P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution
2026-06-17 • Machine Learning
Machine Learning
AI summaryⓘ
The authors created a new method called P-K-GCN to make detailed simulations of things that change over space and time, like heart signals, easier to do from rough, simple data. They use a special graph-based technique to understand space, and a math tool called the Koopman operator to make the time part easier to predict. They also add physical rules to make sure the predictions follow real-world laws. Their tests show this method works better than others for recreating detailed heart data from sparse measurements.
spatiotemporal dynamicssuper-resolutiongraph convolutional networkKoopman operatorphysics-informed learningRademacher complexitygeneralization boundscardiac electrodynamicsspline-based GCNlatent space
Authors
Xizhuo, Zhang, Zekai Wang, Fei Liu, Bing Yao
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.