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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.06158 |
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| _version_ | 1866908705173274624 |
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| author | Koupaï, Armand Kassaï Boudec, Lise Le Serrano, Louis Gallinari, Patrick |
| author_facet | Koupaï, Armand Kassaï Boudec, Lise Le Serrano, Louis Gallinari, Patrick |
| contents | Solving time-dependent parametric partial differential equations (PDEs) remains a fundamental challenge for neural solvers, particularly when generalizing across a wide range of physical parameters and dynamics. When data is uncertain or incomplete-as is often the case-a natural approach is to turn to generative models. We introduce ENMA, a generative neural operator designed to model spatio-temporal dynamics arising from physical phenomena. ENMA predicts future dynamics in a compressed latent space using a generative masked autoregressive transformer trained with flow matching loss, enabling tokenwise generation. Irregularly sampled spatial observations are encoded into uniform latent representations via attention mechanisms and further compressed through a spatio-temporal convolutional encoder. This allows ENMA to perform in-context learning at inference time by conditioning on either past states of the target trajectory or auxiliary context trajectories with similar dynamics. The result is a robust and adaptable framework that generalizes to new PDE regimes and supports one-shot surrogate modeling of time-dependent parametric PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ENMA: Tokenwise Autoregression for Generative Neural PDE Operators Koupaï, Armand Kassaï Boudec, Lise Le Serrano, Louis Gallinari, Patrick Machine Learning Solving time-dependent parametric partial differential equations (PDEs) remains a fundamental challenge for neural solvers, particularly when generalizing across a wide range of physical parameters and dynamics. When data is uncertain or incomplete-as is often the case-a natural approach is to turn to generative models. We introduce ENMA, a generative neural operator designed to model spatio-temporal dynamics arising from physical phenomena. ENMA predicts future dynamics in a compressed latent space using a generative masked autoregressive transformer trained with flow matching loss, enabling tokenwise generation. Irregularly sampled spatial observations are encoded into uniform latent representations via attention mechanisms and further compressed through a spatio-temporal convolutional encoder. This allows ENMA to perform in-context learning at inference time by conditioning on either past states of the target trajectory or auxiliary context trajectories with similar dynamics. The result is a robust and adaptable framework that generalizes to new PDE regimes and supports one-shot surrogate modeling of time-dependent parametric PDEs. |
| title | ENMA: Tokenwise Autoregression for Generative Neural PDE Operators |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.06158 |