Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting
This work addresses forecasting challenges in systems like cardiac dynamics, offering a novel method for improved accuracy, though it appears incremental as it combines existing techniques like GCNs and Transformers.
The paper tackles spatiotemporal dynamics forecasting on irregular geometric domains by proposing TK-GCN, a two-stage framework that integrates geometry-aware spatial encoding with long-range temporal modeling, resulting in superior predictive accuracy across various forecast horizons compared to state-of-the-art baselines.
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.