Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 71 tok/s
Gemini 2.5 Pro 46 tok/s Pro
GPT-5 Medium 27 tok/s Pro
GPT-5 High 30 tok/s Pro
GPT-4o 93 tok/s Pro
Kimi K2 207 tok/s Pro
GPT OSS 120B 460 tok/s Pro
Claude Sonnet 4.5 36 tok/s Pro
2000 character limit reached

Canonical and Noncanonical Hamiltonian Operator Inference (2304.06262v2)

Published 13 Apr 2023 in cs.LG and math.DS

Abstract: A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (59)
  1. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.7054, doi:https://doi.org/10.1002/nme.7054. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7054
  2. doi:https://doi.org/10.1016/j.jcp.2021.110841. URL https://www.sciencedirect.com/science/article/pii/S0021999121007361
  3. doi:https://doi.org/10.1016/j.cma.2022.114764. URL https://www.sciencedirect.com/science/article/pii/S004578252200113X
  4. arXiv:2212.08939.
  5. doi:https://doi.org/10.1016/j.jcp.2022.111348. URL https://www.sciencedirect.com/science/article/pii/S0021999122004107
  6. doi:https://doi.org/10.1016/j.cma.2022.115717. URL https://www.sciencedirect.com/science/article/pii/S0045782522006727
  7. doi:https://doi.org/10.1016/j.cma.2016.03.025. URL https://www.sciencedirect.com/science/article/pii/S0045782516301104
  8. doi:10.1017/S0962492921000064.
  9. doi:https://doi.org/10.1016/j.cma.2020.113433. URL https://www.sciencedirect.com/science/article/pii/S0045782520306186
  10. doi:https://doi.org/10.1016/j.jcp.2006.10.026. URL https://www.sciencedirect.com/science/article/pii/S0021999106005535
  11. doi:https://doi.org/10.1016/j.jcp.2008.11.015. URL https://www.sciencedirect.com/science/article/pii/S0021999108006098
  12. doi:https://doi.org/10.1016/j.physd.2003.03.001. URL https://www.sciencedirect.com/science/article/pii/S0167278903003841
  13. doi:https://doi.org/10.1016/j.jcp.2012.04.019. URL https://www.sciencedirect.com/science/article/pii/S0021999112002008
  14. doi:https://doi.org/10.1016/j.jcp.2020.109789. URL https://www.sciencedirect.com/science/article/pii/S0021999120305635
  15. arXiv:2203.16492.
  16. doi:https://doi.org/10.1016/j.jcp.2016.05.037. URL https://www.sciencedirect.com/science/article/pii/S0021999116301826
  17. doi:https://doi.org/10.1016/j.cma.2014.01.011. URL https://www.sciencedirect.com/science/article/pii/S0045782514000164
  18. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6625, doi:https://doi.org/10.1002/nme.6625. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6625
  19. arXiv:2304.09229.
  20. doi:https://doi.org/10.1016/j.jcp.2018.05.019. URL https://www.sciencedirect.com/science/article/pii/S002199911830319X
  21. arXiv:2208.09360.
  22. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.4684, doi:https://doi.org/10.1002/fld.4684. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.4684
  23. arXiv:2203.06361.
  24. doi:https://doi.org/10.1016/S0167-2789(03)00227-6. URL https://www.sciencedirect.com/science/article/pii/S0167278903002276
  25. arXiv:https://doi.org/10.1137/140959602, doi:10.1137/140959602. URL https://doi.org/10.1137/140959602
  26. doi:10.1109/CDC.2009.5400045.
  27. doi:10.1364/JOSAA.12.001657. URL https://opg.optica.org/josaa/abstract.cfm?URI=josaa-12-8-1657
  28. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.4820, doi:https://doi.org/10.1002/nme.4820. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4820
  29. doi:10.48550/ARXIV.1407.6118. URL https://arxiv.org/abs/1407.6118
