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Reconstructing the Magnetic Field in an Arbitrary Domain via Data-driven Bayesian Methods and Numerical Simulations (2404.15745v3)

Published 24 Apr 2024 in physics.comp-ph, astro-ph.HE, cs.NA, and math.NA

Abstract: Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in deducing the most probable parameter values that align with the collected data. This study introduces an algorithm for reconstructing parameters by addressing an inverse problem formulated through differential equations underpinned by uncertain boundary conditions or variant parameters. We adopt a Bayesian approach for parameter inference, delineating the establishment of prior, likelihood, and posterior distributions, and the subsequent resolution of the maximum a posteriori problem via numerical optimization techniques. The proposed algorithm is applied to the task of magnetic field reconstruction within a conical domain, demonstrating precise recovery of the true parameter values.

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References (41)
  1. doi:10.1016/c2009-0-61134-x. URL https://doi.org/10.1016%2Fc2009-0-61134-x
  2. doi:10.1088/0266-5611/24/3/034009. URL https://doi.org/10.1088/0266-5611/24/3/034009
  3. doi:10.1017/s0962492919000059. URL https://doi.org/10.1017/s0962492919000059
  4. doi:10.1134/s0965542520060044. URL https://doi.org/10.1134/s0965542520060044
  5. doi:10.1017/s0962492910000061.
  6. doi:10.1016/j.jcp.2016.03.055. URL https://doi.org/10.1016/j.jcp.2016.03.055
  7. doi:10.1007/978-3-7091-2486-4_3. URL https://doi.org/10.1007/978-3-7091-2486-4_3
  8. doi:10.1051/0004-6361:20041839. URL https://doi.org/10.1051/0004-6361:20041839
  9. doi:10.1515/cmam-2022-0121. URL https://doi.org/10.1515/cmam-2022-0121
  10. doi:10.3389/fspas.2021.727076. URL https://doi.org/10.3389/fspas.2021.727076
  11. doi:10.1029/2022ja030512. URL https://doi.org/10.1029/2022ja030512
  12. doi:10.1088/1367-2630/aad35a. URL https://doi.org/10.1088/1367-2630/aad35a
  13. doi:10.1051/0004-6361/202346423. URL http://dx.doi.org/10.1051/0004-6361/202346423
  14. doi:10.1016/j.jcp.2018.10.045. URL http://dx.doi.org/10.1016/j.jcp.2018.10.045
  15. doi:10.1038/s42254-021-00314-5. URL http://dx.doi.org/10.1038/s42254-021-00314-5
  16. doi:10.1021/acs.jcim.3c01870. URL http://dx.doi.org/10.1021/acs.jcim.3c01870
  17. doi:10.1109/msp.2019.2950557. URL http://dx.doi.org/10.1109/MSP.2019.2950557
  18. doi:10.1098/rspa.2022.0648. URL http://dx.doi.org/10.1098/rspa.2022.0648
  19. doi:10.1137/s0036144500380934. URL http://dx.doi.org/10.1137/S0036144500380934
  20. doi:10.1088/1367-2630/ac706c. URL http://dx.doi.org/10.1088/1367-2630/ac706c
  21. doi:10.1007/b138659.
  22. doi:10.1007/s10444-009-9131-x.
  23. doi:10.1016/j.jcp.2018.12.025.
  24. doi:10.1016/j.jcp.2021.110194.
  25. doi:10.1016/j.jcp.2022.111262.
  26. doi:10.1002/9780470316801.
  27. doi:10.1007/978-0-387-84858-7.
  28. doi:10.1016/0377-0427(87)90125-7.
  29. doi:10.1016/b978-0-12-816514-0.00017-5.
  30. doi:10.1016/s0375-9601(97)00474-x.
  31. doi:10.1109/cec.2002.1004459.
  32. doi:10.1111/1467-9868.00294.
  33. doi:10.1145/2566630.
  34. doi:10.21105/joss.03982.
  35. doi:10.1145/3524456.
  36. doi:10.1137/16m1073352.
  37. doi:10.1137/15m1047696.
  38. doi:10.1029/2020gc009349.
  39. doi:10.1017/s0962492904000212.
  40. doi:10.1137/0712047.
  41. doi:10.1051/0004-6361/202140486. URL http://dx.doi.org/10.1051/0004-6361/202140486

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