ENMA: Tokenwise Autoregression for Generative Neural PDE Operators

• URL: http://arxiv.org/abs/2506.06158v1
• Date: Fri, 06 Jun 2025 15:25:14 GMT
• Title: ENMA: Tokenwise Autoregression for Generative Neural PDE Operators
• Authors: Armand Kassaï Koupaï, Lise Le Boudec, Louis Serrano, Patrick Gallinari,
• Abstract summary: We introduce ENMA, a generative neural-temporal operator designed to model dynamics arising from physical phenomena.<n>ENMA predicts future dynamics compressed latent space using a generative masked autoregressive transformer trained with flow matching loss.<n>The framework generalizes to new PDE regimes and supports one-shot surrogate modeling of time-dependent parametric PDEs.
• Score: 12.314585849869797
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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