PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929500686647296 |
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| author | Liu, Yuxuan Sun, Jingmin He, Xinjie Pinney, Griffin Zhang, Zecheng Schaeffer, Hayden |
| author_facet | Liu, Yuxuan Sun, Jingmin He, Xinjie Pinney, Griffin Zhang, Zecheng Schaeffer, Hayden |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_09811 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics Liu, Yuxuan Sun, Jingmin He, Xinjie Pinney, Griffin Zhang, Zecheng Schaeffer, Hayden Machine Learning Numerical Analysis 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. |
| title | PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics |
| topic | Machine Learning Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2409.09811 |