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）
This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman variants-scalar-gated, per-mode gated, MLP-shaped spectral mapping, and low-rank Koopman operators which generalize and interpolate between strictly stable Koopman operators and unconstrained linear latent dynamics. Our formulation enables explicit control over the spectrum, stability, and rank of the linear transition operator while retaining compatibility with expressive nonlinear backbones such as Patchtst, Autoformer, and Informer. We evaluate the proposed operators in a large-scale benchmark that also includes LSTM, DLinear, and simple diagonal State-Space Models (SSMs), as well as lightweight transformer variants. Experiments across multiple horizons and patch lengths show that learnable Koopman models provide a favorable bias-variance trade-off, improved conditioning, and more interpretable latent dynamics. We provide a full spectral analysis, including eigenvalue trajectories, stability envelopes, and learned spectral distributions. Our results demonstrate that learnable Koopman operators are effective, stable, and theoretically principled components for deep forecasting.
SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting
Department of Electrical and Computer Engineering, McGill University, Montreal, Canada（麦吉尔大学电气与计算机工程系）；Amazon Science. This work does not relate to the author’s position at Amazon（亚马逊科学）；Mila - Quebec Artificial Intelligence Institute, Montreal, Canada（魁北克人工智能研究所）；ILLS - International Laboratory on Learning Systems, Montreal, Canada（学习系统国际实验室）
Probabilistic forecasting of complex phenomena is paramount to various scientific disciplines and applications. Despite the generality and importance of the problem, general mathematical techniques that allow for stable long-term forecasts with calibrated uncertainty measures are lacking. For most time series models, the difficulty of obtaining accurate probabilistic future time step predictions increases with the prediction horizon. In this paper, we introduce a surprisingly simple approach that characterizes time-varying distributions and enables reasonably accurate predictions thousands of …
End-to-End Neural Decomposition with Koopman Operators for Time-Series Forecasting
National Taiwan University（台湾大学）；National Institute of Information and Communications Technology（信息通信研究机构）；Research Center for Information Technology Innovation（资讯科技创新研究中心）
UC Los Angeles（加州大学洛杉矶分校）；ICSI（国际计算机科学研究所）；UC Berkeley（加州大学伯克利分校）
Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our net…
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））
With the accumulation of meteorological big data, data-driven models for short-term precipitation forecasting have shown increasing promise. We focus on Koopman operator analysis, which is a data-driven scheme to discover governing laws in observed data. We propose a method to apply this scheme to phenomena accompanying advection currents such as precipitation. The proposed method decomposes time evolutions of the phenomena between advection currents under a velocity field and changes in physical quantities under Lagrangian coordinates. The advection currents are estimated by kinematic analysi…
DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecasting
Helmholtz Center for Environmental Research-UFZ（海德堡环境研究中心-UFZ）；Delft Center for Systems and Control（代尔夫特系统与控制中心）；School of Engineering, University of Pittsburgh（匹兹堡大学工程学院）
Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systems
ElectroScience Laboratory, The Ohio State University（电科学实验室，俄亥俄州立大学）；Department of Electrical and Computer Engineering, The Ohio State University（电气与计算机工程系，俄亥俄州立大学）；SLAC National Accelerator Laboratory, Stanford University（斯坦福大学SLAC国家加速器实验室）
Munich Data Science Institute（慕尼黑数据科学研究所）；School of Computation, Information and Technology, Technical University of Munich（技术大学慕尼黑计算、信息与技术学院）；Interdisciplinary Center for Scientific Computing (IWR)（跨学科科学计算中心）；Department of Mathematics and Computer Science, Heidelberg University（海德堡大学数学与计算机科学系）
NTT Communication Science Laboratories（NTT通信科学实验室）；Osaka University（大阪大学）；RIKEN（理化学研究所）
We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data are small. The proposed model is based on the Koopman operator theory, where the decay rate and frequency information is used by restricting the eigenvalues of the Koopman operator that describe linear evolution in a Koopman space. We use neural networks to find an appropriate Koopman space, which are trained by minimizing multi-step forecasting and backcastin…
DB2-TransF: All You Need Is Learnable Daubechies Wavelets for Time Series Forecasting
organization= Department of Computer Science \& Engineering \& Communication \& Engineering , addressline= G B Pant , city= New Delhi , postcode= 580007 , state= Delhi , country= India；organization= Department of Computer Science \& Engineering , addressline= Indian Institute of Technology , city= Dharwad , postcode= 580007 , state= Karnataka , country= India
Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling
University of Electronic Science and Technology of China（电子科技大学）；The Hong Kong Polytechnic University（香港理工大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；University of Cambridge（剑桥大学）
VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting
College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件学院）；National Engineering Laboratory for Big Data System Computing Technology, Shenzhen University（深圳大学国家大数据系统计算技术工程实验室）
A Time-Series Foundation Model by Universal Delay Embedding
Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）；Shanghai Jiao Tong University（上海交通大学）；Fudan University（复旦大学）；Ocean University of China（中国海洋大学）；South China University of Technology（华南理工大学）
Revealing the Potential of Learnable Perturbation Ensemble Forecast Model for Tropical Cyclone Prediction
Artificial Intelligence Innovation and Incubation Institute（人工智能创新与孵化院）；Department of Atmospheric and Oceanic Sciences（大气科学系）；Institute of Atmospheric Sciences（大气科学研究院）；Shanghai Academy of Artificial Intelligence for Science（上海人工智能科学研究院）
Differential Convolutional Fuzzy Time Series Forecasting
University of Electronic Science and Technology of China（电子科技大学）；Huawei Cloud（华为云）；China Mobile Information Technology Center（中国移动信息技术中心）；Vanderbilt University（范德堡大学）
FreqLens: Interpretable Frequency Attribution for Time Series Forecasting
Independent Researcher（独立研究者）；Indiana University at Bloomington（印第安纳大学布卢明顿分校）；National Yang Ming Chiao Tung University；National Taiwan University（国立台湾大学）；Boise State University（博伊州立大学）
FilterNet: Harnessing Frequency Filters for Time Series Forecasting
North China Institute of Computing Technology（华北计算技术研究所）；State Information Center of China（中国国家信息中心）；Beijing Institute of Technology（北京理工大学）；Tongji University（同济大学）；University of Science and Technology of China（中国科学技术大学）；University of Oxford（牛津大学）
Time-series forecasting plays an important role in many real-world scenarios, such as equipment life cycle forecasting, weather forecasting, and traffic flow forecasting. It can be observed from recent research that a variety of transformer-based models have shown remarkable results in time-series forecasting. However, there are still some issues that limit the ability of transformer-based models on time-series forecasting tasks: (i) learning directly on raw data is susceptible to noise due to its complex and unstable feature representation; (ii) the self-attention mechanisms pay insufficient …
Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting
Charles F. Dolan School of Business, Fairfield University（Fairfield大学商学院）；Department of Industrial & Systems Engineering, The University of Tennessee（田纳西大学工业与系统工程系）
Forecasting of multivariate time-series is an important problem that has applications in traffic management, cellular network configuration, and quantitative finance. A special case of the problem arises when there is a graph available that captures the relationships between the time-series. In this paper we propose a novel learning architecture that achieves performance competitive with or better than the best existing algorithms, without requiring knowledge of the graph. The key element of our proposed architecture is the learnable fully connected hard graph gating mechanism that enables the…
