Reconstruction of unknown monotone nonlinear operators in semilinear elliptic models using optimal inputs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915153397678080 |
|---|---|
| author | Bartsch, Jan Buchwald, Simon Ciaramella, Gabriele Volkwein, Stefan |
| author_facet | Bartsch, Jan Buchwald, Simon Ciaramella, Gabriele Volkwein, Stefan |
| contents | Physical models often contain unknown functions and relations. The goal of our work is to answer the question of how one should excite or control a system under consideration in an appropriate way to be able to reconstruct an unknown nonlinear relation. To answer this question, we propose a greedy reconstruction algorithm within an offline-online strategy. We apply this strategy to a two-dimensional semilinear elliptic model. Our identification is based on the application of several space-dependent excitations (also called controls). These specific controls are designed by the algorithm in order to obtain a deeper insight into the underlying physical problem and a more precise reconstruction of the unknown relation. We perform numerical simulations that demonstrate the effectiveness of our approach which is not limited to the current type of equation. Since our algorithm provides not only a way to determine unknown operators by existing data but also protocols for new experiments, it is a holistic concept to tackle the problem of improving physical models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction of unknown monotone nonlinear operators in semilinear elliptic models using optimal inputs Bartsch, Jan Buchwald, Simon Ciaramella, Gabriele Volkwein, Stefan Optimization and Control Analysis of PDEs 35K57, 35R30, 49N45, 49M41, 93B30 Physical models often contain unknown functions and relations. The goal of our work is to answer the question of how one should excite or control a system under consideration in an appropriate way to be able to reconstruct an unknown nonlinear relation. To answer this question, we propose a greedy reconstruction algorithm within an offline-online strategy. We apply this strategy to a two-dimensional semilinear elliptic model. Our identification is based on the application of several space-dependent excitations (also called controls). These specific controls are designed by the algorithm in order to obtain a deeper insight into the underlying physical problem and a more precise reconstruction of the unknown relation. We perform numerical simulations that demonstrate the effectiveness of our approach which is not limited to the current type of equation. Since our algorithm provides not only a way to determine unknown operators by existing data but also protocols for new experiments, it is a holistic concept to tackle the problem of improving physical models. |
| title | Reconstruction of unknown monotone nonlinear operators in semilinear elliptic models using optimal inputs |
| topic | Optimization and Control Analysis of PDEs 35K57, 35R30, 49N45, 49M41, 93B30 |
| url | https://arxiv.org/abs/2405.12153 |