Publikation: A Non-intrusive Neural-Network Based BFGS Algorithm for Parameter Estimation in Non-stationary Elasticity
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2025
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SEQUEIRA, Adélia, Hrsg., Ana SILVESTRE, Hrsg., Svilen S. VALTCHEV, Hrsg. und andere. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1. Cham: Springer, 2025, S. 324-334. Lecture Notes in Computational Science and Engineering (LNCSE). 153. ISBN 978-3-031-86172-7. Verfügbar unter: doi: 10.1007/978-3-031-86173-4_33
Zusammenfassung
We present a non-intrusive gradient and a non-intrusive BFGS algorithm for parameter estimation problems in non-stationary elasticity. To avoid multiple (and potentially expensive) solutions of the underlying partial differential equation (PDE), we approximate the PDE solver by a neural network within the algorithms. The network is trained offline for a given set of parameters. The algorithms are applied to an unsteady linear-elastic contact problem; their convergence and approximation properties are investigated numerically.
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510 Mathematik
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European Conference on Numerical Mathematics and Advanced Applications : ENUMATH 2023, 4. Sept. 2023 - 8. Sept. 2023, Lisbon, Portugal
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FREI, Stefan, Jan REICHLE, Stefan VOLKWEIN, 2025. A Non-intrusive Neural-Network Based BFGS Algorithm for Parameter Estimation in Non-stationary Elasticity. European Conference on Numerical Mathematics and Advanced Applications : ENUMATH 2023. Lisbon, Portugal, 4. Sept. 2023 - 8. Sept. 2023. In: SEQUEIRA, Adélia, Hrsg., Ana SILVESTRE, Hrsg., Svilen S. VALTCHEV, Hrsg. und andere. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1. Cham: Springer, 2025, S. 324-334. Lecture Notes in Computational Science and Engineering (LNCSE). 153. ISBN 978-3-031-86172-7. Verfügbar unter: doi: 10.1007/978-3-031-86173-4_33BibTex
@inproceedings{Frei2025Nonin-73352,
title={A Non-intrusive Neural-Network Based BFGS Algorithm for Parameter Estimation in Non-stationary Elasticity},
year={2025},
doi={10.1007/978-3-031-86173-4_33},
number={153},
isbn={978-3-031-86172-7},
address={Cham},
publisher={Springer},
series={Lecture Notes in Computational Science and Engineering (LNCSE)},
booktitle={Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 1},
pages={324--334},
editor={Sequeira, Adélia and Silvestre, Ana and Valtchev, Svilen S.},
author={Frei, Stefan and Reichle, Jan and Volkwein, Stefan}
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