DeepKoopFormer: a Koopman enhanced transformer based architecture for time series forecasting

Abstract Time series forecasting plays a vital role across scientific, industrial, and environmental domains, especially when dealing with high-dimensional and nonlinear systems. While Transformer models have recently achieved state-of-the-art performance in long-range forecasting, they often suffer from interpretability issues and instability in the presence of noise or dynamical uncertainty. We propose , a forecasting framework that combines Transformer-based sequence modeling with Koopman-inspired latent linear dynamics to improve stability, interpretability, and long-horizon robustness. Our model features a modular encoder–propagator–decoder structure, where temporal dynamics are learned via a spectrally constrained, linear Koopman-inspired propagator in a latent space. We impose structural guarantees—i.e., bounded spectral radius, Lyapunov-based energy regularization, and orthogonal parameterization—to ensure stability and interpretability. Comprehensive evaluations are conducted on dynamical systems, climate dataset, financial time series, and electricity generation dataset using the package that is prepared for this purpose. Across all experiments, consistently outperforms standard LSTM and baseline Transformer models in terms of accuracy, robustness to noise, and long-term forecasting stability. These results establish as a flexible, interpretable, and robust framework for forecasting in high-dimensional and dynamical settings.