Global S&T Development Trend Analysis Platform of Resources and Environment
DOI | 10.1038/s41467-019-10542-0 |
Deep learning for universal linear embeddings of nonlinear dynamics | |
Lusch, Bethany1,2; Kutz, J. Nathan1; Brunton, Steven L.1,2 | |
2019-06-24 | |
发表期刊 | NATURE COMMUNICATIONS
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ISSN | 2041-1723 |
出版年 | 2018 |
卷号 | 9 |
文章类型 | Article |
语种 | 英语 |
国家 | USA |
英文摘要 | Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear has the potential to enable nonlinear prediction, estimation, and control using linear theory. The Koopman operator is a leading data-driven embedding, and its eigenfunctions provide intrinsic coordinates that globally linearize the dynamics. However, identifying and representing these eigenfunctions has proven challenging. This work leverages deep learning to discover representations of Koopman eigenfunctions from data. Our network is parsimonious and interpretable by construction, embedding the dynamics on a low-dimensional manifold. We identify nonlinear coordinates on which the dynamics are globally linear using a modified auto-encoder. We also generalize Koopman representations to include a ubiquitous class of systems with continuous spectra. Our framework parametrizes the continuous frequency using an auxiliary network, enabling a compact and efficient embedding, while connecting our models to decades of asymptotics. Thus, we benefit from the power of deep learning, while retaining the physical interpretability of Koopman embeddings. |
领域 | 资源环境 |
收录类别 | SCI-E |
WOS记录号 | WOS:000451046200007 |
WOS关键词 | SPECTRAL PROPERTIES ; MODE DECOMPOSITION ; VARIATIONAL APPROACH ; SYSTEMS ; IDENTIFICATION ; REDUCTION ; OPERATOR |
WOS类目 | Multidisciplinary Sciences |
WOS研究方向 | Science & Technology - Other Topics |
URL | 查看原文 |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://119.78.100.173/C666/handle/2XK7JSWQ/204423 |
专题 | 资源环境科学 |
作者单位 | 1.Univ Washington, Dept Appl Math, Seattle, WA 98195 USA; 2.Univ Washington, Dept Mech Engn, Seattle, WA 98195 USA |
推荐引用方式 GB/T 7714 | Lusch, Bethany,Kutz, J. Nathan,Brunton, Steven L.. Deep learning for universal linear embeddings of nonlinear dynamics[J]. NATURE COMMUNICATIONS,2019,9. |
APA | Lusch, Bethany,Kutz, J. Nathan,&Brunton, Steven L..(2019).Deep learning for universal linear embeddings of nonlinear dynamics.NATURE COMMUNICATIONS,9. |
MLA | Lusch, Bethany,et al."Deep learning for universal linear embeddings of nonlinear dynamics".NATURE COMMUNICATIONS 9(2019). |
条目包含的文件 | 条目无相关文件。 |
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