Petar Bevanda, Max Beier, Sebastian Kerz, Armin Lederer, Stefan Sosnowski, Sandra Hirche
备注：
Revised version submitted to IEEE Control Systems Letters (L-CSS) with substantially revised exposition, evaluation and proof of Lemma 2 (previously Lemma 8)
System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor representations - allowing for simplified prediction, analysis and control. However, finding meaningful finite-dimensional representations for prediction is difficult as it involves determining features that are both Koopman-invariant (evolve linearly under the dynamics) as well as relevant (spanning the original state) - a generally unsupervised problem. In this work, we present Koopmanizing Flows - a novel continuous-time framework for supervised learning of linear predictors for a class of nonlinear dynamics. In our model construction a latent diffeomorphically related linear system unfolds into a linear predictor through the composition with a monomial basis. The lifting, its linear dynamics and state reconstruction are learned simultaneously, while an unconstrained parameterization of Hurwitz matrices ensures asymptotic stability regardless of the operator approximation accuracy. The superior efficacy of Koopmanizing Flows is demonstrated in comparison to a state-of-the-art method on the well-known LASA handwriting benchmark.
Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control
Max Planck Institute of Geoanthropology（马克斯·普朗克地理人类学研究所）；Department of Electrical Engineering and Information Technology, University of Naples（那不勒斯大学电气工程与信息学院）
Koopman Dreamer: Spectrally Constrained Latent Dynamics for Stable World-Model Imagination
College of Intelligence Science and Technology, National University of Defense Technology（国防科技大学智能科学与技术学院）；School of Engineering, Newcastle University（纽卡斯尔大学工程学院）
Finding separatrices of dynamical flows with Deep Koopman Eigenfunctions
Faculty of Mathematics（数学系）；Technion – Israel Institute of Technology（技术学院–以色列理工学院）；Rappaport Faculty of Medicine and Network Biology Research Laboratory（医学与网络生物学研究实验室）
Dynamic Systems Lab, University College London（伦敦大学学院动态系统实验室）；Department of Earth Science and Engineering, Imperial College London（伦敦帝国理工学院地球科学与工程系）；Santa Fe Institute（圣达菲研究所）；CEREA, ENPC and EDF R&D, Institut Polytechnique de Paris（巴黎理工学院CEREA、ENPC和EDF R&D）；School of Statistics and Data Science, Shanghai University of Finance and Economics（上海金融学院统计与数据科学学院）；Institute of Big Data Research, Shanghai University of Finance and Economics（上海金融学院大数据研究所）
Koopman Spectrum Nonlinear Regulators and Efficient Online Learning
University of Washington（华盛顿大学）；Ehime University（爱媛大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所高级智能项目中心）；Et Cetera Robotics；Keio University（庆应义塾大学）；Harvard University（哈佛大学）；Osaka University（大阪大学）
Hybrid Scheme of Kinematic Analysis and Lagrangian Koopman Operator Analysis for Short-term Precipitation Forecasting
Graduate School of Engineering（工学研究生院）；University of Yamanashi（山梨大学）；Department of Civil and Environmental Engineering（土木与环境工程系）；National Research Institute for Earth Science and Disaster Resilience (NIED)（日本国立地球科学与防灾研究所（NIED））
Koopman Regularized Deep Speech Disentanglement for Speaker Verification
School of Electronics and Computer Science, University of Southampton（电子与计算机科学学院，南安普顿大学）；Marine Geosciences, National Oceanography Centre（海洋科学，国家海洋学中心）
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
Department of Mathematics, Imperial College London（帝国理工学院数学系）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）
Learning Generalizable Reconstruction of High-Dimensional Neural Dynamics
Heidelberg University（海德堡大学）；Interdisciplinary Centre for Scientific Computing (IWR)（跨学科科学计算中心（IWR））；Department of Mathematics and Computer Science（数学与计算机科学系）
Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems
Graduate School of Information Science and Technology, The University of Osaka（大阪大学信息科学与技术研究生院）；Center for Advanced Intelligence Project, RIKEN（理化学研究所先进智能项目中心）
