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arXiv · 2506.06158

ENMA: Tokenwise Autoregression for Generative Neural PDE Operators

Armand Kassaï Koupaï·Lise Le Boudec·Louis Serrano·Patrick Gallinari
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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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Armand Kassaï Koupaï, Lise Le Boudec, Louis Serrano, Patrick Gallinari. 2025-12-11. ENMA: Tokenwise Autoregression for Generative Neural PDE Operators. https://arxiv.org/abs/2506.06158

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