URL: http://arxiv.org/abs/2109.07573

- id: SahaLearning2020
  accessed:
    - year: 2020
      month: 12
      day: 10
  author:
    - family: Saha
      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: SigristPhysics2013
  accessed:
    - year: 2021
      month: 1
      day: 14
  author:
    - family: Sigrist
      given: Fabio Roman Albert
  citation-key: SigristPhysics2013
  contributor:
    - family: Künsch
      given: Hansruedi
    - family: Guttorp
      given: Peter
  DOI: 10.3929/ETHZ-A-009900551
  issued:
    - year: 2013
  language: en
  medium: application/pdf
  page: 1 Band
  publisher: ETH Zurich
  title: Physics based dynamic modeling of space-time data
  type: thesis
  URL: http://hdl.handle.net/20.500.11850/67669

- id: TartakovskyLearning2018
  accessed:
    - year: 2020
      month: 9
      day: 16
  author:
    - family: Tartakovsky
      given: Alexandre M.
    - family: Marrero
      given: Carlos Ortiz
    - family: Perdikaris
      given: Paris
    - family: Tartakovsky
      given: Guzel D.
    - family: Barajas-Solano
      given: David
  citation-key: TartakovskyLearning2018
  issued:
    - year: 2018
      month: 8
      day: 10
  language: en
  title: >-
    Learning Parameters and Constitutive Relationships with Physics Informed
    Deep Neural Networks
  type: article-journal
  URL: https://arxiv.org/abs/1808.03398v2

- id: ThuereyPhysicsbased2021
  author:
    - family: Thuerey
      given: Nils
    - family: Holl
      given: Philipp
    - family: Mueller
      given: Maximilian
    - family: Schnell
      given: Patrick
    - family: Trost
      given: Felix
    - family: Um
      given: Kiwon
  citation-key: ThuereyPhysicsbased2021
  issued:
    - year: 2021
  publisher: WWW
  title: Physics-based deep learning
  type: book
  URL: https://physicsbaseddeeplearning.org

- id: UmDifferentiable
  author:
    - family: Um
      given: Kiwon
    - family: Holl
      given: Philipp
  citation-key: UmDifferentiable
  issued:
    - year: 2021
  language: en
  page: '5'
  title: >-
    Differentiable Physics for Improving the Accuracy of Iterative PDE-Solvers
    with Neural Networks
  type: paper-conference

- id: UmSolverintheLoop2021
  accessed:
    - year: 2021
      month: 8
      day: 31
  author:
    - family: Um
      given: Kiwon
    - family: Brand
      given: Robert
    - family: Fei
      given: Yun
    - family: Holl
      given: Philipp
    - family: Thuerey
      given: Nils
  citation-key: UmSolverintheLoop2021
  container-title: arXiv:2007.00016 [physics]
  issued:
    - year: 2021
      month: 1
      day: 5
  title: >-
    Solver-in-the-Loop: Learning from Differentiable Physics to Interact with
    Iterative PDE-Solvers
  type: article-journal
  URL: http://arxiv.org/abs/2007.00016

- id: WangPhysicsinformed2020
  accessed:
    - year: 2022
      month: 4
      day: 27
  author:
    - family: Wang
      given: Rui
    - family: Kashinath
      given: Karthik
    - family: Mustafa
      given: Mustafa
    - family: Albert
      given: Adrian
    - family: Yu
      given: Rose
  citation-key: WangPhysicsinformed2020
  collection-title: KDD '20
  container-title: >-
    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:
    - year: 2020
      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
  type: paper-conference
  URL: http://arxiv.org/abs/1911.08655
...
