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| Home > Publications database > A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms > print |
| 001 | 917550 | ||
| 005 | 20240712112853.0 | ||
| 024 | 7 | _ | |a 10.48550/ARXIV.2211.12386 |2 doi |
| 024 | 7 | _ | |a 2128/33638 |2 Handle |
| 037 | _ | _ | |a FZJ-2023-00752 |
| 100 | 1 | _ | |a Doncevic, Danimir |0 P:(DE-Juel1)180221 |b 0 |u fzj |
| 245 | _ | _ | |a A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms |
| 260 | _ | _ | |c 2022 |b arXiv |
| 336 | 7 | _ | |a Preprint |b preprint |m preprint |0 PUB:(DE-HGF)25 |s 1673944665_28073 |2 PUB:(DE-HGF) |
| 336 | 7 | _ | |a WORKING_PAPER |2 ORCID |
| 336 | 7 | _ | |a Electronic Article |0 28 |2 EndNote |
| 336 | 7 | _ | |a preprint |2 DRIVER |
| 336 | 7 | _ | |a ARTICLE |2 BibTeX |
| 336 | 7 | _ | |a Output Types/Working Paper |2 DataCite |
| 520 | _ | _ | |a 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. |
| 536 | _ | _ | |a 1121 - Digitalization and Systems Technology for Flexibility Solutions (POF4-112) |0 G:(DE-HGF)POF4-1121 |c POF4-112 |f POF IV |x 0 |
| 536 | _ | _ | |a HDS LEE - Helmholtz School for Data Science in Life, Earth and Energy (HDS LEE) (HDS-LEE-20190612) |0 G:(DE-Juel1)HDS-LEE-20190612 |c HDS-LEE-20190612 |x 1 |
| 588 | _ | _ | |a Dataset connected to DataCite |
| 650 | _ | 7 | |a Machine Learning (cs.LG) |2 Other |
| 650 | _ | 7 | |a Numerical Analysis (math.NA) |2 Other |
| 650 | _ | 7 | |a FOS: Computer and information sciences |2 Other |
| 650 | _ | 7 | |a FOS: Mathematics |2 Other |
| 700 | 1 | _ | |a Mitsos, Alexander |0 P:(DE-Juel1)172025 |b 1 |u fzj |
| 700 | 1 | _ | |a Guo, Yue |0 P:(DE-HGF)0 |b 2 |
| 700 | 1 | _ | |a Li, Qianxiao |0 P:(DE-HGF)0 |b 3 |
| 700 | 1 | _ | |a Dietrich, Felix |0 P:(DE-HGF)0 |b 4 |
| 700 | 1 | _ | |a Dahmen, Manuel |0 P:(DE-Juel1)172097 |b 5 |e Corresponding author |u fzj |
| 700 | 1 | _ | |a Kevrekidis, Ioannis G. |0 P:(DE-HGF)0 |b 6 |e Corresponding author |
| 773 | _ | _ | |a 10.48550/ARXIV.2211.12386 |
| 856 | 4 | _ | |u https://juser.fz-juelich.de/record/917550/files/2211.12386.pdf |y OpenAccess |
| 909 | C | O | |o oai:juser.fz-juelich.de:917550 |p openaire |p open_access |p VDB |p driver |p dnbdelivery |
| 910 | 1 | _ | |a Forschungszentrum Jülich |0 I:(DE-588b)5008462-8 |k FZJ |b 0 |6 P:(DE-Juel1)180221 |
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| 910 | 1 | _ | |a RWTH Aachen |0 I:(DE-588b)36225-6 |k RWTH |b 1 |6 P:(DE-Juel1)172025 |
| 910 | 1 | _ | |a Forschungszentrum Jülich |0 I:(DE-588b)5008462-8 |k FZJ |b 5 |6 P:(DE-Juel1)172097 |
| 913 | 1 | _ | |a DE-HGF |b Forschungsbereich Energie |l Energiesystemdesign (ESD) |1 G:(DE-HGF)POF4-110 |0 G:(DE-HGF)POF4-112 |3 G:(DE-HGF)POF4 |2 G:(DE-HGF)POF4-100 |4 G:(DE-HGF)POF |v Digitalisierung und Systemtechnik |9 G:(DE-HGF)POF4-1121 |x 0 |
| 914 | 1 | _ | |y 2022 |
| 915 | _ | _ | |a OpenAccess |0 StatID:(DE-HGF)0510 |2 StatID |
| 920 | _ | _ | |l yes |
| 920 | 1 | _ | |0 I:(DE-Juel1)IEK-10-20170217 |k IEK-10 |l Modellierung von Energiesystemen |x 0 |
| 980 | 1 | _ | |a FullTexts |
| 980 | _ | _ | |a preprint |
| 980 | _ | _ | |a VDB |
| 980 | _ | _ | |a UNRESTRICTED |
| 980 | _ | _ | |a I:(DE-Juel1)IEK-10-20170217 |
| 981 | _ | _ | |a I:(DE-Juel1)ICE-1-20170217 |
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