  30. doi:10.48550/ARXIV.2109.12367. URL https://arxiv.org/abs/2109.12367
  31. doi:https://doi.org/10.1016/j.ifacol.2022.09.138. URL https://www.sciencedirect.com/science/article/pii/S2405896322013398
  32. arXiv:https://doi.org/10.1137/17M1111991, doi:10.1137/17M1111991. URL https://doi.org/10.1137/17M1111991
  33. doi:10.1007/s10915-018-0653-6. URL https://doi.org/10.1007/s10915-018-0653-6
  34. arXiv:2206.01792.
  35. doi:https://doi.org/10.1016/j.cma.2016.11.016. URL https://www.sciencedirect.com/science/article/pii/S0045782516308477
  36. doi:10.48550/ARXIV.2112.10815. URL https://arxiv.org/abs/2112.10815
  37. arXiv:https://doi.org/10.1137/15M1055085, doi:10.1137/15M1055085. URL https://doi.org/10.1137/15M1055085
  38. doi:https://doi.org/10.1016/j.cma.2022.115709. URL https://www.sciencedirect.com/science/article/pii/S0045782522006648
  39. doi:https://doi.org/10.1016/j.physd.2020.132401. URL https://www.sciencedirect.com/science/article/pii/S0167278919307651
  40. doi:https://doi.org/10.1016/j.cma.2021.114296. URL https://www.sciencedirect.com/science/article/pii/S0045782521005910
  41. doi:10.2514/1.J057791. URL https://doi.org/10.2514/1.J057791
  42. arXiv:https://doi.org/10.1080/03036758.2020.1863237, doi:10.1080/03036758.2020.1863237. URL https://doi.org/10.1080/03036758.2020.1863237
  43. arXiv:https://doi.org/10.2514/1.J058943, doi:10.2514/1.J058943. URL https://doi.org/10.2514/1.J058943
  44. arXiv:https://arc.aiaa.org/doi/pdf/10.2514/6.2023-0330, doi:10.2514/6.2023-0330. URL https://arc.aiaa.org/doi/abs/10.2514/6.2023-0330
  45. doi:https://doi.org/10.1016/j.jcp.2022.111689. URL https://www.sciencedirect.com/science/article/pii/S0021999122007525
  46. arXiv:2210.07710.
  47. doi:https://doi.org/10.1016/j.cma.2022.115336. URL https://www.sciencedirect.com/science/article/pii/S0045782522004273
  48. E. Celledoni, V. Grimm, R. I. McLachlan, D. I. McLaren, D. O’Neale, B. Owren, G. R. W. Quispel, Preserving energy resp. dissipation in numerical pdes using the “average vector field”method, Journal of Computational Physics 231 (20) (2012) 6770–6789. doi:https://doi.org/10.1016/j.jcp.2012.06.022. URL https://www.sciencedirect.com/science/article/pii/S0021999112003373
  49. arXiv:https://doi.org/10.1063/1.526530, doi:10.1063/1.526530. URL https://doi.org/10.1063/1.526530
  50. arXiv:hep-th/0011052.
  51. doi:10.1007/s002110100282. URL https://doi.org/10.1007/s002110100282
  52. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.7056, doi:https://doi.org/10.1002/nme.7056. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7056
  53. doi:https://doi.org/10.1016/j.aml.2013.06.005. URL https://www.sciencedirect.com/science/article/pii/S0893965913001924
  54. doi:10.1137/19M1292448. URL https://doi.org/10.1137/19M1292448
  55. arXiv:https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1972.0032, doi:10.1098/rsta.1972.0032. URL https://royalsocietypublishing.org/doi/abs/10.1098/rsta.1972.0032
  56. doi:10.1038/s41592-019-0686-2.
  57. doi:https://doi.org/10.1016/j.cma.2017.02.006. URL https://www.sciencedirect.com/science/article/pii/S0045782516310982
  58. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6982, doi:https://doi.org/10.1002/nme.6982. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6982
  59. doi:10.1080/03036758.2020.1863237. URL https://doi.org/10.1080/03036758.2020.1863237
Citations (18)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up