Naval Information Warfare Center Pacific（太平洋海军信息战中心）；San Diego State University（圣地亚哥州立大学）；University of California Irvine（加州大学欧文分校）；University of California San Diego（加州大学圣地亚哥分校）
Daniel J. Alford-Lago, Christopher W. Curtis, Alexander T. Ihler, Opal Issan
备注：
22 pages, 6 figures; Added detail to section 2, typos corrected, made naming consistent; Updated authors and affiliations, updated figures 2-6, updated abstract; Added new results section, updated figures, 16 figures, 1 table
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of this infinite-dimensional operator can be difficult. The extended dynamic mode decomposition (EDMD) is one such method for generating approximations to Koopman spectra and modes, but the EDMD method faces its own set of challenges due to the need of user defined observables. To address this issue, we explore the use of autoencoder networks to simultaneously find optimal families of observables which also generate both accurate embeddings of the flow into a space of observables and submersions of the observables back into flow coordinates. This network results in a global transformation of the flow and affords future state prediction via the EDMD and the decoder network. We call this method the deep learning dynamic mode decomposition (DLDMD). The method is tested on canonical nonlinear data sets and is shown to produce results that outperform a standard DMD approach and enable data-driven prediction where the standard DMD fails.
IRCNN$^{+}$: An Enhanced Iterative Residual Convolutional Neural Network for Non-stationary Signal Decomposition
Guangdong University of Finance and Economics（广东财经大学）；Istituto di Astrofisica e Planetologia Spaziali（天体物理学与行星科学研究所）；Istituto Nazionale di Geofisica e Vulcanologia（国家地球物理与火山学研究所）；Georgia Institute of Technology（佐治亚理工学院）；Sun Yat-sen University（中山大学）
FLDmamba: Integrating Fourier and Laplace Transform Decomposition with Mamba for Enhanced Time Series Prediction
University of Hong Kong（香港大学）；Westlake University（西拉雅大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Tsinghua University（清华大学）；University of Queensland（昆士兰大学）
Key Labroatory of Symbolic Computation and Knowledge Engineering of Ministry of Education（符号计算与知识工程教育部重点实验室）；Jilin University（吉林大学）；Knowledge Engineering of Ministry of Education（知识工程教育部）；Changchun, 130012, China（长春，130012，中国）
