ENMA用生成式Transformer实现物理方程的高效建模与快速泛化。
ENMA: Tokenwise Autoregression for Generative Neural PDE Operators
- 基于掩码自回归Transformer和流匹配损失，实现时空动态逐标记生成。
- 在不规则采样数据上通过注意力机制统一编码，支持单次学习建模新方程。
- 适用于需要快速适应新物理场景的科学计算与仿真任务。
求解时变参数偏微分方程（PDEs）仍是神经求解器的核心挑战，尤其在广泛物理参数与动力学下泛化能力受限。当数据存在不确定性或不完整时，生成模型成为自然选择。本文提出ENMA，一种用于建模物理现象时空动态的生成式神经算子。ENMA利用生成式掩码自回归Transformer，在压缩隐空间中预测未来动态，实现逐标记生成。不规则采样的空间观测通过注意力机制编码为统一隐表示，并经时空卷积编码器进一步压缩。该架构可在推理时进行上下文学习，通过目标轨迹历史状态或具有相似动力学的辅助轨迹进行条件输入。结果表明，ENMA具备强鲁棒性与可扩展性，能泛化至新PDE范式，并支持对时变参数化PDE的一次性代理建模。
原文摘要 · Abstract (English)
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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