{"title":"PROSE-FD:用于学习流体力学预测多算子的多模态 PDE 基础模型","authors":"Yuxuan Liu, Jingmin Sun, Xinjie He, Griffin Pinney, Zecheng Zhang, Hayden Schaeffer","doi":"arxiv-2409.09811","DOIUrl":null,"url":null,"abstract":"We propose PROSE-FD, a zero-shot multimodal PDE foundational model for\nsimultaneous prediction of heterogeneous two-dimensional physical systems\nrelated to distinct fluid dynamics settings. These systems include shallow\nwater equations and the Navier-Stokes equations with incompressible and\ncompressible flow, regular and complex geometries, and different buoyancy\nsettings. This work presents a new transformer-based multi-operator learning\napproach that fuses symbolic information to perform operator-based data\nprediction, i.e. non-autoregressive. By incorporating multiple modalities in\nthe inputs, the PDE foundation model builds in a pathway for including\nmathematical descriptions of the physical behavior. We pre-train our foundation\nmodel on 6 parametric families of equations collected from 13 datasets,\nincluding over 60K trajectories. Our model outperforms popular operator\nlearning, computer vision, and multi-physics models, in benchmark forward\nprediction tasks. We test our architecture choices with ablation studies.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"43 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\",\"doi\":\"arxiv-2409.09811\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose PROSE-FD, a zero-shot multimodal PDE foundational model for\\nsimultaneous prediction of heterogeneous two-dimensional physical systems\\nrelated to distinct fluid dynamics settings. These systems include shallow\\nwater equations and the Navier-Stokes equations with incompressible and\\ncompressible flow, regular and complex geometries, and different buoyancy\\nsettings. This work presents a new transformer-based multi-operator learning\\napproach that fuses symbolic information to perform operator-based data\\nprediction, i.e. non-autoregressive. By incorporating multiple modalities in\\nthe inputs, the PDE foundation model builds in a pathway for including\\nmathematical descriptions of the physical behavior. We pre-train our foundation\\nmodel on 6 parametric families of equations collected from 13 datasets,\\nincluding over 60K trajectories. Our model outperforms popular operator\\nlearning, computer vision, and multi-physics models, in benchmark forward\\nprediction tasks. We test our architecture choices with ablation studies.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"43 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09811\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09811","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.