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

TL;DR

PROSE-FD is a multimodal PDE foundation model that uses transformer-based multi-operator learning to predict diverse fluid dynamics systems without task-specific training, integrating symbolic physical descriptions.

Contribution

It introduces a zero-shot, multimodal PDE foundation model that fuses symbolic information for operator learning across multiple fluid dynamics scenarios.

Findings

Outperforms existing operator learning and physics models in benchmarks

Pre-trained on 60K trajectories from 13 datasets across 6 equation families

Effective in zero-shot prediction of complex fluid systems

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.