--- references: - id: AlnaesFEniCS2015 author: - family: Alnæs given: Martin S. - family: Blechta given: Jan - family: Hake given: Johan - family: Johansson given: August - family: Kehlet given: Benjamin - family: Logg given: Anders - family: Richardson given: Chris - family: Ring given: Johannes - family: Rognes given: Marie E. - family: Wells given: Garth N. citation-key: AlnaesFEniCS2015 container-title: Archive of Numerical Software DOI: 10.11588/ans.2015.100.20553 issue: '100' issued: - year: 2015 title: The FEniCS project version 1.5 type: article-journal volume: '3' - id: AlnaesUFC2012 author: - family: Alnæs given: Martin S. - family: Logg given: Anders - family: Mardal given: Kent-Andre citation-key: AlnaesUFC2012 container-title: >- Automated solution of differential equations by the finite element method, volume 84 of lecture notes in computational science and engineering editor: - family: Logg given: Anders - family: Mardal given: Kent-Andre - family: Wells given: Garth N. issued: - year: 2012 publisher: Springer section: '16' title: 'UFC: a finite element code generation interface' type: chapter - id: AlnaesUFL2012 author: - family: Alnæs given: Martin S. citation-key: AlnaesUFL2012 container-title: >- Automated solution of differential equations by the finite element method, volume 84 of lecture notes in computational science and engineering editor: - family: Logg given: Anders - family: Mardal given: Kent-Andre - family: Wells given: Garth N. issued: - year: 2012 publisher: Springer section: '17' title: 'UFL: a finite element form language' type: chapter - id: AlnaesUnified2009 author: - family: Alnæs given: Martin S. - family: Logg given: Anders - family: Mardal given: Kent-Andre - family: Skavhaug given: Ola - family: Langtangen given: Hans Petter citation-key: AlnaesUnified2009 container-title: International Journal of Computational Science and Engineering DOI: 10.1504/IJCSE.2009.029160 issue: '4' issued: - year: 2009 page: 231–244 title: Unified framework for finite element assembly type: article-journal volume: '4' - id: AlnaesUnified2014 author: - family: Alnæs given: Martin S. - family: Logg given: Anders - family: Ølgaard given: Kristian B. - family: Rognes given: Marie E. - family: Wells given: Garth N. citation-key: AlnaesUnified2014 container-title: ACM Transactions on Mathematical Software DOI: 10.1145/2566630 issue: '2' issued: - year: 2014 title: >- Unified Form Language: A domain-specific language for weak formulations of partial differential equations type: article-journal volume: '40' - id: AnderssonCasADi2019 accessed: - year: 2020 month: 4 day: 16 author: - family: Andersson given: Joel A. E. - family: Gillis given: Joris - family: Horn given: Greg - family: Rawlings given: James B. - family: Diehl given: Moritz citation-key: AnderssonCasADi2019 container-title: Mathematical Programming Computation container-title-short: Math. Prog. Comp. DOI: 10.1007/s12532-018-0139-4 ISSN: 1867-2949, 1867-2957 issue: '1' issued: - year: 2019 month: 3 language: en page: 1-36 title: 'CasADi: a software framework for nonlinear optimization and optimal control' type: article-journal URL: http://www.optimization-online.org/DB_FILE/2018/01/6420.pdf volume: '11' - id: BarbaCFD2018 accessed: - year: 2021 month: 6 day: 29 author: - family: Barba given: Lorena A. - family: Forsyth given: Gilbert F. citation-key: BarbaCFD2018 container-title: Journal of Open Source Education DOI: 10.21105/jose.00021 ISSN: 2577-3569 issue: '16' issued: - year: 2018 month: 11 day: 12 language: en page: '21' title: 'CFD Python: the 12 steps to Navier-Stokes equations' type: article-journal URL: https://jose.theoj.org/papers/10.21105/jose.00021 volume: '2' - 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: CimrmanMultiscale2019 accessed: - year: 2021 month: 6 day: 29 author: - family: Cimrman given: Robert - family: Lukeš given: Vladimír - family: Rohan given: Eduard citation-key: CimrmanMultiscale2019 container-title: Advances in Computational Mathematics container-title-short: Adv Comput Math DOI: 10.1007/s10444-019-09666-0 ISSN: 1572-9044 issue: '4' issued: - year: 2019 month: 8 day: 1 language: en page: 1897-1921 title: Multiscale finite element calculations in Python using SfePy type: article-journal volume: '45' - id: KirbyAlgorithm2004 author: - family: Kirby given: Robert C. citation-key: KirbyAlgorithm2004 container-title: ACM Transactions on Mathematical Software DOI: 10.1145/1039813.1039820 issue: '4' issued: - year: 2004 page: 502–516 title: >- Algorithm 839: FIAT, a new paradigm for computing finite element basis functions type: article-journal volume: '30' - id: KirbyCompiler2006 author: - family: Kirby given: Robert C. - family: Logg given: Anders citation-key: