Solver-in-the-loop approach to closure of shell models of turbulence
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_ | 1866915228573237248 |
|---|---|
| author | Freitas, André Um, Kiwon Desbrun, Mathieu Buzzicotti, Michele Biferale, Luca |
| author_facet | Freitas, André Um, Kiwon Desbrun, Mathieu Buzzicotti, Michele Biferale, Luca |
| contents | This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a neural network model to interact with the differential equation solver over time during the training process. The closure model is, then, naturally exposed to equations-informed input distributions by accounting for prior corrections over the temporal evolution in training. Such a characteristic makes this approach depart from the conventional a priori instantaneous training paradigm and often leads to a more accurate and stable closure model. Our study demonstrates that the closure learned via this a posteriori approach is able to reproduce high-order statistical moments of interest also in closures of high Reynolds number turbulence. Moreover, we investigate the performance of the learned model by experimenting with the effect of unrolling in time, which has remained for the most part unexplored in the literature. Finally, we discuss potential extensions of this approach to Navier-Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solver-in-the-loop approach to closure of shell models of turbulence Freitas, André Um, Kiwon Desbrun, Mathieu Buzzicotti, Michele Biferale, Luca Fluid Dynamics Chaotic Dynamics This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a neural network model to interact with the differential equation solver over time during the training process. The closure model is, then, naturally exposed to equations-informed input distributions by accounting for prior corrections over the temporal evolution in training. Such a characteristic makes this approach depart from the conventional a priori instantaneous training paradigm and often leads to a more accurate and stable closure model. Our study demonstrates that the closure learned via this a posteriori approach is able to reproduce high-order statistical moments of interest also in closures of high Reynolds number turbulence. Moreover, we investigate the performance of the learned model by experimenting with the effect of unrolling in time, which has remained for the most part unexplored in the literature. Finally, we discuss potential extensions of this approach to Navier-Stokes equations. |
| title | Solver-in-the-loop approach to closure of shell models of turbulence |
| topic | Fluid Dynamics Chaotic Dynamics |
| url | https://arxiv.org/abs/2411.13194 |