Single-ensemble multilevel Monte Carlo for discrete ensemble Kalman methods
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_ | 1866915153391386624 |
|---|---|
| author | Bouillon, Arne Ingelaere, Toon Samaey, Giovanni |
| author_facet | Bouillon, Arne Ingelaere, Toon Samaey, Giovanni |
| contents | Ensemble Kalman methods solve problems in domains such as filtering and inverse problems with interacting particles that evolve over time. For computationally expensive problems, the cost of attaining a high accuracy quickly becomes prohibitive. We exploit a hierarchy of approximations to the underlying forward model and apply multilevel Monte Carlo (MLMC) techniques, improving the asymptotic cost-to-error relation. More specifically, we use MLMC at each time step to estimate the interaction term in a single, globally-coupled ensemble. This technique was proposed by Hoel et al. for the ensemble Kalman filter; our goal is to study its applicability to a broader family of ensemble Kalman methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Single-ensemble multilevel Monte Carlo for discrete ensemble Kalman methods Bouillon, Arne Ingelaere, Toon Samaey, Giovanni Numerical Analysis Ensemble Kalman methods solve problems in domains such as filtering and inverse problems with interacting particles that evolve over time. For computationally expensive problems, the cost of attaining a high accuracy quickly becomes prohibitive. We exploit a hierarchy of approximations to the underlying forward model and apply multilevel Monte Carlo (MLMC) techniques, improving the asymptotic cost-to-error relation. More specifically, we use MLMC at each time step to estimate the interaction term in a single, globally-coupled ensemble. This technique was proposed by Hoel et al. for the ensemble Kalman filter; our goal is to study its applicability to a broader family of ensemble Kalman methods. |
| title | Single-ensemble multilevel Monte Carlo for discrete ensemble Kalman methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.10146 |