{"title":"FB-HyDON:通过超网络和有限基域分解对复杂 PDE 进行参数高效的物理信息算子学习","authors":"Milad Ramezankhani, Rishi Yash Parekh, Anirudh Deodhar, Dagnachew Birru","doi":"arxiv-2409.09207","DOIUrl":null,"url":null,"abstract":"Deep operator networks (DeepONet) and neural operators have gained\nsignificant attention for their ability to map infinite-dimensional function\nspaces and perform zero-shot super-resolution. However, these models often\nrequire large datasets for effective training. While physics-informed operators\noffer a data-agnostic learning approach, they introduce additional training\ncomplexities and convergence issues, especially in highly nonlinear systems. To\novercome these challenges, we introduce Finite Basis Physics-Informed\nHyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic\ndomain decomposition. By leveraging hypernetworks and finite basis functions,\nFB-HyDON effectively mitigates the training limitations associated with\nexisting physics-informed operator learning methods. We validated our approach\non the high-frequency harmonic oscillator, Burgers' equation at different\nviscosity levels, and Allen-Cahn equation demonstrating substantial\nimprovements over other operator learning models.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition\",\"authors\":\"Milad Ramezankhani, Rishi Yash Parekh, Anirudh Deodhar, Dagnachew Birru\",\"doi\":\"arxiv-2409.09207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Deep operator networks (DeepONet) and neural operators have gained\\nsignificant attention for their ability to map infinite-dimensional function\\nspaces and perform zero-shot super-resolution. However, these models often\\nrequire large datasets for effective training. While physics-informed operators\\noffer a data-agnostic learning approach, they introduce additional training\\ncomplexities and convergence issues, especially in highly nonlinear systems. To\\novercome these challenges, we introduce Finite Basis Physics-Informed\\nHyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic\\ndomain decomposition. By leveraging hypernetworks and finite basis functions,\\nFB-HyDON effectively mitigates the training limitations associated with\\nexisting physics-informed operator learning methods. We validated our approach\\non the high-frequency harmonic oscillator, Burgers' equation at different\\nviscosity levels, and Allen-Cahn equation demonstrating substantial\\nimprovements over other operator learning models.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-13\",\"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-2409.09207\",\"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-2409.09207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition
Deep operator networks (DeepONet) and neural operators have gained
significant attention for their ability to map infinite-dimensional function
spaces and perform zero-shot super-resolution. However, these models often
require large datasets for effective training. While physics-informed operators
offer a data-agnostic learning approach, they introduce additional training
complexities and convergence issues, especially in highly nonlinear systems. To
overcome these challenges, we introduce Finite Basis Physics-Informed
HyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic
domain decomposition. By leveraging hypernetworks and finite basis functions,
FB-HyDON effectively mitigates the training limitations associated with
existing physics-informed operator learning methods. We validated our approach
on the high-frequency harmonic oscillator, Burgers' equation at different
viscosity levels, and Allen-Cahn equation demonstrating substantial
improvements over other operator learning models.