Modeling Spatially Varying Physical Dynamics for Spatiotemporal Predictive Learning

Yijun Lin, Yao-Yi Chiang

Abstract: Recent advances in incorporating physical knowledge into deep neural networks can estimate previously unknown governing partial differential equations (PDEs) in a data-driven way. They have shown promising results in spatiotemporal predictive learning. However, these methods typically assume universal governing PDEs across space, which is impractical for modeling complex spatiotemporal phenomena with high spatial variability (e.g., climate). Also, they cannot effectively model the evolution of potential errors in estimating the physical dynamics over time. This paper introduces a physics-guided neural network, SVPNet, which learns effective physical representations by estimating the error evolution in physics states for correction and modeling spatially varying physical dynamics to predict the next state. Experiments carried out in four scenarios, including benchmarks and real-world datasets, show that SVPNet outperforms state-of-the-art methods in spatiotemporal prediction tasks for natural processes and significantly improves prediction when training data are limited. Ablation studies also highlight that SVPNet is powerful in capturing physical dynamics in complex physical systems.