{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:47:20Z","timestamp":1760028440883,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T00:00:00Z","timestamp":1738713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation for Research and Technology\u2014Hellas Synergy Grant Program"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/computation13020037","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T05:50:36Z","timestamp":1738734636000},"page":"37","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reconstructing the Magnetic Field in an Arbitrary Domain via Data-Driven Bayesian Methods and Numerical Simulations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4478-935X","authenticated-orcid":false,"given":"Georgios E.","family":"Pavlou","sequence":"first","affiliation":[{"name":"Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, GR-71110 Heraklion, Greece"}]},{"given":"Vasiliki","family":"Pavlidou","sequence":"additional","affiliation":[{"name":"Institute of Astrophysics, Foundation for Research and Technology-Hellas, Vasilika Vouton, GR-71110 Heraklion, Greece"},{"name":"Department of Physics, University of Crete, GR-70013 Heraklion, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9613-7639","authenticated-orcid":false,"given":"Vagelis","family":"Harmandaris","sequence":"additional","affiliation":[{"name":"Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, GR-71110 Heraklion, Greece"},{"name":"Department of Mathematics and Applied Mathematics, University of Crete, GR-71409 Heraklion, Greece"},{"name":"Computation-Based Science and Technology Research Center, The Cyprus Institute, Nicosia 2121, Cyprus"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Aster, R.C., Borchers, B., and Thurber, C.H. 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