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Adaptive reduced basis trust region methods for parameter identification problems

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2024

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Keil, Tim
Ohlberger, Mario
Kaltenbacher, Barbara

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Deutsche Forschungsgemeinschaft (DFG): OH 98/11-1
Deutsche Forschungsgemeinschaft (DFG): VO 1658/6-1
Deutsche Forschungsgemeinschaft (DFG): EXC 2044 39068558

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Computational Science and Engineering. Springer. 2024, 1(1), 3. eISSN 2948-1597. Verfügbar unter: doi: 10.1007/s44207-024-00002-z

Zusammenfassung

In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such methods typically require a large number of forward solutions, which makes the use of the reduced basis method attractive to reduce computational complexity. However, the considered inverse problems are typically ill-posed due to their infinite-dimensional parameter space. Moreover, the infinite-dimensional parameter space makes it impossible to build and certify classical reduced-order models efficiently in a so-called “offline phase”. We thus propose a new algorithm that adaptively builds a reduced parameter space in the online phase. The enrichment of the reduced parameter space is naturally inherited from the Tikhonov regularization within an iteratively regularized Gauß-Newton method. Finally, the adaptive parameter space reduction is combined with a certified reduced basis state space reduction within an adaptive error-aware trust region framework. Numerical experiments are presented to show the efficiency of the combined parameter and state space reduction for inverse parameter identification problems with distributed reaction or diffusion coefficients.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Parameter identification, Reduced basis method, Model reduction, Inverse problems

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ISO 690KARTMANN, Michael, Tim KEIL, Mario OHLBERGER, Stefan VOLKWEIN, Barbara KALTENBACHER, 2024. Adaptive reduced basis trust region methods for parameter identification problems. In: Computational Science and Engineering. Springer. 2024, 1(1), 3. eISSN 2948-1597. Verfügbar unter: doi: 10.1007/s44207-024-00002-z
BibTex
@article{Kartmann2024-09-23Adapt-71864,
  year={2024},
  doi={10.1007/s44207-024-00002-z},
  title={Adaptive reduced basis trust region methods for parameter identification problems},
  number={1},
  volume={1},
  journal={Computational Science and Engineering},
  author={Kartmann, Michael and Keil, Tim and Ohlberger, Mario and Volkwein, Stefan and Kaltenbacher, Barbara},
  note={Article Number: 3}
}
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