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\n\n \n \n \n \n \n \n Differentiable programming across the PDE and Machine Learning barrier.\n \n \n \n \n\n\n \n Bouziani, N.; Ham, D. A.; and Farsi, A.\n\n\n \n\n\n\n
arXiv preprint arXiv:2409.06085. 2024.\n
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@article{Bouziani2024,\n author = {Bouziani, Nacime and Ham, David A. and Farsi, Ado},\n eprint = {2409.06085},\n journal = {arXiv preprint arXiv:2409.06085},\n title = {Differentiable programming across the {PDE} and {Machine} {Learning} barrier},\n url = {https://arxiv.org/abs/2409.06085},\n year = {2024}\n}\n\n
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\n\n \n \n \n \n \n \n Consistent point data assimilation in Firedrake and Icepack.\n \n \n \n \n\n\n \n Nixon-Hill, R. W.; Shapero, D.; Cotter, C. J.; and Ham, D. A.\n\n\n \n\n\n\n
Geoscientific Model Development, 17(13): 5369–5386. 2024.\n
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@article{nixonhill2023consistent,\n author = {Nixon-Hill, R. W. and Shapero, D. and Cotter, C. J. and Ham, D. A.},\n doi = {10.5194/gmd-17-5369-2024},\n journal = {Geoscientific Model Development},\n number = {13},\n pages = {5369--5386},\n title = {Consistent point data assimilation in Firedrake and Icepack},\n url = {https://gmd.copernicus.org/articles/17/5369/2024/},\n volume = {17},\n year = {2024}\n}\n\n
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\n\n \n \n \n \n \n Physics-driven machine learning models coupling PyTorch and Firedrake.\n \n \n \n\n\n \n Bouziani, N.; and Ham, D. A.\n\n\n \n\n\n\n In
ICLR 2023 Workshop on Physics for Machine Learning, 2023. \n
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@inproceedings{Bouziani2023,\n author = {Bouziani, Nacime and Ham, David A.},\n booktitle = {{ICLR} 2023 {Workshop} on {Physics} for {Machine} {Learning}},\n doi = {10.48550/arXiv.2303.06871},\n title = {Physics-driven machine learning models coupling {PyTorch} and {Firedrake}},\n year = {2023}\n}\n\n
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\n\n \n \n \n \n \n Firedrake User Manual.\n \n \n \n\n\n \n Ham, D. A.; Kelly, P. H. J.; Mitchell, L.; Cotter, C. J.; Kirby, R. C.; Sagiyama, K.; Bouziani, N.; Vorderwuelbecke, S.; Gregory, T. J.; Betteridge, J.; Shapero, D. R.; Nixon-Hill, R. W.; Ward, C. J.; Farrell, P. E.; Brubeck, P. D.; Marsden, I.; Gibson, T. H.; Homolya, M.; Sun, T.; McRae, A. T. T.; Luporini, F.; Gregory, A.; Lange, M.; Funke, S. W.; Rathgeber, F.; Bercea, G.; and Markall, G. R.\n\n\n \n\n\n\n Imperial College London and University of Oxford and Baylor University and University of Washington, First edition edition, 5 2023.\n
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@manual{FiredrakeUserManual,\n author = {David A. Ham and Paul H. J. Kelly and Lawrence\nMitchell and Colin J. Cotter and Robert C. Kirby and Koki Sagiyama and\nNacime Bouziani and Sophia Vorderwuelbecke and Thomas J. Gregory and\nJack Betteridge and Daniel R. Shapero and Reuben W. Nixon-Hill and\nConnor J. Ward and Patrick E. Farrell and Pablo D. Brubeck and India\nMarsden and Thomas H. Gibson and Miklós Homolya and Tianjiao Sun and\nAndrew T. T. McRae and Fabio Luporini and Alastair Gregory and\nMichael Lange and Simon W. Funke and Florian Rathgeber and\nGheorghe-Teodor Bercea and Graham R. Markall},\n doi = {10.25561/104839},\n edition = {First edition},\n month = {5},\n organization = {Imperial College London and University of Oxford and\nBaylor University and University of Washington},\n title = {Firedrake User Manual},\n year = {2023}\n}\n\n
