arXiv:2511.21861cs.LGcs.AI2025-11中稿 · AAAI被引 9

PDE-FM统一建模多物理领域偏微分方程,实现跨领域高效迁移。

Towards a Foundation Model for Partial Differential Equations Across Physics Domains

  • 采用空间-谱令牌化与物理感知条件,结合Mamba架构建模动态
  • 在12个数据集上平均降低46%的VRMSE,6个领域达顶尖水平
  • 适合需要跨物理场景迁移的科学模拟与通用仿真研究者

我们提出PDE-FM,一种模块化的物理信息机器学习基础模型,可统一处理异构偏微分方程系统中的空间、谱和时间推理。PDE-FM融合空间-谱令牌化、物理感知条件与基于Mamba的状态空间主干,配合算子理论解码器,实现复杂物理动态的可扩展、高数据效率建模。相比任务专用神经算子,PDE-FM仅需一次预训练即可在新物理域中直接迁移,无需架构或数据定制。在涵盖流体、辐射、弹性与天体物理现象的The Well基准12个2D/3D数据集上评估,其在6个领域达到当前最优精度,平均VRMSE降低46%。模型展现出强跨物理泛化能力,在湍流与辐射系统中表现尤为突出,同时保持对线性与稳态系统的高性能。结果表明,大规模跨物理过程预训练可生成可迁移的动力学表征,为多物理仿真与科学发现的统一代理模型迈出关键一步。

原文摘要 · Abstract (English)

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral tokenization, physics-aware conditioning, and a Mamba-based state-space backbone with an operator-theoretic decoder, enabling scalable and data-efficient modeling of complex physical dynamics. In contrast to task-specific neural operators, PDE-FM is pretrained once on diverse PDE datasets and can be transferred to new physical regimes without architectural or data-specific modifications. Evaluated on twelve 2D and 3D datasets from The Well benchmark - spanning hydrodynamic, radiative, elastic, and astrophysical phenomena - PDE-FM achieves state-of-the-art accuracy in six domains, reducing mean VRMSE by 46% relative to prior operator-learning baselines. The model demonstrates robust cross-physics generalization, excelling in turbulent and radiative systems while maintaining strong performance in linear and steady-state regimes. These results suggest that large-scale pretraining across diverse physical processes can yield transferable representations of dynamics, marking a step toward unified, foundation-level surrogates for multi-physics simulation and scientific discovery.

偏微分方程基础模型物理信息跨域泛化

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