Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control

Researchers propose a new family of learnable Koopman operators that combine linear dynamical systems theory with deep learning for time series forecasting. The approach integrates with existing transformer architectures like Patchtst and Autoformer, offering improved stability and interpretability in predictive models.

• →Four new learnable Koopman variants enable explicit control over spectrum, stability, and rank of linear transition operators.
• →The approach is compatible with popular transformer architectures including Patchtst, Autoformer, and Informer.
• →Large-scale benchmarks show learnable Koopman models provide favorable bias-variance trade-off compared to LSTM and other methods.
• →The models offer improved conditioning and more interpretable latent dynamics for time series prediction.
• →Full spectral analysis demonstrates theoretical stability and effectiveness of the proposed operators.