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\n\n \n \n \n \n \n \n Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond.\n \n \n \n \n\n\n \n Gibson, T. H.; Mitchell, L.; Ham, D. A.; and Cotter, C. J.\n\n\n \n\n\n\n 2020.\n
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@misc{Gibson2018,\n archiveprefix = {arXiv},\n author = {Thomas H. Gibson and Lawrence Mitchell and David A.\nHam and Colin J. Cotter},\n doi = {10.5194/gmd-13-735-2020},\n eprint = {1802.00303},\n journal = {Geoscientific model development.},\n number = {2},\n pages = {735--761},\n primaryclass = {cs.MS},\n publisher = {Copernicus Publications},\n title = {{Slate: extending Firedrake's domain-specific abstraction to\nhybridized solvers for geoscience and beyond.}},\n url = {https://arxiv.org/abs/1802.00303},\n volume = {13},\n year = {2020}\n}\n\n
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\n\n \n \n \n \n \n \n Recursive, Parameter-Free, Explicitly Defined Interpolation Nodes for Simplices.\n \n \n \n \n\n\n \n Isaac, T.\n\n\n \n\n\n\n
SIAM Journal on Scientific Computing, 42(6): A4046-A4062. 2020.\n
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@article{Isaac2020,\n author = {Tobin Isaac},\n doi = {10.1137/20M1321802},\n eprint = {2002.09421},\n journal = {SIAM Journal on Scientific Computing},\n number = {6},\n pages = {A4046-A4062},\n title = {{Recursive, Parameter-Free, Explicitly Defined Interpolation Nodes for Simplices}},\n url = {https://arxiv.org/abs/2002.09421},\n volume = {42},\n year = {2020}\n}\n\n
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SIAM Journal on Scientific Computing, 40(1): C76-C98. 2018.\n
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@article{Kirby2017,\n archiveprefix = {arXiv},\n author = {Robert C. Kirby and Lawrence Mitchell},\n doi = {10.1137/17M1133208},\n eprint = {1706.01346},\n journal = {SIAM Journal on Scientific Computing},\n number = {1},\n pages = {C76-C98},\n primaryclass = {cs.MS},\n title = {{Solver composition across the PDE/linear algebra\nbarrier}},\n url = {https://arxiv.org/abs/1706.01346},\n volume = {40},\n year = {2018}\n}\n\n
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\n\n \n \n \n \n \n \n Code generation for generally mapped finite elements.\n \n \n \n \n\n\n \n Kirby, R. C.; and Mitchell, L.\n\n\n \n\n\n\n 2018.\n
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@misc{Kirby2018,\n archiveprefix = {arXiv},\n author = {Robert C. Kirby and Lawrence Mitchell},\n eprint = {1808.05513},\n primaryclass = {cs.MS},\n title = {Code generation for generally mapped finite\nelements},\n url = {https://arxiv.org/abs/1808.05513},\n year = {2018}\n}\n\n
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@misc{Homolya2017a,\n archiveprefix = {arXiv},\n author = {Mikl\\'os Homolya and Robert C. Kirby and David A.\nHam},\n eprint = {1711.02473},\n primaryclass = {cs.MS},\n title = {{Exposing and exploiting structure: optimal code\ngeneration for high-order finite element methods}},\n url = {https://arxiv.org/abs/1711.02473},\n year = {2017}\n}\n\n
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\n\n \n \n \n \n \n An algorithm for the optimization of finite element integration loops.\n \n \n \n\n\n \n Luporini, F.; Ham, D. A.; and Kelly, P. H. J.\n\n\n \n\n\n\n
ACM Transactions on Mathematical Software, 44(1): 3:1–3:26. 2017.\n
