Recurrent Neural Network based linear embeddings for time evolution of non-linear dynamics

• Item type: SIG Technical Reports(1)
• 公開日: 2019-07-17
• タイトル: Recurrent Neural Network based linear embeddings for time evolution of non-linear dynamics
• タイトル / 言語: en
• タイトル: Recurrent Neural Network based linear embeddings for time evolution of non-linear dynamics
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: 機械学習
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo
• 著者所属: Information Technology Center, The University of Tokyo
• 著者所属: Information Technology Center, The University of Tokyo
• 著者所属(英): en
• 著者所属(英): Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo
• 著者所属(英): en
• 著者所属(英): Information Technology Center, The University of Tokyo
• 著者所属(英): en
• 著者所属(英): Information Technology Center, The University of Tokyo
• 著者名: Shlok, Mohta; Kengo, Nakajima; Takashi, Shimokawabe
• 著者名(英): Shlok, Mohta; Kengo, Nakajima; Takashi, Shimokawabe
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: In modern dynamical system modeling, finding coordinate transformation for representing highly non-linear dynamics in terms of approximate linear dynamics has been of crucial importance for enabling non-linear control, estimation, and prediction. Recently developed interest in Koopman operator theory has shown that its eigenfunctions can provide such coordinates that intrinsically linearize the global dynamics [11], [6], [2], [14]. But finding and representation of such eigenfunctions have been challenging. The present work leverages deep learning methods, specifically Recurrent Neural Networks (RNNs) [15] for discovering the Koopman eigenfunction representations and exploit RNNs ability to model temporal dependencies, to allow multi-step evolution of the dynamics, as long forecasting for such systems still remains a major challenge [16]. It has been shown by [11], that such embeddings can be found using deep neural networks. Current work is an incremental work on the network architecture, which is interpretable in terms of Koopman theory and parsimonious, allowing augmentation to the lacking interpretability to deep learning architectures, while capturing the fewest meaningful eigenfunctions. Some other challenges related to modeling such architectures are discussed in future work.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: In modern dynamical system modeling, finding coordinate transformation for representing highly non-linear dynamics in terms of approximate linear dynamics has been of crucial importance for enabling non-linear control, estimation, and prediction. Recently developed interest in Koopman operator theory has shown that its eigenfunctions can provide such coordinates that intrinsically linearize the global dynamics [11], [6], [2], [14]. But finding and representation of such eigenfunctions have been challenging. The present work leverages deep learning methods, specifically Recurrent Neural Networks (RNNs) [15] for discovering the Koopman eigenfunction representations and exploit RNNs ability to model temporal dependencies, to allow multi-step evolution of the dynamics, as long forecasting for such systems still remains a major challenge [16]. It has been shown by [11], that such embeddings can be found using deep neural networks. Current work is an incremental work on the network architecture, which is interpretable in terms of Koopman theory and parsimonious, allowing augmentation to the lacking interpretability to deep learning architectures, while capturing the fewest meaningful eigenfunctions. Some other challenges related to modeling such architectures are discussed in future work.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN10463942
• 書誌情報: 研究報告ハイパフォーマンスコンピューティング（HPC）; 巻 2019-HPC-170, 号 11, p. 1-6, 発行日 2019-07-17
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2188-8841
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会