ENMA: Tokenwise Autoregression for Generative Neural PDE Operators

TL;DR

ENMA introduces a generative neural operator using tokenwise autoregression and attention mechanisms to model and predict complex spatio-temporal PDE dynamics, enabling flexible, one-shot surrogate modeling across diverse physical regimes.

Contribution

It presents ENMA, a novel generative neural operator with tokenwise autoregressive capabilities, for modeling and predicting PDE dynamics with irregular data and in-context learning.

Findings

Supports in-context learning with irregular data

Generalizes across diverse PDE regimes

Enables one-shot surrogate modeling

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.