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Digital twins of nonlinear dynamical systems: A perspective (2309.11461v1)

Published 20 Sep 2023 in cs.LG, math.DS, nlin.CD, and physics.data-an

Abstract: Digital twins have attracted a great deal of recent attention from a wide range of fields. A basic requirement for digital twins of nonlinear dynamical systems is the ability to generate the system evolution and predict potentially catastrophic emergent behaviors so as to providing early warnings. The digital twin can then be used for system "health" monitoring in real time and for predictive problem solving. In particular, if the digital twin forecasts a possible system collapse in the future due to parameter drifting as caused by environmental changes or perturbations, an optimal control strategy can be devised and executed as early intervention to prevent the collapse. Two approaches exist for constructing digital twins of nonlinear dynamical systems: sparse optimization and machine learning. The basics of these two approaches are described and their advantages and caveats are discussed.

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References (66)
  1. IEEE Access 8, 21980-22012 (2020).
  2. Int. J. Aerospace Eng. 2011, 154798 (2011).
  3. Nature 573, 274-277 (2019).
  4. Front. Gene. 9, 31 (2018).
  5. S. M. Schwartz, K. Wildenhaus, A. Bucher, B. Byrd, Digital twins and the emerging science of self: Implications for digital health experience design and “small” data. Front. Comp. Sci. 2, 31 (2020).
  6. Science 371, 1105-1106 (2021).
  7. P. Voosen, Europe builds ‘digital twin’ of earth to hone climate forecasts. Science 370, 16-17 (2020).
  8. Nat. Clim. Change 11, 80-83 (2021).
  9. Complex Sys. 1, 417-452 (1987).
  10. E. M. Bollt, Controlling chaos and the inverse frobenius-perron problem: global stabilization of arbitrary invariant measures. Int. J. Bif. Chaos 10, 1033-1050 (2000).
  11. Physica D 227, 78-99 (2007).
  12. Phys. Rev. Lett. 106, 154101 (2011).
  13. Phys. Rev. X 1, 021021 (2011).
  14. EPL (Europhys. Lett.) 94, 48006 (2011).
  15. Phys. Rev. E 85, 056220 (2012).
  16. Phys. Rev. E 85, 065201 (2012).
  17. Entropy 16, 3889-3902 (2014).
  18. Sci. Rep. 4, 3944 (2014).
  19. Nat. Commun. 5, 4323 (2014).
  20. R. Soc. Open Sci. 3, 150577 (2016).
  21. IEEE Trans. Info. Theory 52, 489-509 (2006).
  22. Comm. Pure Appl. Math. 59, 1207-1223 (2006).
  23. D. Donoho, Compressed sensing. IEEE Trans. Info. Theory 52, 1289-1306 (2006).
  24. R. G. Baraniuk, Compressed sensing. IEEE Signal Process. Mag. 24, 118-121 (2007).
  25. IEEE Signal Process. Mag. 25, 21-30 (2008).
  26. Chaos 33, 033111 (2023).
  27. H. Jaeger, The “echo state” approach to analysing and training recurrent neural networks-with an erratum note. German National Research Center for Information Technology GMD Technical Report 148, 13 (2001).
  28. Neur. Comp. 14, 2531-2560 (2002).
  29. Science 304, 78-80 (2004).
  30. Phys. Rev. E 91, 020801 (2015).
  31. Phys. Rev. X 7, 011015 (2017).
  32. Chaos 27, 121102 (2017).
  33. Chaos 27, 041102 (2017).
  34. Phys. Rev. Lett. 120, 024102 (2018).
  35. T. L. Carroll, Using reservoir computers to distinguish chaotic signals. Phys. Rev. E 98, 052209 (2018).
  36. Phys. Rev. E 98, 023111 (2018).
  37. Chaos 28, 043118 (2018).
  38. Chaos 29, 123108 (2019).
  39. Phys. Rev. Research 1, 033056 (2019).
  40. Neu. Net. 115, 100–123 (2019).
  41. Phys. Rev. Research 2, 012080 (2020).
  42. Chaos 30, 083114 (2020).
  43. Phys. Rev. Lett. 125, 088103 (2020).
  44. Phys. Rev. Research 3, 013090 (2021).
  45. Chaos 31, 033149 (2021).
  46. Nat. Machine Intell. 3, 316–323 (2021).
  47. Phys. Rev. Resesearch 3, 023237 (2021).
  48. J. Phys. Complexity 2, 035014 (2021).
  49. E. Bollt, On explaining the surprising success of reservoir computing forecaster of chaos? the universal machine learning dynamical system with contrast to var and dmd. Chaos 31, 013108 (2021).
  50. Nat. Commun. 12, 1–8 (2021).
  51. T. L. Carroll, Optimizing memory in reservoir computers. Chaos 32, 023123 (2022).
  52. Phys. Rep. 644, 1-76 (2016).
  53. Y.-C. Lai, Finding nonlinear system equations and complex network structures from data: A sparse optimization approach. Chaos 31, 082101 (2021).
  54. K. Ikeda, Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 30, 257-261 (1979).
  55. Phys. Rev. Lett. 45, 709–712 (1980).
  56. J. Opt. Soc. Ame. B 2, 552–564 (1985).
  57. Ame. Naturalist 144, 873–879 (1994).
  58. Phys. Rep. 521, 205–228 (2012).
  59. Phys. Rep. 531, 173–199 (2013).
  60. Phys. Rev. E 104, 014205 (2021).
  61. Phys. Rev. Lett. 64, 821–824 (1990).
  62. Phys. Rev. Lett. 76, 1804–1807 (1996).
  63. Phys. Rev. Lett. 76, 1816–1819 (1996).
  64. Phys. Rev. E 73, 026214 (2006).
  65. Phys. Rev. Lett. 98, 108102 (2007).
  66. Chaos 21, 033108 (2011).
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Authors (1)

  1. Ying-Cheng Lai