{"title":"Neural Downscaling for Complex Systems: from Large-scale to Small-scale by Neural Operator","authors":"Pengyu Lai, Jing Wang, Rui Wang, Dewu Yang, Haoqi Fei, Hui Xu","doi":"arxiv-2403.13016","DOIUrl":null,"url":null,"abstract":"Predicting and understanding the chaotic dynamics in complex systems is\nessential in various applications. However, conventional approaches, whether\nfull-scale simulations or small-scale omissions, fail to offer a comprehensive\nsolution. This instigates exploration into whether modeling or omitting\nsmall-scale dynamics could benefit from the well-captured large-scale dynamics.\nIn this paper, we introduce a novel methodology called Neural Downscaling (ND),\nwhich integrates neural operator techniques with the principles of inertial\nmanifold and nonlinear Galerkin theory. ND effectively infers small-scale\ndynamics within a complementary subspace from corresponding large-scale\ndynamics well-represented in a low-dimensional space. The effectiveness and\ngeneralization of the method are demonstrated on the complex systems governed\nby the Kuramoto-Sivashinsky and Navier-Stokes equations. As the first\ncomprehensive deterministic model targeting small-scale dynamics, ND sheds\nlight on the intricate spatiotemporal nonlinear dynamics of complex systems,\nrevealing how small-scale dynamics are intricately linked with and influenced\nby large-scale dynamics.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"102 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.13016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Predicting and understanding the chaotic dynamics in complex systems is
essential in various applications. However, conventional approaches, whether
full-scale simulations or small-scale omissions, fail to offer a comprehensive
solution. This instigates exploration into whether modeling or omitting
small-scale dynamics could benefit from the well-captured large-scale dynamics.
In this paper, we introduce a novel methodology called Neural Downscaling (ND),
which integrates neural operator techniques with the principles of inertial
manifold and nonlinear Galerkin theory. ND effectively infers small-scale
dynamics within a complementary subspace from corresponding large-scale
dynamics well-represented in a low-dimensional space. The effectiveness and
generalization of the method are demonstrated on the complex systems governed
by the Kuramoto-Sivashinsky and Navier-Stokes equations. As the first
comprehensive deterministic model targeting small-scale dynamics, ND sheds
light on the intricate spatiotemporal nonlinear dynamics of complex systems,
revealing how small-scale dynamics are intricately linked with and influenced
by large-scale dynamics.