P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution

• URL: http://arxiv.org/abs/2606.19303v1
• Date: Wed, 17 Jun 2026 17:26:51 GMT
• Title: P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution
• Abstract summary: We propose a sparse-augedmented Koopman-GCN-dynamics for continuous super-resolution on irregular irregular geometries.<n>We show that our method achieves superior accuracy compared to baseline models.
• Score: 33.587225826716356
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: High-fidelity simulation of spatiotemporal dynamics is computationally prohibitive, necessitating efficient super-resolution techniques to reconstruct high-resolution data from coarse-grained inputs. Traditional data-driven methods often lack physical constraints, and simple physics-informed learning struggles with irregular spatial geometries and intricately evolving temporal dynamics. To tackle these challenges, we propose a Physics-augmented Koopman-enhanced Graph Convolutional Network (P-K-GCN) for spatiotemporal super-resolution on irregular geometries. Specifically, a continuous spline-based GCN is first designed to extract spatial dependencies directly from coarse graph, and Koopman operator theory is incorporated to project the nonlinear dynamics into a compact latent space where temporal progression is linearized. Second, we augment the optimization objective with a physics-based loss to force the data-driven reconstructions to adhere to physical laws for improving predictive fidelity and robustness. Finally, we provide a rigorous theoretical analysis, establishing that the physics augmentation and Koopman regularization mathematically guarantees a reduction in super-resolution error by diminishing Rademacher complexity and tightening generalization bounds. We evaluate our framework on reconstructing spatially high-resolution cardiac electrodynamics across a 3D heart geometry from sparse low-resolution measurements. Numerical experiments demonstrate that our method achieves superior accuracy compared to baseline models.

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