Enabling arbitrary inference in spatio-temporal dynamic systems: A physics-inspired perspective

Modern spatio-temporal learning techniques usually exploit sampled discrete observations to foresee the future. Actually, spatio-temporal dynamics are continuous and evolve continuously across time and space, thus modeling spatio-temporal dynamics in a continuous space can be a long-standing challenge. Existing deep learning architectures often fail to generalize to unseen regions and new graph topologies, while many physics-driven approaches are confined to Euclidean grids and poorly scale to complex graph structures. To address this gap, we propose PhySTA, a physics-inspired spatio-temporal learning framework designed for efficient and scalable arbitrary inference over graph-structured data. PhySTA integrates two key modules: (1) Continuous Operator-based Spectrum-Temporal Learning (CoSTL), which leverages a Graph-Time Fourier Neural Operator combined with Time-Gated Spectral Segmentation Perception to model continuous dynamics in operator space, and (2) Adaptive Multi-scale Interaction (AMI) that constructs multi-scale subgraphs and introduces node-edge coupled convolution to capture discrete interaction patterns and refine continuous predictions. By bridging operator learning with node-edge-graph interaction, PhySTA achieves both continuity-aware dynamic modeling and hierarchical interactive refinement. Extensive experiments across large-scale benchmarks demonstrate that PhySTA attains state-of-the-art accuracy while reducing computation cost and lowering parameter overhead.