PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

• URL: http://arxiv.org/abs/2409.09811v1
• Date: Sun, 15 Sep 2024 18:20:15 GMT
• Title: PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
• Authors: Yuxuan Liu, Jingmin Sun, Xinjie He, Griffin Pinney, Zecheng Zhang, Hayden Schaeffer,
• Abstract summary: We propose a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow.
• Score: 3.770825791788951
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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