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@ARTICLE{Wedemeyer:1052747,
      author       = {Wedemeyer, Moritz and Cramer, Eike and Mitsos, Alexander
                      and Dahmen, Manuel},
      title        = {{D}ata-{D}riven {C}onditional {F}lexibility {I}ndex},
      publisher    = {arXiv},
      reportid     = {FZJ-2026-01104},
      year         = {2026},
      abstract     = {With the increasing flexibilization of processes,
                      determining robust scheduling decisions has become an
                      important goal. Traditionally, the flexibility index has
                      been used to identify safe operating schedules by
                      approximating the admissible uncertainty region using simple
                      admissible uncertainty sets, such as hypercubes. Presently,
                      available contextual information, such as forecasts, has not
                      been considered to define the admissible uncertainty set
                      when determining the flexibility index. We propose the
                      conditional flexibility index (CFI), which extends the
                      traditional flexibility index in two ways: by learning the
                      parametrized admissible uncertainty set from historical data
                      and by using contextual information to make the admissible
                      uncertainty set conditional. This is achieved using a
                      normalizing flow that learns a bijective mapping from a
                      Gaussian base distribution to the data distribution. The
                      admissible latent uncertainty set is constructed as a
                      hypersphere in the latent space and mapped to the data
                      space. By incorporating contextual information, the CFI
                      provides a more informative estimate of flexibility by
                      defining admissible uncertainty sets in regions that are
                      more likely to be relevant under given conditions. Using an
                      illustrative example, we show that no general statement can
                      be made about data-driven admissible uncertainty sets
                      outperforming simple sets, or conditional sets outperforming
                      unconditional ones. However, both data-driven and
                      conditional admissible uncertainty sets ensure that only
                      regions of the uncertain parameter space containing
                      realizations are considered. We apply the CFI to a
                      security-constrained unit commitment example and demonstrate
                      that the CFI can improve scheduling quality by incorporating
                      temporal information.},
      keywords     = {Machine Learning (cs.LG) (Other) / FOS: Computer and
                      information sciences (Other)},
      cin          = {ICE-1},
      cid          = {I:(DE-Juel1)ICE-1-20170217},
      pnm          = {1121 - Digitalization and Systems Technology for
                      Flexibility Solutions (POF4-112) / HDS LEE - Helmholtz
                      School for Data Science in Life, Earth and Energy (HDS LEE)
                      (HDS-LEE-20190612)},
      pid          = {G:(DE-HGF)POF4-1121 / G:(DE-Juel1)HDS-LEE-20190612},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2601.16028},
      url          = {https://juser.fz-juelich.de/record/1052747},
}