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@ARTICLE{Munteanu:622215,
      author       = {Munteanu, Valentin and Starostin, Vladimir and Greco,
                      Alessandro and Pithan, Linus and Gerlach, Alexander and
                      Hinderhofer, Alexander and Kowarik, Stefan and Schreiber,
                      Frank},
      title        = {{N}eural network analysis of neutron and {X}-ray
                      reflectivity data incorporating prior knowledge},
      journal      = {Journal of applied crystallography},
      volume       = {57},
      number       = {2},
      issn         = {1600-5767},
      address      = {Copenhagen},
      publisher    = {Munksgaard},
      reportid     = {PUBDB-2025-00253},
      pages        = {456-469},
      year         = {2024},
      abstract     = {Due to the ambiguity related to the lack of phase
                      information, determining the physical parameters of
                      multilayer thin films from measured neutron and X-ray
                      reflectivity curves is, on a fundamental level, an
                      underdetermined inverse problem. This ambiguity poses
                      limitations on standard neural networks, constraining the
                      range and number of considered parameters in previous
                      machine learning solutions. To overcome this challenge, a
                      novel training procedure has been designed which
                      incorporates dynamic prior boundaries for each physical
                      parameter as additional inputs to the neural network. In
                      this manner, the neural network can be trained
                      simultaneously on all well-posed subintervals of a larger
                      parameter space in which the inverse problem is
                      underdetermined. During inference, users can flexibly input
                      their own prior knowledge about the physical system to
                      constrain the neural network prediction to distinct target
                      subintervals in the parameter space. The effectiveness of
                      the method is demonstrated in various scenarios, including
                      multilayer structures with a box model parameterization and
                      a physics-inspired special parameterization of the
                      scattering length density profile for a multilayer
                      structure. In contrast to previous methods, this approach
                      scales favourably when increasing the complexity of the
                      inverse problem, working properly even for a five-layer
                      multilayer model and a periodic multilayer model with up to
                      17 open parameters.},
      cin          = {FS-EC},
      ddc          = {540},
      cid          = {I:(DE-H253)FS-EC-20120731},
      pnm          = {623 - Data Management and Analysis (POF4-623)},
      pid          = {G:(DE-HGF)POF4-623},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:38596736},
      UT           = {WOS:001208800100024},
      doi          = {10.1107/S1600576724002115},
      url          = {https://bib-pubdb1.desy.de/record/622215},
}