While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a merging of machine learning tools with what is called the dynamic mode decomposition (DMD). This general approach has been shown to be an especially promising avenue for accurate model development. Building on this prior body of work, we develop a deep learning DMD based method which makes use of the fundamental insight of Takens' Embedding Theorem to build an adaptive learning scheme that better approximates higher dimensional and chaotic dynamics. We call this method the Deep Learning Hankel DMD (DLHDMD). We likewise explore how our method learns mappings which tend, after successful training, to significantly change the mutual information between dimensions in the dynamics. This appears to be a key feature in enhancing the DMD overall, and it should help provide further insight for developing other deep learning methods for time series analysis and model generation.
Super-resolution Multi-signal Direction-of-Arrival Estimation by Hankel-structured Sensing and Decomposition
Center for Connected Autonomy and AI（连接自主与人工智能中心）；Dept. of Electrical Engineering and Computer Science（电气工程与计算机科学系）；Florida Atlantic University（佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）；AFRL/RI（空军研究实验室/RI）
Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting
Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Tongji University（同济大学）；The University of Hong Kong（香港大学）；The Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Nagoya Institute of Technology（名古屋工业大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Seoul National University College of Medicine（首尔大学医学院）；Seoul National University Bundang Hospital（首尔大学盆唐医院）
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）
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）
Bayesian dynamic mode decomposition for real-time ship motion digital twinning
National Research Council（国家研究委员会）；Defence Research and Development Canada（加拿大国防研究与发展局）；Naval Surface Warfare Center-Carderock Division（海军水面作战中心卡德罗克分部）
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）
