Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting

TL;DR

This paper introduces TK-GCN, a novel framework combining Koopman-enhanced graph convolutional networks and Transformers to improve long-range spatiotemporal forecasting on irregular domains, outperforming existing methods.

Contribution

The paper presents a new two-stage approach integrating Koopman-based spatial encoding with Transformer-based temporal modeling for enhanced spatiotemporal forecasting.

Findings

TK-GCN achieves superior accuracy over state-of-the-art baselines.

The Koopman embedding improves temporal consistency in latent space.

Transformer effectively captures long-range dependencies in complex systems.

Abstract

Spatiotemporal dynamics forecasting is inherently challenging, particularly in systems defined over irregular geometric domains, due to the need to jointly capture complex spatial correlations and nonlinear temporal dynamics. To tackle these challenges, we propose TK-GCN, a two-stage framework that integrates geometry-aware spatial encoding with long-range temporal modeling. In the first stage, a Koopman-enhanced Graph Convolutional Network (K-GCN) is developed to embed the high-dimensional dynamics distributed on spatially irregular domains into a latent space where the evolution of system states is approximately linear. By leveraging Koopman operator theory, this stage enhances the temporal consistency during the latent learning. In the second stage, a Transformer module is employed to model the temporal progression within the Koopman-encoded latent space. Through the self-attention mechanism, the Transformer captures long-range temporal dependencies, enabling accurate forecasting over extended horizons. We evaluate TK-GCN in spatiotemporal cardiac dynamics forecasting and benchmark its performance against several state-of-the-art baselines. Experimental results and ablation studies show that TK-GCN consistently delivers superior predictive accuracy across a range of forecast horizons, demonstrating its capability to effectively model complex spatial structures and nonlinear temporal dynamics.