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.

翻译：我们提出了PROSE-FD，一种零样本多模态偏微分方程基础模型，用于同时预测与不同流体动力学设置相关的异质二维物理系统。这些系统包括浅水方程以及具有不可压缩和可压缩流动、规则和复杂几何形状、不同浮力设置的Navier-Stokes方程。本工作提出了一种新的基于Transformer的多算子学习方法，该方法融合符号信息以执行基于算子的数据预测，即非自回归预测。通过在输入中融入多种模态，该偏微分方程基础模型构建了一条纳入物理行为数学描述的途径。我们在从13个数据集中收集的6个参数方程族上预训练了我们的基础模型，包含超过60K条轨迹。在基准前向预测任务中，我们的模型优于流行的算子学习、计算机视觉和多物理场模型。我们通过消融研究验证了我们的架构选择。