% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@ARTICLE{Doncevic:917550,
      author       = {Doncevic, Danimir and Mitsos, Alexander and Guo, Yue and
                      Li, Qianxiao and Dietrich, Felix and Dahmen, Manuel and
                      Kevrekidis, Ioannis G.},
      title        = {{A} {R}ecursively {R}ecurrent {N}eural {N}etwork ({R}2{N}2)
                      {A}rchitecture for {L}earning {I}terative {A}lgorithms},
      publisher    = {arXiv},
      reportid     = {FZJ-2023-00752},
      year         = {2022},
      abstract     = {Meta-learning of numerical algorithms for a given task
                      consist of the data-driven identification and adaptation of
                      an algorithmic structure and the associated hyperparameters.
                      To limit the complexity of the meta-learning problem, neural
                      architectures with a certain inductive bias towards
                      favorable algorithmic structures can, and should, be used.
                      We generalize our previously introduced Runge-Kutta neural
                      network to a recursively recurrent neural network (R2N2)
                      superstructure for the design of customized iterative
                      algorithms. In contrast to off-the-shelf deep learning
                      approaches, it features a distinct division into modules for
                      generation of information and for the subsequent assembly of
                      this information towards a solution. Local information in
                      the form of a subspace is generated by subordinate, inner,
                      iterations of recurrent function evaluations starting at the
                      current outer iterate. The update to the next outer iterate
                      is computed as a linear combination of these evaluations,
                      reducing the residual in this space, and constitutes the
                      output of the network. We demonstrate that regular training
                      of the weight parameters inside the proposed superstructure
                      on input/output data of various computational problem
                      classes yields iterations similar to Krylov solvers for
                      linear equation systems, Newton-Krylov solvers for nonlinear
                      equation systems, and Runge-Kutta integrators for ordinary
                      differential equations. Due to its modularity, the
                      superstructure can be readily extended with functionalities
                      needed to represent more general classes of iterative
                      algorithms traditionally based on Taylor series expansions.},
      keywords     = {Machine Learning (cs.LG) (Other) / Numerical Analysis
                      (math.NA) (Other) / FOS: Computer and information sciences
                      (Other) / FOS: Mathematics (Other)},
      cin          = {IEK-10},
      cid          = {I:(DE-Juel1)IEK-10-20170217},
      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.2211.12386},
      url          = {https://juser.fz-juelich.de/record/917550},
}