Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Time Series ForecastingSimilar Papers 제목 키워드 기반
DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecasting
Time series forecasting plays a vital role across scientific, industrial, and environmental domains, especially when dealing with high-dimensional and nonlinear systems. While Transformer-based models have recently achie…
Time Series ForecastingSynthetic Time Series Forecasting with Transformer Architectures: Extensive Simulation Benchmarks
Time series forecasting plays a critical role in domains such as energy, finance, and healthcare, where accurate predictions inform decision-making under uncertainty. Although Transformer-based models have demonstrated s…
BenchmarkingDecision Making Under UncertaintyInductive BiasTime Series+1Deep Koopman-layered Model with Universal Property Based on Toeplitz Matrices
We propose deep Koopman-layered models with learnable parameters in the form of Toeplitz matrices for analyzing the transition of the dynamics of time-series data. The proposed model has both theoretical solidness and fl…
subspace methodsTime SeriesSKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representat…
Time SeriesTime Series ForecastingKODA: A Data-Driven Recursive Model for Time Series Forecasting and Data Assimilation using Koopman Operators
Approaches based on Koopman operators have shown great promise in forecasting time series data generated by complex nonlinear dynamical systems (NLDS). Although such approaches are able to capture the latent state repres…
Time SeriesTime Series Forecasting