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@article{Luporini2017,\n archiveprefix = {arXiv},\n author = {Fabio Luporini and David A. Ham and Paul H. J.\nKelly},\n doi = {10.1145/3054944},\n eprint = {1604.05872},\n journal = {ACM Transactions on Mathematical Software},\n number = {1},\n pages = {3:1--3:26},\n primaryclass = {cs.MS},\n title = {An algorithm for the optimization of finite element\nintegration loops},\n volume = {44},\n year = {2017}\n}\n\n
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\n\n \n \n \n \n \n \n A parallel edge orientation algorithm for quadrilateral meshes.\n \n \n \n \n\n\n \n Homolya, M.; and Ham, D. A.\n\n\n \n\n\n\n
SIAM Journal on Scientific Computing, 38(5): S48–S61. 2016.\n
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@article{Homolya2016,\n archiveprefix = {arXiv},\n author = {Mikl\\'os Homolya and David A. Ham},\n doi = {10.1137/15M1021325},\n eprint = {1505.03357},\n journal = {SIAM Journal on Scientific Computing},\n number = {5},\n pages = {S48--S61},\n primaryclass = {cs.MS},\n title = {A parallel edge orientation algorithm for\nquadrilateral meshes},\n url = {https://arxiv.org/abs/1505.03357},\n volume = {38},\n year = {2016}\n}\n\n
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\n\n \n \n \n \n \n \n Efficient mesh management in Firedrake using PETSc-DMPlex.\n \n \n \n \n\n\n \n Lange, M.; Mitchell, L.; Knepley, M. G.; and Gorman, G. J.\n\n\n \n\n\n\n
SIAM Journal on Scientific Computing, 38(5): S143–S155. 2016.\n
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@article{Lange2016,\n archiveprefix = {arXiv},\n author = {Michael Lange and Lawrence Mitchell and Matthew G.\nKnepley and Gerard J. Gorman},\n doi = {10.1137/15M1026092},\n eprint = {1506.07749},\n journal = {SIAM Journal on Scientific Computing},\n number = {5},\n pages = {S143--S155},\n primaryclass = {cs.MS},\n title = {Efficient mesh management in {Firedrake} using\n{PETSc-DMPlex}},\n url = {https://arxiv.org/abs/1506.07749},\n volume = {38},\n year = {2016}\n}\n\n
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\n\n \n \n \n \n \n \n Automated generation and symbolic manipulation of tensor product finite elements.\n \n \n \n \n\n\n \n McRae, A. T. T.; Bercea, G.; Mitchell, L.; Ham, D. A.; and Cotter, C. J.\n\n\n \n\n\n\n
SIAM Journal on Scientific Computing, 38(5): S25–S47. 2016.\n
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@article{McRae2016,\n archiveprefix = {arXiv},\n author = {Andrew T. T. McRae and Gheorghe-Teodor Bercea and\nLawrence Mitchell and David A. Ham and Colin J.\nCotter},\n doi = {10.1137/15M1021167},\n eprint = {1411.2940},\n journal = {SIAM Journal on Scientific Computing},\n number = {5},\n pages = {S25--S47},\n primaryclass = {math.NA},\n title = {Automated generation and symbolic manipulation of\ntensor product finite elements},\n url = {https://arxiv.org/abs/1411.2940},\n volume = {38},\n year = {2016}\n}\n\n
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\n\n \n \n \n \n \n \n High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling.\n \n \n \n \n\n\n \n Mitchell, L.; and Müller, E. H.\n\n\n \n\n\n\n
Journal of Computational Physics, 327: 1–18. 2016.\n
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@article{Mitchell2016,\n archiveprefix = {arXiv},\n author = {Lawrence Mitchell and Eike Hermann M\\"uller},\n doi = {10.1016/j.jcp.2016.09.037},\n eprint = {1605.00492},\n journal = {Journal of Computational Physics},\n pages = {1--18},\n primaryclass = {cs.MS},\n title = {High level implementation of geometric multigrid\nsolvers for finite element problems: applications in\natmospheric modelling},\n url = {https://arxiv.org/abs/1605.00492},\n volume = {327},\n year = {2016}\n}\n\n
