PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
<|reference_start|>PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics: 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.<|reference_end|>
@article{liu2024prose-fd:,
    title={PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple
  Operators for Forecasting Fluid Dynamics},
    author={Yuxuan Liu, Jingmin Sun, Xinjie He, Griffin Pinney, Zecheng Zhang,
  Hayden Schaeffer},
    journal={arXiv preprint arXiv:2409.09811},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.09811},
    primaryClass={cs.LG cs.NA math.NA physics.flu-dyn}
}