PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
This work addresses the challenge of predicting diverse fluid dynamics scenarios for researchers and engineers, though it appears incremental as it builds on existing transformer and operator learning methods.
The authors tackled the problem of forecasting fluid dynamics across multiple physical systems by proposing PROSE-FD, a zero-shot multimodal PDE foundation model that simultaneously predicts heterogeneous two-dimensional systems, including shallow water and Navier-Stokes equations, and outperforms existing models in benchmark tasks.
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.