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@ARTICLE{Schweidtmann:905555,
      author       = {Schweidtmann, Artur M. and Weber, Jana M. and Wende,
                      Christian and Netze, Linus and Mitsos, Alexander},
      title        = {{O}bey validity limits of data-driven models through
                      topological data analysis and one-class classification},
      journal      = {Optimization and engineering},
      volume       = {23},
      issn         = {1389-4420},
      address      = {Dordrecht [u.a.]},
      publisher    = {Springer Science + Business Media B.V},
      reportid     = {FZJ-2022-00796},
      pages        = {855–876},
      year         = {2022},
      abstract     = {Data-driven models are becoming increasingly popular in
                      engineering, on their own or in combination with mechanistic
                      models. Commonly, the trained models are subsequently used
                      in model-based optimization of design and/or operation of
                      processes. Thus, it is critical to ensure that data-driven
                      models are not evaluated outside their validity domain
                      during process optimization. We propose a method to learn
                      this validity domain and encode it as constraints in process
                      optimization. We first perform a topological data analysis
                      using persistent homology identifying potential holes or
                      separated clusters in the training data. In case clusters or
                      holes are identified, we train a one-class classifier, i.e.,
                      a one-class support vector machine, on the training data
                      domain and encode it as constraints in the subsequent
                      process optimization. Otherwise, we construct the convex
                      hull of the data and encode it as constraints. We finally
                      perform deterministic global process optimization with the
                      data-driven models subject to their respective validity
                      constraints. To ensure computational tractability, we
                      develop a reduced-space formulation for trained one-class
                      support vector machines and show that our formulation
                      outperforms common full-space formulations by a factor of
                      over 3000, making it a viable tool for engineering
                      applications. The method is ready-to-use and available
                      open-source as part of our MeLOn toolbox
                      (https://git.rwth-aachen.de/avt.svt/public/MeLOn).},
      cin          = {IEK-10},
      ddc          = {690},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      pnm          = {899 - ohne Topic (POF4-899)},
      pid          = {G:(DE-HGF)POF4-899},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000650093300002},
      doi          = {10.1007/s11081-021-09608-0},
      url          = {https://juser.fz-juelich.de/record/905555},
}