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@ARTICLE{Bangun:1048804,
      author       = {Bangun, Arya and Töllner, Maximilian and Zhao, Xuan and
                      Kübel, Christian and Scharr, Hanno},
      title        = {{F}low{TIE}: {F}low-based {T}ransport of {I}ntensity
                      {E}quation for {P}hase {G}radient {E}stimation from
                      4{D}-{STEM} {D}ata},
      publisher    = {arXiv},
      reportid     = {FZJ-2025-04917},
      year         = {2025},
      abstract     = {We introduce FlowTIE, a neural-network-based framework for
                      phase reconstruction from 4D-Scanning Transmission Electron
                      Microscopy (STEM) data, which integrates the Transport of
                      Intensity Equation (TIE) with a flow-based representation of
                      the phase gradient. This formulation allows the model to
                      bridge data-driven learning with physics-based priors,
                      improving robustness under dynamical scattering conditions
                      for thick specimen. The validation on simulated datasets of
                      crystalline materials, benchmarking to classical TIE and
                      gradient-based optimization methods are presented. The
                      results demonstrate that FlowTIE improves phase
                      reconstruction accuracy, fast, and can be integrated with a
                      thick specimen model, namely multislice method.},
      keywords     = {Machine Learning (cs.LG) (Other) / FOS: Computer and
                      information sciences (Other)},
      cin          = {IAS-8},
      cid          = {I:(DE-Juel1)IAS-8-20210421},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2511.07633},
      url          = {https://juser.fz-juelich.de/record/1048804},
}