Reconstructing the system coefficients for coupled harmonic oscillators
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914576614817792 |
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| author | Bartsch, Jan Barakat, Ahmed A. Buchwald, Simon Ciaramella, Gabriele Volkwein, Stefan Weig, Eva M. |
| author_facet | Bartsch, Jan Barakat, Ahmed A. Buchwald, Simon Ciaramella, Gabriele Volkwein, Stefan Weig, Eva M. |
| contents | Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this research question within the framework of inverse problems. In this work, we consider optimization techniques to solve the inverse problem using Tikhonov regularization and data from laboratory experiments. We propose an iterative strategy that eliminates the need for further laboratory experiments. Our method is applied to identify the coupling and damping coefficients in a system of oscillators, ensuring an efficient and experiment-free approach. We present our results and compare them with those obtained from an alternative, purely experimental approach. By employing our proposed strategy, we demonstrate a significant reduction in the number of laboratory experiments required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstructing the system coefficients for coupled harmonic oscillators Bartsch, Jan Barakat, Ahmed A. Buchwald, Simon Ciaramella, Gabriele Volkwein, Stefan Weig, Eva M. Optimization and Control 34A30, 34A55, 34C15, 93B30 Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this research question within the framework of inverse problems. In this work, we consider optimization techniques to solve the inverse problem using Tikhonov regularization and data from laboratory experiments. We propose an iterative strategy that eliminates the need for further laboratory experiments. Our method is applied to identify the coupling and damping coefficients in a system of oscillators, ensuring an efficient and experiment-free approach. We present our results and compare them with those obtained from an alternative, purely experimental approach. By employing our proposed strategy, we demonstrate a significant reduction in the number of laboratory experiments required. |
| title | Reconstructing the system coefficients for coupled harmonic oscillators |
| topic | Optimization and Control 34A30, 34A55, 34C15, 93B30 |
| url | https://arxiv.org/abs/2412.07301 |