用符号信息融合的Transformer模型，一次预测多种流体动力学系统。
PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
- 基于Transformer的多算子学习，融合数学符号进行非自回归预测。
- 在60,000条轨迹上预训练，覆盖13个数据集和6类方程族。
- 首次实现跨复杂几何、可压缩/不可压缩流的统一建模，适合多物理场研究者。
我们提出PROSE-FD，一种零样本的多模态偏微分方程（PDE）基础模型，可同时预测多种二维流体动力学系统。涵盖浅水方程、不可压缩与可压缩的纳维-斯托克斯方程，以及规则与复杂几何、不同浮力条件下的系统。该方法采用基于Transformer的多算子学习框架，融合符号信息实现基于算子的数据预测（非自回归）。通过在输入中引入多模态信息，模型内置了物理行为的数学描述路径。我们在来自13个数据集的6个参数化方程族上进行预训练，包含超过6万条轨迹。在基准前向预测任务中，该模型优于主流的算子学习、计算机视觉和多物理场模型。通过消融实验验证了架构设计的有效性。
原文摘要 · Abstract (English)
We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.
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