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\n\n \n \n \n \n \n \n Firedrake: Automating the Finite Element Method by Composing Abstractions.\n \n \n \n \n\n\n \n Rathgeber, F.; Ham, D. A.; Mitchell, L.; Lange, M.; Luporini, F.; Mcrae, A. T. T.; Bercea, G.; Markall, G. R.; and Kelly, P. H. J.\n\n\n \n\n\n\n
ACM Trans. Math. Softw., 43(3): 24:1–24:27. 2016.\n
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@article{Rathgeber2016,\n archiveprefix = {arXiv},\n author = {Rathgeber, Florian and Ham, David A. and Mitchell,\nLawrence and Lange, Michael and Luporini, Fabio and\nMcrae, Andrew T. T. and Bercea, Gheorghe-Teodor and\nMarkall, Graham R. and Kelly, Paul H. J.},\n doi = {10.1145/2998441},\n eprint = {1501.01809},\n journal = {ACM Trans. Math. Softw.},\n number = {3},\n pages = {24:1--24:27},\n primaryclass = {cs.MS},\n title = {Firedrake: Automating the Finite Element Method by\nComposing Abstractions},\n url = {https://arxiv.org/abs/1501.01809},\n volume = {43},\n year = {2016}\n}\n\n
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\n\n \n \n \n \n \n \n Cross-Loop Optimization of Arithmetic Intensity for Finite Element Local Assembly.\n \n \n \n \n\n\n \n Luporini, F.; Varbanescu, A. L.; Rathgeber, F.; Bercea, G.; Ramanujam, J.; Ham, D. A.; and Kelly, P. H. J.\n\n\n \n\n\n\n
ACM Transactions on Architecture and Code Optimization, 11(4): 57:1–57:25. 2015.\n
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@article{Luporini2015,\n author = {Fabio Luporini and Ana Lucia Varbanescu and Florian\nRathgeber and Gheorghe-Teodor Bercea and J.\nRamanujam and David A. Ham and Paul H. J. Kelly},\n doi = {10.1145/2687415},\n journal = {ACM Transactions on Architecture and Code\nOptimization},\n number = {4},\n pages = {57:1--57:25},\n title = {Cross-Loop Optimization of Arithmetic Intensity for\nFinite Element Local Assembly},\n url = {http://doi.acm.org/10.1145/2687415},\n volume = {11},\n year = {2015}\n}\n\n
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International Journal for Numerical Methods in Fluids, 71: 80–97. 2013.\n
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@article{Markall2012,\n author = {Graham R. Markall and A. Slemmer and David A. Ham\nand Paul H. J. Kelly and Chris D. Cantwell and\nSpencer J. Sherwin},\n doi = {10.1002/fld.3648},\n journal = {International Journal for Numerical Methods in\nFluids},\n pages = {80--97},\n title = {Finite element assembly strategies on multi- and\nmany-core architectures},\n url = {http://dx.doi.org/10.1002/fld.3648},\n volume = {71},\n year = {2013}\n}\n\n
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\n\n \n \n \n \n \n \n Towards generating optimised finite element solvers for GPUs from high-level specifications.\n \n \n \n \n\n\n \n Markall, G. R.; Ham, D. A.; and Kelly, P. H. J.\n\n\n \n\n\n\n
Procedia Computer Science, 1(1): 1815–1823. 2010.\n
ICCS 2010\n\n
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@article{Markall2010,\n author = {Graham R. Markall and David A. Ham and Paul H. J.\nKelly},\n doi = {10.1016/j.procs.2010.04.203},\n journal = {Procedia Computer Science},\n note = {{ICCS} 2010},\n number = {1},\n pages = {1815--1823},\n title = {Towards generating optimised finite element solvers\nfor GPUs from high-level specifications},\n url = {http://dx.doi.org/10.1016/j.procs.2010.04.203},\n volume = {1},\n year = {2010}\n}\n\n
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