KirbyCompiler2006 container-title: ACM Transactions on Mathematical Software DOI: 10.1145/1163641.1163644 issue: '3' issued: - year: 2006 title: A compiler for variational forms type: article-journal volume: '32' - id: KirbyFIAT2012 author: - family: Kirby given: Robert C. citation-key: KirbyFIAT2012 container-title: >- Automated solution of differential equations by the finite element method, volume 84 of lecture notes in computational science and engineering editor: - family: Logg given: Anders - family: Mardal given: Kent-Andre - family: Wells given: Garth N. issued: - year: 2012 publisher: Springer section: '13' title: 'FIAT: Numerical construction of finite element basis functions,' type: chapter - 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: LoggAutomated2012 author: - family: Logg given: Anders - family: Mardal given: Kent-Andre - family: Wells given: Garth N. - literal: others citation-key: LoggAutomated2012 DOI: 10.1007/978-3-642-23099-8 ISBN: 978-3-642-23098-1 issued: - year: 2012 publisher: Springer title: Automated solution of differential equations by the finite element method type: book - id: LoggDOLFIN2010 author: - family: Logg given: Anders - family: Wells given: Garth N. citation-key: LoggDOLFIN2010 container-title: ACM Transactions on Mathematical Software DOI: 10.1145/1731022.1731030 issue: '2' issued: - year: 2010 title: 'DOLFIN: Automated finite element computing' type: article-journal volume: '37' - id: LoggDOLFIN2012 author: - family: Logg given: Anders - family: Wells given: Garth N. - family: Hake given: Johan citation-key: LoggDOLFIN2012 container-title: >- Automated solution of differential equations by the finite element method, volume 84 of lecture notes in computational science and engineering editor: - family: Logg given: Anders - family: Mardal given: Kent-Andre - family: Wells given: Garth N. issued: - year: 2012 publisher: Springer section: '10' title: 'DOLFIN: a C++/Python finite element library' type: chapter - id: LoggFFC2012 author: - family: Logg given: Anders - family: Ølgaard given: Kristian B. - family: Rognes given: Marie E. - family: Wells given: Garth N. citation-key: LoggFFC2012 container-title: >- Automated solution of differential equations by the finite element method, volume 84 of lecture notes in computational science and engineering editor: - family: Logg given: Anders - family: Mardal given: Kent-Andre - family: Wells given: Garth N. issued: - year: 2012 publisher: Springer section: '11' title: 'FFC: the FEniCS form compiler' type: chapter - 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: PawarCFD2019 accessed: - year: 2021 month: 6 day: 29 author: - family: Pawar given: Suraj - family: San given: Omer citation-key: PawarCFD2019 container-title: Fluids DOI: 10.3390/fluids4030159 issue: '3' issued: - year: 2019 month: 9 language: en number: '3' page: '159' publisher: Multidisciplinary Digital Publishing Institute title: >- CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid Dynamics type: article-journal URL: https://www.mdpi.com/2311-5521/4/3/159 volume: '4' - 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: RackauckasComparison2018 accessed: - year: 2019 month: 1 day: 29 author: - family: Rackauckas given: Christopher - family: Ma given: Yingbo - family: Dixit given: Vaibhav - family: Guo given: Xingjian - family: Innes given: Mike - family: Revels given: Jarrett - family: Nyberg given: Joakim - family: Ivaturi given: Vijay citation-key: RackauckasComparison2018 container-title: arXiv:1812.01892 [cs] issued: - year: 2018 month: 12 day: 5 title: >- A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions type: article-journal URL: http://arxiv.org/abs/1812.01892 - id: RackauckasGeneralized2020 author: - family: Rackauckas given: Chris - family: Edelman given: Alan - family: Fischer given: Keno - family: Innes given: Mike - family: Saba given: Elliot - family: Shah given: Viral B - family: Tebbutt given: Will citation-key: RackauckasGeneralized2020 container-title: MIT web domain issued: - year: 2020 language: en page: '6' title: >- Generalized Physics-Informed Learning Through Language-Wide Differentiable Programming type: article-journal URL: https://dspace.mit.edu/handle/1721.1/137320 - 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: SchiesserNumerical1991 author: - family: Schiesser given: William E. citation-key: SchiesserNumerical1991 edition: 1st edition event-place: San Diego ISBN: 978-0-12-624130-3 issued: - year: 1991 month: 7 day: 12 language: English number-of-pages: '326' publisher: Academic Press publisher-place: San Diego title: 'The Numerical Method of Lines: Integration of Partial Differential Equations' type: book - 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 ...