AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields
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_ | 1866914979619274752 |
|---|---|
| author | Serrano, Louis Wang, Thomas X Naour, Etienne Le Vittaut, Jean-Noël Gallinari, Patrick |
| author_facet | Serrano, Louis Wang, Thomas X Naour, Etienne Le Vittaut, Jean-Noël Gallinari, Patrick |
| contents | We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields Serrano, Louis Wang, Thomas X Naour, Etienne Le Vittaut, Jean-Noël Gallinari, Patrick Machine Learning We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors. |
| title | AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2406.02176 |