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@ARTICLE{Schulze:1044204,
      author       = {Schulze, Jan C. and Mitsos, Alexander},
      title        = {{N}onlinear {M}odel {O}rder {R}eduction of {D}ynamical
                      {S}ystems in {P}rocess {E}ngineering: {R}eview and
                      {C}omparison},
      publisher    = {arXiv},
      reportid     = {FZJ-2025-03093},
      year         = {2025},
      abstract     = {Computationally cheap yet accurate enough dynamical models
                      are vital for real-time capable nonlinear optimization and
                      model-based control. When given a computationally expensive
                      high-order prediction model, a reduction to a lower-order
                      simplified model can enable such real-time applications.
                      Herein, we review state-of-the-art nonlinear model order
                      reduction methods and provide a theoretical comparison of
                      method properties. Additionally, we discuss both
                      general-purpose methods and tailored approaches for
                      (chemical) process systems and we identify similarities and
                      differences between these methods. As manifold-Galerkin
                      approaches currently do not account for inputs in the
                      construction of the reduced state subspace, we extend these
                      methods to dynamical systems with inputs. In a comparative
                      case study, we apply eight established model order reduction
                      methods to an air separation process model: POD-Galerkin,
                      nonlinear-POD-Galerkin, manifold-Galerkin, dynamic mode
                      decomposition, Koopman theory, manifold learning with latent
                      predictor, compartment modeling, and model aggregation.
                      Herein, we do not investigate hyperreduction (reduction of
                      FLOPS). Based on our findings, we discuss strengths and
                      weaknesses of the model order reduction methods.},
      keywords     = {Systems and Control (eess.SY) (Other) / Machine Learning
                      (cs.LG) (Other) / Differential Geometry (math.DG) (Other) /
                      Dynamical Systems (math.DS) (Other) / Optimization and
                      Control (math.OC) (Other) / FOS: Electrical engineering,
                      electronic engineering, information engineering (Other) /
                      FOS: Computer and information sciences (Other) / FOS:
                      Mathematics (Other)},
      cin          = {ICE-1},
      cid          = {I:(DE-Juel1)ICE-1-20170217},
      pnm          = {899 - ohne Topic (POF4-899)},
      pid          = {G:(DE-HGF)POF4-899},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2506.12819},
      url          = {https://juser.fz-juelich.de/record/1044204},
}